Remove an unused uniform.

[nageru] / flow.cpp

#define NO_SDL_GLEXT 1

#include <epoxy/gl.h>

#include <SDL2/SDL.h>
#include <SDL2/SDL_error.h>
#include <SDL2/SDL_events.h>
#include <SDL2/SDL_image.h>
#include <SDL2/SDL_keyboard.h>
#include <SDL2/SDL_mouse.h>
#include <SDL2/SDL_video.h>

#include <assert.h>
#include <getopt.h>
#include <stdio.h>
#include <unistd.h>

#include "util.h"

#include <algorithm>
#include <deque>
#include <memory>
#include <map>
#include <stack>
#include <vector>

#define BUFFER_OFFSET(i) ((char *)nullptr + (i))

using namespace std;

SDL_Window *window;

// Operating point 3 (10 Hz on CPU, excluding preprocessing).
constexpr float patch_overlap_ratio = 0.75f;
constexpr unsigned coarsest_level = 5;
constexpr unsigned finest_level = 1;
constexpr unsigned patch_size_pixels = 12;

// Weighting constants for the different parts of the variational refinement.
// These don't correspond 1:1 to the values given in the DIS paper,
// since we have different normalizations and ranges in some cases.
// These are found through a simple grid search on some MPI-Sintel data,
// although the error (EPE) seems to be fairly insensitive to the precise values.
// Only the relative values matter, so we fix alpha (the smoothness constant)
// at unity and tweak the others.
float vr_alpha = 1.0f, vr_delta = 0.25f, vr_gamma = 0.25f;

bool enable_timing = true;
bool enable_variational_refinement = true;  // Just for debugging.
bool enable_interpolation = false;

// Some global OpenGL objects.
// TODO: These should really be part of DISComputeFlow.
GLuint nearest_sampler, linear_sampler, zero_border_sampler;
GLuint vertex_vbo;

// Structures for asynchronous readback. We assume everything is the same size (and GL_RG16F).
struct ReadInProgress {
        GLuint pbo;
        string filename0, filename1;
        string flow_filename, ppm_filename;  // Either may be empty for no write.
};
stack<GLuint> spare_pbos;
deque<ReadInProgress> reads_in_progress;

int find_num_levels(int width, int height)
{
        int levels = 1;
        for (int w = width, h = height; w > 1 || h > 1; ) {
                w >>= 1;
                h >>= 1;
                ++levels;
        }
        return levels;
}

string read_file(const string &filename)
{
        FILE *fp = fopen(filename.c_str(), "r");
        if (fp == nullptr) {
                perror(filename.c_str());
                exit(1);
        }

        int ret = fseek(fp, 0, SEEK_END);
        if (ret == -1) {
                perror("fseek(SEEK_END)");
                exit(1);
        }

        int size = ftell(fp);

        ret = fseek(fp, 0, SEEK_SET);
        if (ret == -1) {
                perror("fseek(SEEK_SET)");
                exit(1);
        }

        string str;
        str.resize(size);
        ret = fread(&str[0], size, 1, fp);
        if (ret == -1) {
                perror("fread");
                exit(1);
        }
        if (ret == 0) {
                fprintf(stderr, "Short read when trying to read %d bytes from %s\n",
                                size, filename.c_str());
                exit(1);
        }
        fclose(fp);

        return str;
}


GLuint compile_shader(const string &shader_src, GLenum type)
{
        GLuint obj = glCreateShader(type);
        const GLchar* source[] = { shader_src.data() };
        const GLint length[] = { (GLint)shader_src.size() };
        glShaderSource(obj, 1, source, length);
        glCompileShader(obj);

        GLchar info_log[4096];
        GLsizei log_length = sizeof(info_log) - 1;
        glGetShaderInfoLog(obj, log_length, &log_length, info_log);
        info_log[log_length] = 0;
        if (strlen(info_log) > 0) {
                fprintf(stderr, "Shader compile log: %s\n", info_log);
        }

        GLint status;
        glGetShaderiv(obj, GL_COMPILE_STATUS, &status);
        if (status == GL_FALSE) {
                // Add some line numbers to easier identify compile errors.
                string src_with_lines = "/*   1 */ ";
                size_t lineno = 1;
                for (char ch : shader_src) {
                        src_with_lines.push_back(ch);
                        if (ch == '\n') {
                                char buf[32];
                                snprintf(buf, sizeof(buf), "/* %3zu */ ", ++lineno);
                                src_with_lines += buf;
                        }
                }

                fprintf(stderr, "Failed to compile shader:\n%s\n", src_with_lines.c_str());
                exit(1);
        }

        return obj;
}

enum MipmapPolicy {
        WITHOUT_MIPMAPS,
        WITH_MIPMAPS
};

GLuint load_texture(const char *filename, unsigned *width_ret, unsigned *height_ret, MipmapPolicy mipmaps)
{
        SDL_Surface *surf = IMG_Load(filename);
        if (surf == nullptr) {
                fprintf(stderr, "IMG_Load(%s): %s\n", filename, IMG_GetError());
                exit(1);
        }

        // For whatever reason, SDL doesn't support converting to YUV surfaces
        // nor grayscale, so we'll do it ourselves.
        SDL_Surface *rgb_surf = SDL_ConvertSurfaceFormat(surf, SDL_PIXELFORMAT_RGBA32, /*flags=*/0);
        if (rgb_surf == nullptr) {
                fprintf(stderr, "SDL_ConvertSurfaceFormat(%s): %s\n", filename, SDL_GetError());
                exit(1);
        }

        SDL_FreeSurface(surf);

        unsigned width = rgb_surf->w, height = rgb_surf->h;
        const uint8_t *sptr = (uint8_t *)rgb_surf->pixels;
        unique_ptr<uint8_t[]> pix(new uint8_t[width * height * 4]);

        // Extract the Y component, and convert to bottom-left origin.
        for (unsigned y = 0; y < height; ++y) {
                unsigned y2 = height - 1 - y;
                memcpy(pix.get() + y * width * 4, sptr + y2 * rgb_surf->pitch, width * 4);
        }
        SDL_FreeSurface(rgb_surf);

        int num_levels = (mipmaps == WITH_MIPMAPS) ? find_num_levels(width, height) : 1;

        GLuint tex;
        glCreateTextures(GL_TEXTURE_2D, 1, &tex);
        glTextureStorage2D(tex, num_levels, GL_RGBA8, width, height);
        glTextureSubImage2D(tex, 0, 0, 0, width, height, GL_RGBA, GL_UNSIGNED_BYTE, pix.get());

        if (mipmaps == WITH_MIPMAPS) {
                glGenerateTextureMipmap(tex);
        }

        *width_ret = width;
        *height_ret = height;

        return tex;
}

GLuint link_program(GLuint vs_obj, GLuint fs_obj)
{
        GLuint program = glCreateProgram();
        glAttachShader(program, vs_obj);
        glAttachShader(program, fs_obj);
        glLinkProgram(program);
        GLint success;
        glGetProgramiv(program, GL_LINK_STATUS, &success);
        if (success == GL_FALSE) {
                GLchar error_log[1024] = {0};
                glGetProgramInfoLog(program, 1024, nullptr, error_log);
                fprintf(stderr, "Error linking program: %s\n", error_log);
                exit(1);
        }
        return program;
}

GLuint generate_vbo(GLint size, GLsizeiptr data_size, const GLvoid *data)
{
        GLuint vbo;
        glCreateBuffers(1, &vbo);
        glBufferData(GL_ARRAY_BUFFER, data_size, data, GL_STATIC_DRAW);
        glNamedBufferData(vbo, data_size, data, GL_STATIC_DRAW);
        return vbo;
}

GLuint fill_vertex_attribute(GLuint vao, GLuint glsl_program_num, const string &attribute_name, GLint size, GLenum type, GLsizeiptr data_size, const GLvoid *data)
{
        int attrib = glGetAttribLocation(glsl_program_num, attribute_name.c_str());
        if (attrib == -1) {
                return -1;
        }

        GLuint vbo = generate_vbo(size, data_size, data);

        glBindBuffer(GL_ARRAY_BUFFER, vbo);
        glEnableVertexArrayAttrib(vao, attrib);
        glVertexAttribPointer(attrib, size, type, GL_FALSE, 0, BUFFER_OFFSET(0));
        glBindBuffer(GL_ARRAY_BUFFER, 0);

        return vbo;
}

void bind_sampler(GLuint program, GLint location, GLuint texture_unit, GLuint tex, GLuint sampler)
{
        if (location == -1) {
                return;
        }

        glBindTextureUnit(texture_unit, tex);
        glBindSampler(texture_unit, sampler);
        glProgramUniform1i(program, location, texture_unit);
}

// A class that caches FBOs that render to a given set of textures.
// It never frees anything, so it is only suitable for rendering to
// the same (small) set of textures over and over again.
template<size_t num_elements>
class PersistentFBOSet {
public:
        void render_to(const array<GLuint, num_elements> &textures);

        // Convenience wrappers.
        void render_to(GLuint texture0, enable_if<num_elements == 1> * = nullptr) {
                render_to({{texture0}});
        }

        void render_to(GLuint texture0, GLuint texture1, enable_if<num_elements == 2> * = nullptr) {
                render_to({{texture0, texture1}});
        }

        void render_to(GLuint texture0, GLuint texture1, GLuint texture2, enable_if<num_elements == 3> * = nullptr) {
                render_to({{texture0, texture1, texture2}});
        }

        void render_to(GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3, enable_if<num_elements == 4> * = nullptr) {
                render_to({{texture0, texture1, texture2, texture3}});
        }

private:
        // TODO: Delete these on destruction.
        map<array<GLuint, num_elements>, GLuint> fbos;
};

template<size_t num_elements>
void PersistentFBOSet<num_elements>::render_to(const array<GLuint, num_elements> &textures)
{
        auto it = fbos.find(textures);
        if (it != fbos.end()) {
                glBindFramebuffer(GL_FRAMEBUFFER, it->second);
                return;
        }

        GLuint fbo;
        glCreateFramebuffers(1, &fbo);
        GLenum bufs[num_elements];
        for (size_t i = 0; i < num_elements; ++i) {
                glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0 + i, textures[i], 0);
                bufs[i] = GL_COLOR_ATTACHMENT0 + i;
        }
        glNamedFramebufferDrawBuffers(fbo, num_elements, bufs);

        fbos[textures] = fbo;
        glBindFramebuffer(GL_FRAMEBUFFER, fbo);
}

// Convert RGB to grayscale, using Rec. 709 coefficients.
class GrayscaleConversion {
public:
        GrayscaleConversion();
        void exec(GLint tex, GLint gray_tex, int width, int height);

private:
        PersistentFBOSet<1> fbos;
        GLuint gray_vs_obj;
        GLuint gray_fs_obj;
        GLuint gray_program;
        GLuint gray_vao;

        GLuint uniform_tex;
};

GrayscaleConversion::GrayscaleConversion()
{
        gray_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        gray_fs_obj = compile_shader(read_file("gray.frag"), GL_FRAGMENT_SHADER);
        gray_program = link_program(gray_vs_obj, gray_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &gray_vao);
        glBindVertexArray(gray_vao);

        GLint position_attrib = glGetAttribLocation(gray_program, "position");
        glEnableVertexArrayAttrib(gray_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_tex = glGetUniformLocation(gray_program, "tex");
}

void GrayscaleConversion::exec(GLint tex, GLint gray_tex, int width, int height)
{
        glUseProgram(gray_program);
        bind_sampler(gray_program, uniform_tex, 0, tex, nearest_sampler);

        glViewport(0, 0, width, height);
        fbos.render_to(gray_tex);
        glBindVertexArray(gray_vao);
        glUseProgram(gray_program);
        glDisable(GL_BLEND);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Compute gradients in every point, used for the motion search.
// The DIS paper doesn't actually mention how these are computed,
// but seemingly, a 3x3 Sobel operator is used here (at least in
// later versions of the code), while a [1 -8 0 8 -1] kernel is
// used for all the derivatives in the variational refinement part
// (which borrows code from DeepFlow). This is inconsistent,
// but I guess we're better off with staying with the original
// decisions until we actually know having different ones would be better.
class Sobel {
public:
        Sobel();
        void exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_height);

private:
        PersistentFBOSet<1> fbos;
        GLuint sobel_vs_obj;
        GLuint sobel_fs_obj;
        GLuint sobel_program;
        GLuint sobel_vao;

        GLuint uniform_tex;
};

Sobel::Sobel()
{
        sobel_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        sobel_fs_obj = compile_shader(read_file("sobel.frag"), GL_FRAGMENT_SHADER);
        sobel_program = link_program(sobel_vs_obj, sobel_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &sobel_vao);
        glBindVertexArray(sobel_vao);

        GLint position_attrib = glGetAttribLocation(sobel_program, "position");
        glEnableVertexArrayAttrib(sobel_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_tex = glGetUniformLocation(sobel_program, "tex");
}

void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_height)
{
        glUseProgram(sobel_program);
        bind_sampler(sobel_program, uniform_tex, 0, tex0_view, nearest_sampler);

        glViewport(0, 0, level_width, level_height);
        fbos.render_to(grad0_tex);
        glBindVertexArray(sobel_vao);
        glUseProgram(sobel_program);
        glDisable(GL_BLEND);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Motion search to find the initial flow. See motion_search.frag for documentation.
class MotionSearch {
public:
        MotionSearch();
        void exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GLuint flow_tex, GLuint flow_out_tex, int level_width, int level_height, int prev_level_width, int prev_level_height, int width_patches, int height_patches);

private:
        PersistentFBOSet<1> fbos;

        GLuint motion_vs_obj;
        GLuint motion_fs_obj;
        GLuint motion_search_program;
        GLuint motion_search_vao;

        GLuint uniform_inv_image_size, uniform_inv_prev_level_size;
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
};

MotionSearch::MotionSearch()
{
        motion_vs_obj = compile_shader(read_file("motion_search.vert"), GL_VERTEX_SHADER);
        motion_fs_obj = compile_shader(read_file("motion_search.frag"), GL_FRAGMENT_SHADER);
        motion_search_program = link_program(motion_vs_obj, motion_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &motion_search_vao);
        glBindVertexArray(motion_search_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(motion_search_program, "position");
        glEnableVertexArrayAttrib(motion_search_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_inv_image_size = glGetUniformLocation(motion_search_program, "inv_image_size");
        uniform_inv_prev_level_size = glGetUniformLocation(motion_search_program, "inv_prev_level_size");
        uniform_image0_tex = glGetUniformLocation(motion_search_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(motion_search_program, "image1_tex");
        uniform_grad0_tex = glGetUniformLocation(motion_search_program, "grad0_tex");
        uniform_flow_tex = glGetUniformLocation(motion_search_program, "flow_tex");
}

void MotionSearch::exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GLuint flow_tex, GLuint flow_out_tex, int level_width, int level_height, int prev_level_width, int prev_level_height, int width_patches, int height_patches)
{
        glUseProgram(motion_search_program);

        bind_sampler(motion_search_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
        bind_sampler(motion_search_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
        bind_sampler(motion_search_program, uniform_grad0_tex, 2, grad0_tex, zero_border_sampler);
        bind_sampler(motion_search_program, uniform_flow_tex, 3, flow_tex, linear_sampler);

        glProgramUniform2f(motion_search_program, uniform_inv_image_size, 1.0f / level_width, 1.0f / level_height);
        glProgramUniform2f(motion_search_program, uniform_inv_prev_level_size, 1.0f / prev_level_width, 1.0f / prev_level_height);

        glViewport(0, 0, width_patches, height_patches);
        fbos.render_to(flow_out_tex);
        glBindVertexArray(motion_search_vao);
        glUseProgram(motion_search_program);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Do “densification”, ie., upsampling of the flow patches to the flow field
// (the same size as the image at this level). We draw one quad per patch
// over its entire covered area (using instancing in the vertex shader),
// and then weight the contributions in the pixel shader by post-warp difference.
// This is equation (3) in the paper.
//
// We accumulate the flow vectors in the R/G channels (for u/v) and the total
// weight in the B channel. Dividing R and G by B gives the normalized values.
class Densify {
public:
        Densify();
        void exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint dense_flow_tex, int level_width, int level_height, int width_patches, int height_patches);

private:
        PersistentFBOSet<1> fbos;

        GLuint densify_vs_obj;
        GLuint densify_fs_obj;
        GLuint densify_program;
        GLuint densify_vao;

        GLuint uniform_patch_size;
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
};

Densify::Densify()
{
        densify_vs_obj = compile_shader(read_file("densify.vert"), GL_VERTEX_SHADER);
        densify_fs_obj = compile_shader(read_file("densify.frag"), GL_FRAGMENT_SHADER);
        densify_program = link_program(densify_vs_obj, densify_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &densify_vao);
        glBindVertexArray(densify_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(densify_program, "position");
        glEnableVertexArrayAttrib(densify_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_patch_size = glGetUniformLocation(densify_program, "patch_size");
        uniform_image0_tex = glGetUniformLocation(densify_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(densify_program, "image1_tex");
        uniform_flow_tex = glGetUniformLocation(densify_program, "flow_tex");
}

void Densify::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint dense_flow_tex, int level_width, int level_height, int width_patches, int height_patches)
{
        glUseProgram(densify_program);

        bind_sampler(densify_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
        bind_sampler(densify_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
        bind_sampler(densify_program, uniform_flow_tex, 2, flow_tex, nearest_sampler);

        glProgramUniform2f(densify_program, uniform_patch_size,
                float(patch_size_pixels) / level_width,
                float(patch_size_pixels) / level_height);

        glViewport(0, 0, level_width, level_height);
        glEnable(GL_BLEND);
        glBlendFunc(GL_ONE, GL_ONE);
        glBindVertexArray(densify_vao);
        fbos.render_to(dense_flow_tex);
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width_patches * height_patches);
}

// Warp I_1 to I_w, and then compute the mean (I) and difference (I_t) of
// I_0 and I_w. The prewarping is what enables us to solve the variational
// flow for du,dv instead of u,v.
//
// Also calculates the normalized flow, ie. divides by z (this is needed because
// Densify works by additive blending) and multiplies by the image size.
//
// See variational_refinement.txt for more information.
class Prewarp {
public:
        Prewarp();
        void exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint normalized_flow_tex, GLuint I_tex, GLuint I_t_tex, int level_width, int level_height);

private:
        PersistentFBOSet<3> fbos;

        GLuint prewarp_vs_obj;
        GLuint prewarp_fs_obj;
        GLuint prewarp_program;
        GLuint prewarp_vao;

        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
};

Prewarp::Prewarp()
{
        prewarp_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        prewarp_fs_obj = compile_shader(read_file("prewarp.frag"), GL_FRAGMENT_SHADER);
        prewarp_program = link_program(prewarp_vs_obj, prewarp_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &prewarp_vao);
        glBindVertexArray(prewarp_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(prewarp_program, "position");
        glEnableVertexArrayAttrib(prewarp_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_image0_tex = glGetUniformLocation(prewarp_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(prewarp_program, "image1_tex");
        uniform_flow_tex = glGetUniformLocation(prewarp_program, "flow_tex");
}

void Prewarp::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint I_tex, GLuint I_t_tex, GLuint normalized_flow_tex, int level_width, int level_height)
{
        glUseProgram(prewarp_program);

        bind_sampler(prewarp_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
        bind_sampler(prewarp_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
        bind_sampler(prewarp_program, uniform_flow_tex, 2, flow_tex, nearest_sampler);

        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
        glBindVertexArray(prewarp_vao);
        fbos.render_to(I_tex, I_t_tex, normalized_flow_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// From I, calculate the partial derivatives I_x and I_y. We use a four-tap
// central difference filter, since apparently, that's tradition (I haven't
// measured quality versus a more normal 0.5 (I[x+1] - I[x-1]).)
// The coefficients come from
//
//   https://en.wikipedia.org/wiki/Finite_difference_coefficient
//
// Also computes β_0, since it depends only on I_x and I_y.
class Derivatives {
public:
        Derivatives();
        void exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height);

private:
        PersistentFBOSet<2> fbos;

        GLuint derivatives_vs_obj;
        GLuint derivatives_fs_obj;
        GLuint derivatives_program;
        GLuint derivatives_vao;

        GLuint uniform_tex;
};

Derivatives::Derivatives()
{
        derivatives_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        derivatives_fs_obj = compile_shader(read_file("derivatives.frag"), GL_FRAGMENT_SHADER);
        derivatives_program = link_program(derivatives_vs_obj, derivatives_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &derivatives_vao);
        glBindVertexArray(derivatives_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(derivatives_program, "position");
        glEnableVertexArrayAttrib(derivatives_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_tex = glGetUniformLocation(derivatives_program, "tex");
}

void Derivatives::exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height)
{
        glUseProgram(derivatives_program);

        bind_sampler(derivatives_program, uniform_tex, 0, input_tex, nearest_sampler);

        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
        glBindVertexArray(derivatives_vao);
        fbos.render_to(I_x_y_tex, beta_0_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Calculate the smoothness constraints between neighboring pixels;
// s_x(x,y) stores smoothness between pixel (x,y) and (x+1,y),
// and s_y(x,y) stores between (x,y) and (x,y+1). We'll sample with
// border color (0,0) later, so that there's zero diffusion out of
// the border.
//
// See variational_refinement.txt for more information.
class ComputeSmoothness {
public:
        ComputeSmoothness();
        void exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height);

private:
        PersistentFBOSet<2> fbos;

        GLuint smoothness_vs_obj;
        GLuint smoothness_fs_obj;
        GLuint smoothness_program;
        GLuint smoothness_vao;

        GLuint uniform_flow_tex, uniform_diff_flow_tex;
        GLuint uniform_alpha;
};

ComputeSmoothness::ComputeSmoothness()
{
        smoothness_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        smoothness_fs_obj = compile_shader(read_file("smoothness.frag"), GL_FRAGMENT_SHADER);
        smoothness_program = link_program(smoothness_vs_obj, smoothness_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &smoothness_vao);
        glBindVertexArray(smoothness_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(smoothness_program, "position");
        glEnableVertexArrayAttrib(smoothness_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_flow_tex = glGetUniformLocation(smoothness_program, "flow_tex");
        uniform_diff_flow_tex = glGetUniformLocation(smoothness_program, "diff_flow_tex");
        uniform_alpha = glGetUniformLocation(smoothness_program, "alpha");
}

void ComputeSmoothness::exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height)
{
        glUseProgram(smoothness_program);

        bind_sampler(smoothness_program, uniform_flow_tex, 0, flow_tex, nearest_sampler);
        bind_sampler(smoothness_program, uniform_diff_flow_tex, 1, diff_flow_tex, nearest_sampler);
        glProgramUniform1f(smoothness_program, uniform_alpha, vr_alpha);

        glViewport(0, 0, level_width, level_height);

        glDisable(GL_BLEND);
        glBindVertexArray(smoothness_vao);
        fbos.render_to(smoothness_x_tex, smoothness_y_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);

        // Make sure the smoothness on the right and upper borders is zero.
        // We could have done this by making (W-1)xH and Wx(H-1) textures instead
        // (we're sampling smoothness with all-zero border color), but we'd
        // have to adjust the sampling coordinates, which is annoying.
        glClearTexSubImage(smoothness_x_tex, 0,  level_width - 1, 0, 0,   1, level_height, 1,  GL_RED, GL_FLOAT, nullptr);
        glClearTexSubImage(smoothness_y_tex, 0,  0, level_height - 1, 0,  level_width, 1, 1,   GL_RED, GL_FLOAT, nullptr);
}

// Set up the equations set (two equations in two unknowns, per pixel).
// We store five floats; the three non-redundant elements of the 2x2 matrix (A)
// as 32-bit floats, and the two elements on the right-hand side (b) as 16-bit
// floats. (Actually, we store the inverse of the diagonal elements, because
// we only ever need to divide by them.) This fits into four u32 values;
// R, G, B for the matrix (the last element is symmetric) and A for the two b values.
// All the values of the energy term (E_I, E_G, E_S), except the smoothness
// terms that depend on other pixels, are calculated in one pass.
//
// See variational_refinement.txt for more information.
class SetupEquations {
public:
        SetupEquations();
        void exec(GLuint I_x_y_tex, GLuint I_t_tex, GLuint diff_flow_tex, GLuint flow_tex, GLuint beta_0_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, GLuint equation_tex, int level_width, int level_height);

private:
        PersistentFBOSet<1> fbos;

        GLuint equations_vs_obj;
        GLuint equations_fs_obj;
        GLuint equations_program;
        GLuint equations_vao;

        GLuint uniform_I_x_y_tex, uniform_I_t_tex;
        GLuint uniform_diff_flow_tex, uniform_base_flow_tex;
        GLuint uniform_beta_0_tex;
        GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
        GLuint uniform_gamma, uniform_delta;
};

SetupEquations::SetupEquations()
{
        equations_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        equations_fs_obj = compile_shader(read_file("equations.frag"), GL_FRAGMENT_SHADER);
        equations_program = link_program(equations_vs_obj, equations_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &equations_vao);
        glBindVertexArray(equations_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(equations_program, "position");
        glEnableVertexArrayAttrib(equations_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_I_x_y_tex = glGetUniformLocation(equations_program, "I_x_y_tex");
        uniform_I_t_tex = glGetUniformLocation(equations_program, "I_t_tex");
        uniform_diff_flow_tex = glGetUniformLocation(equations_program, "diff_flow_tex");
        uniform_base_flow_tex = glGetUniformLocation(equations_program, "base_flow_tex");
        uniform_beta_0_tex = glGetUniformLocation(equations_program, "beta_0_tex");
        uniform_smoothness_x_tex = glGetUniformLocation(equations_program, "smoothness_x_tex");
        uniform_smoothness_y_tex = glGetUniformLocation(equations_program, "smoothness_y_tex");
        uniform_gamma = glGetUniformLocation(equations_program, "gamma");
        uniform_delta = glGetUniformLocation(equations_program, "delta");
}

void SetupEquations::exec(GLuint I_x_y_tex, GLuint I_t_tex, GLuint diff_flow_tex, GLuint base_flow_tex, GLuint beta_0_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, GLuint equation_tex, int level_width, int level_height)
{
        glUseProgram(equations_program);

        bind_sampler(equations_program, uniform_I_x_y_tex, 0, I_x_y_tex, nearest_sampler);
        bind_sampler(equations_program, uniform_I_t_tex, 1, I_t_tex, nearest_sampler);
        bind_sampler(equations_program, uniform_diff_flow_tex, 2, diff_flow_tex, nearest_sampler);
        bind_sampler(equations_program, uniform_base_flow_tex, 3, base_flow_tex, nearest_sampler);
        bind_sampler(equations_program, uniform_beta_0_tex, 4, beta_0_tex, nearest_sampler);
        bind_sampler(equations_program, uniform_smoothness_x_tex, 5, smoothness_x_tex, zero_border_sampler);
        bind_sampler(equations_program, uniform_smoothness_y_tex, 6, smoothness_y_tex, zero_border_sampler);
        glProgramUniform1f(equations_program, uniform_delta, vr_delta);
        glProgramUniform1f(equations_program, uniform_gamma, vr_gamma);

        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
        glBindVertexArray(equations_vao);
        fbos.render_to(equation_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Actually solve the equation sets made by SetupEquations, by means of
// successive over-relaxation (SOR).
//
// See variational_refinement.txt for more information.
class SOR {
public:
        SOR();
        void exec(GLuint diff_flow_tex, GLuint equation_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height, int num_iterations);

private:
        PersistentFBOSet<1> fbos;

        GLuint sor_vs_obj;
        GLuint sor_fs_obj;
        GLuint sor_program;
        GLuint sor_vao;

        GLuint uniform_diff_flow_tex;
        GLuint uniform_equation_tex;
        GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
        GLuint uniform_phase;
};

SOR::SOR()
{
        sor_vs_obj = compile_shader(read_file("sor.vert"), GL_VERTEX_SHADER);
        sor_fs_obj = compile_shader(read_file("sor.frag"), GL_FRAGMENT_SHADER);
        sor_program = link_program(sor_vs_obj, sor_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &sor_vao);
        glBindVertexArray(sor_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(sor_program, "position");
        glEnableVertexArrayAttrib(sor_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_diff_flow_tex = glGetUniformLocation(sor_program, "diff_flow_tex");
        uniform_equation_tex = glGetUniformLocation(sor_program, "equation_tex");
        uniform_smoothness_x_tex = glGetUniformLocation(sor_program, "smoothness_x_tex");
        uniform_smoothness_y_tex = glGetUniformLocation(sor_program, "smoothness_y_tex");
        uniform_phase = glGetUniformLocation(sor_program, "phase");
}

void SOR::exec(GLuint diff_flow_tex, GLuint equation_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height, int num_iterations)
{
        glUseProgram(sor_program);

        bind_sampler(sor_program, uniform_diff_flow_tex, 0, diff_flow_tex, nearest_sampler);
        bind_sampler(sor_program, uniform_smoothness_x_tex, 1, smoothness_x_tex, zero_border_sampler);
        bind_sampler(sor_program, uniform_smoothness_y_tex, 2, smoothness_y_tex, zero_border_sampler);
        bind_sampler(sor_program, uniform_equation_tex, 3, equation_tex, nearest_sampler);

        // NOTE: We bind to the texture we are rendering from, but we never write any value
        // that we read in the same shader pass (we call discard for red values when we compute
        // black, and vice versa), and we have barriers between the passes, so we're fine
        // as per the spec.
        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
        glBindVertexArray(sor_vao);
        fbos.render_to(diff_flow_tex);

        for (int i = 0; i < num_iterations; ++i) {
                glProgramUniform1i(sor_program, uniform_phase, 0);
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                glTextureBarrier();
                glProgramUniform1i(sor_program, uniform_phase, 1);
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                if (i != num_iterations - 1) {
                        glTextureBarrier();
                }
        }
}

// Simply add the differential flow found by the variational refinement to the base flow.
// The output is in base_flow_tex; we don't need to make a new texture.
class AddBaseFlow {
public:
        AddBaseFlow();
        void exec(GLuint base_flow_tex, GLuint diff_flow_tex, int level_width, int level_height);

private:
        PersistentFBOSet<1> fbos;

        GLuint add_flow_vs_obj;
        GLuint add_flow_fs_obj;
        GLuint add_flow_program;
        GLuint add_flow_vao;

        GLuint uniform_diff_flow_tex;
};

AddBaseFlow::AddBaseFlow()
{
        add_flow_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        add_flow_fs_obj = compile_shader(read_file("add_base_flow.frag"), GL_FRAGMENT_SHADER);
        add_flow_program = link_program(add_flow_vs_obj, add_flow_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &add_flow_vao);
        glBindVertexArray(add_flow_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(add_flow_program, "position");
        glEnableVertexArrayAttrib(add_flow_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_diff_flow_tex = glGetUniformLocation(add_flow_program, "diff_flow_tex");
}

void AddBaseFlow::exec(GLuint base_flow_tex, GLuint diff_flow_tex, int level_width, int level_height)
{
        glUseProgram(add_flow_program);

        bind_sampler(add_flow_program, uniform_diff_flow_tex, 0, diff_flow_tex, nearest_sampler);

        glViewport(0, 0, level_width, level_height);
        glEnable(GL_BLEND);
        glBlendFunc(GL_ONE, GL_ONE);
        glBindVertexArray(add_flow_vao);
        fbos.render_to(base_flow_tex);

        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

// Take a copy of the flow, bilinearly interpolated and scaled up.
class ResizeFlow {
public:
        ResizeFlow();
        void exec(GLuint in_tex, GLuint out_tex, int input_width, int input_height, int output_width, int output_height);

private:
        PersistentFBOSet<1> fbos;

        GLuint resize_flow_vs_obj;
        GLuint resize_flow_fs_obj;
        GLuint resize_flow_program;
        GLuint resize_flow_vao;

        GLuint uniform_flow_tex;
        GLuint uniform_scale_factor;
};

ResizeFlow::ResizeFlow()
{
        resize_flow_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        resize_flow_fs_obj = compile_shader(read_file("resize_flow.frag"), GL_FRAGMENT_SHADER);
        resize_flow_program = link_program(resize_flow_vs_obj, resize_flow_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &resize_flow_vao);
        glBindVertexArray(resize_flow_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(resize_flow_program, "position");
        glEnableVertexArrayAttrib(resize_flow_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_flow_tex = glGetUniformLocation(resize_flow_program, "flow_tex");
        uniform_scale_factor = glGetUniformLocation(resize_flow_program, "scale_factor");
}

void ResizeFlow::exec(GLuint flow_tex, GLuint out_tex, int input_width, int input_height, int output_width, int output_height)
{
        glUseProgram(resize_flow_program);

        bind_sampler(resize_flow_program, uniform_flow_tex, 0, flow_tex, nearest_sampler);

        glProgramUniform2f(resize_flow_program, uniform_scale_factor, float(output_width) / input_width, float(output_height) / input_height);

        glViewport(0, 0, output_width, output_height);
        glDisable(GL_BLEND);
        glBindVertexArray(resize_flow_vao);
        fbos.render_to(out_tex);

        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

class GPUTimers {
public:
        void print();
        pair<GLuint, GLuint> begin_timer(const string &name, int level);

private:
        struct Timer {
                string name;
                int level;
                pair<GLuint, GLuint> query;
        };
        vector<Timer> timers;
};

pair<GLuint, GLuint> GPUTimers::begin_timer(const string &name, int level)
{
        if (!enable_timing) {
                return make_pair(0, 0);
        }

        GLuint queries[2];
        glGenQueries(2, queries);
        glQueryCounter(queries[0], GL_TIMESTAMP);

        Timer timer;
        timer.name = name;
        timer.level = level;
        timer.query.first = queries[0];
        timer.query.second = queries[1];
        timers.push_back(timer);
        return timer.query;
}

void GPUTimers::print()
{
        for (const Timer &timer : timers) {
                // NOTE: This makes the CPU wait for the GPU.
                GLuint64 time_start, time_end;
                glGetQueryObjectui64v(timer.query.first, GL_QUERY_RESULT, &time_start);
                glGetQueryObjectui64v(timer.query.second, GL_QUERY_RESULT, &time_end);
                //fprintf(stderr, "GPU time used = %.1f ms\n", time_elapsed / 1e6);
                for (int i = 0; i < timer.level * 2; ++i) {
                        fprintf(stderr, " ");
                }
                fprintf(stderr, "%-30s %4.1f ms\n", timer.name.c_str(), GLint64(time_end - time_start) / 1e6);
        }
}

// A simple RAII class for timing until the end of the scope.
class ScopedTimer {
public:
        ScopedTimer(const string &name, GPUTimers *timers)
                : timers(timers), level(0)
        {
                query = timers->begin_timer(name, level);
        }

        ScopedTimer(const string &name, ScopedTimer *parent_timer)
                : timers(parent_timer->timers),
                  level(parent_timer->level + 1)
        {
                query = timers->begin_timer(name, level);
        }

        ~ScopedTimer()
        {
                end();
        }

        void end()
        {
                if (enable_timing && !ended) {
                        glQueryCounter(query.second, GL_TIMESTAMP);
                        ended = true;
                }
        }

private:
        GPUTimers *timers;
        int level;
        pair<GLuint, GLuint> query;
        bool ended = false;
};

class TexturePool {
public:
        GLuint get_texture(GLenum format, GLuint width, GLuint height);
        void release_texture(GLuint tex_num);

private:
        struct Texture {
                GLuint tex_num;
                GLenum format;
                GLuint width, height;
                bool in_use = false;
        };
        vector<Texture> textures;
};

class DISComputeFlow {
public:
        DISComputeFlow(int width, int height);

        enum ResizeStrategy {
                DO_NOT_RESIZE_FLOW,
                RESIZE_FLOW_TO_FULL_SIZE
        };

        // Returns a texture that must be released with release_texture()
        // after use.
        GLuint exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_strategy);

        void release_texture(GLuint tex) {
                pool.release_texture(tex);
        }

private:
        int width, height;
        GLuint initial_flow_tex;
        TexturePool pool;

        // The various passes.
        Sobel sobel;
        MotionSearch motion_search;
        Densify densify;
        Prewarp prewarp;
        Derivatives derivatives;
        ComputeSmoothness compute_smoothness;
        SetupEquations setup_equations;
        SOR sor;
        AddBaseFlow add_base_flow;
        ResizeFlow resize_flow;
};

DISComputeFlow::DISComputeFlow(int width, int height)
        : width(width), height(height)
{
        // Make some samplers.
        glCreateSamplers(1, &nearest_sampler);
        glSamplerParameteri(nearest_sampler, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
        glSamplerParameteri(nearest_sampler, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
        glSamplerParameteri(nearest_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
        glSamplerParameteri(nearest_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);

        glCreateSamplers(1, &linear_sampler);
        glSamplerParameteri(linear_sampler, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
        glSamplerParameteri(linear_sampler, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
        glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
        glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);

        // The smoothness is sampled so that once we get to a smoothness involving
        // a value outside the border, the diffusivity between the two becomes zero.
        // Similarly, gradients are zero outside the border, since the edge is taken
        // to be constant.
        glCreateSamplers(1, &zero_border_sampler);
        glSamplerParameteri(zero_border_sampler, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
        glSamplerParameteri(zero_border_sampler, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
        glSamplerParameteri(zero_border_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);
        glSamplerParameteri(zero_border_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);
        float zero[] = { 0.0f, 0.0f, 0.0f, 0.0f };
        glSamplerParameterfv(zero_border_sampler, GL_TEXTURE_BORDER_COLOR, zero);

        // Initial flow is zero, 1x1.
        glCreateTextures(GL_TEXTURE_2D, 1, &initial_flow_tex);
        glTextureStorage2D(initial_flow_tex, 1, GL_RG16F, 1, 1);
        glClearTexImage(initial_flow_tex, 0, GL_RG, GL_FLOAT, nullptr);
}

GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_strategy)
{
        int prev_level_width = 1, prev_level_height = 1;
        GLuint prev_level_flow_tex = initial_flow_tex;

        GPUTimers timers;

        ScopedTimer total_timer("Total", &timers);
        for (int level = coarsest_level; level >= int(finest_level); --level) {
                char timer_name[256];
                snprintf(timer_name, sizeof(timer_name), "Level %d", level);
                ScopedTimer level_timer(timer_name, &total_timer);

                int level_width = width >> level;
                int level_height = height >> level;
                float patch_spacing_pixels = patch_size_pixels * (1.0f - patch_overlap_ratio);

                // Make sure we have patches at least every Nth pixel, e.g. for width=9
                // and patch_spacing=3 (the default), we put out patch centers in
                // x=0, x=3, x=6, x=9, which is four patches. The fragment shader will
                // lock all the centers to integer coordinates if needed.
                int width_patches = 1 + ceil(level_width / patch_spacing_pixels);
                int height_patches = 1 + ceil(level_height / patch_spacing_pixels);

                // Make sure we always read from the correct level; the chosen
                // mipmapping could otherwise be rather unpredictable, especially
                // during motion search.
                GLuint tex0_view, tex1_view;
                glGenTextures(1, &tex0_view);
                glTextureView(tex0_view, GL_TEXTURE_2D, tex0, GL_R8, level, 1, 0, 1);
                glGenTextures(1, &tex1_view);
                glTextureView(tex1_view, GL_TEXTURE_2D, tex1, GL_R8, level, 1, 0, 1);

                // Create a new texture; we could be fancy and render use a multi-level
                // texture, but meh.
                GLuint grad0_tex = pool.get_texture(GL_RG16F, level_width, level_height);

                // Find the derivative.
                {
                        ScopedTimer timer("Sobel", &level_timer);
                        sobel.exec(tex0_view, grad0_tex, level_width, level_height);
                }

                // Motion search to find the initial flow. We use the flow from the previous
                // level (sampled bilinearly; no fancy tricks) as a guide, then search from there.

                // Create an output flow texture.
                GLuint flow_out_tex = pool.get_texture(GL_RGB16F, width_patches, height_patches);

                // And draw.
                {
                        ScopedTimer timer("Motion search", &level_timer);
                        motion_search.exec(tex0_view, tex1_view, grad0_tex, prev_level_flow_tex, flow_out_tex, level_width, level_height, prev_level_width, prev_level_height, width_patches, height_patches);
                }
                pool.release_texture(grad0_tex);

                // Densification.

                // Set up an output texture (initially zero).
                GLuint dense_flow_tex = pool.get_texture(GL_RGB16F, level_width, level_height);
                glClearTexImage(dense_flow_tex, 0, GL_RGB, GL_FLOAT, nullptr);

                // And draw.
                {
                        ScopedTimer timer("Densification", &level_timer);
                        densify.exec(tex0_view, tex1_view, flow_out_tex, dense_flow_tex, level_width, level_height, width_patches, height_patches);
                }
                pool.release_texture(flow_out_tex);

                // Everything below here in the loop belongs to variational refinement.
                ScopedTimer varref_timer("Variational refinement", &level_timer);

                // Prewarping; create I and I_t, and a normalized base flow (so we don't
                // have to normalize it over and over again, and also save some bandwidth).
                //
                // During the entire rest of the variational refinement, flow will be measured
                // in pixels, not 0..1 normalized OpenGL texture coordinates.
                // This is because variational refinement depends so heavily on derivatives,
                // which are measured in intensity levels per pixel.
                GLuint I_tex = pool.get_texture(GL_R16F, level_width, level_height);
                GLuint I_t_tex = pool.get_texture(GL_R16F, level_width, level_height);
                GLuint base_flow_tex = pool.get_texture(GL_RG16F, level_width, level_height);
                {
                        ScopedTimer timer("Prewarping", &varref_timer);
                        prewarp.exec(tex0_view, tex1_view, dense_flow_tex, I_tex, I_t_tex, base_flow_tex, level_width, level_height);
                }
                pool.release_texture(dense_flow_tex);
                glDeleteTextures(1, &tex0_view);
                glDeleteTextures(1, &tex1_view);

                // Calculate I_x and I_y. We're only calculating first derivatives;
                // the others will be taken on-the-fly in order to sample from fewer
                // textures overall, since sampling from the L1 cache is cheap.
                // (TODO: Verify that this is indeed faster than making separate
                // double-derivative textures.)
                GLuint I_x_y_tex = pool.get_texture(GL_RG16F, level_width, level_height);
                GLuint beta_0_tex = pool.get_texture(GL_R16F, level_width, level_height);
                {
                        ScopedTimer timer("First derivatives", &varref_timer);
                        derivatives.exec(I_tex, I_x_y_tex, beta_0_tex, level_width, level_height);
                }
                pool.release_texture(I_tex);

                // We need somewhere to store du and dv (the flow increment, relative
                // to the non-refined base flow u0 and v0). It starts at zero.
                GLuint du_dv_tex = pool.get_texture(GL_RG16F, level_width, level_height);
                glClearTexImage(du_dv_tex, 0, GL_RG, GL_FLOAT, nullptr);

                // And for smoothness.
                GLuint smoothness_x_tex = pool.get_texture(GL_R16F, level_width, level_height);
                GLuint smoothness_y_tex = pool.get_texture(GL_R16F, level_width, level_height);

                // And finally for the equation set. See SetupEquations for
                // the storage format.
                GLuint equation_tex = pool.get_texture(GL_RGBA32UI, level_width, level_height);

                for (int outer_idx = 0; outer_idx < level + 1; ++outer_idx) {
                        // Calculate the smoothness terms between the neighboring pixels,
                        // both in x and y direction.
                        {
                                ScopedTimer timer("Compute smoothness", &varref_timer);
                                compute_smoothness.exec(base_flow_tex, du_dv_tex, smoothness_x_tex, smoothness_y_tex, level_width, level_height);
                        }

                        // Set up the 2x2 equation system for each pixel.
                        {
                                ScopedTimer timer("Set up equations", &varref_timer);
                                setup_equations.exec(I_x_y_tex, I_t_tex, du_dv_tex, base_flow_tex, beta_0_tex, smoothness_x_tex, smoothness_y_tex, equation_tex, level_width, level_height);
                        }

                        // Run a few SOR (or quasi-SOR, since we're not really Jacobi) iterations.
                        // Note that these are to/from the same texture.
                        {
                                ScopedTimer timer("SOR", &varref_timer);
                                sor.exec(du_dv_tex, equation_tex, smoothness_x_tex, smoothness_y_tex, level_width, level_height, 5);
                        }
                }

                pool.release_texture(I_t_tex);
                pool.release_texture(I_x_y_tex);
                pool.release_texture(beta_0_tex);
                pool.release_texture(smoothness_x_tex);
                pool.release_texture(smoothness_y_tex);
                pool.release_texture(equation_tex);

                // Add the differential flow found by the variational refinement to the base flow,
                // giving the final flow estimate for this level.
                // The output is in diff_flow_tex; we don't need to make a new texture.
                //
                // Disabling this doesn't save any time (although we could easily make it so that
                // it is more efficient), but it helps debug the motion search.
                if (enable_variational_refinement) {
                        ScopedTimer timer("Add differential flow", &varref_timer);
                        add_base_flow.exec(base_flow_tex, du_dv_tex, level_width, level_height);
                }
                pool.release_texture(du_dv_tex);

                if (prev_level_flow_tex != initial_flow_tex) {
                        pool.release_texture(prev_level_flow_tex);
                }
                prev_level_flow_tex = base_flow_tex;
                prev_level_width = level_width;
                prev_level_height = level_height;
        }
        total_timer.end();

        timers.print();

        // Scale up the flow to the final size (if needed).
        if (finest_level == 0 || resize_strategy == DO_NOT_RESIZE_FLOW) {
                return prev_level_flow_tex;
        } else {
                GLuint final_tex = pool.get_texture(GL_RG16F, width, height);
                resize_flow.exec(prev_level_flow_tex, final_tex, prev_level_width, prev_level_height, width, height);
                pool.release_texture(prev_level_flow_tex);
                return final_tex;
        }
}

// Forward-warp the flow half-way (or rather, by alpha). A non-zero “splatting”
// radius fills most of the holes.
class Splat {
public:
        Splat();

        // alpha is the time of the interpolated frame (0..1).
        void exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint flow_tex, GLuint depth_tex, int width, int height, float alpha);

private:
        PersistentFBOSet<2> fbos;

        GLuint splat_vs_obj;
        GLuint splat_fs_obj;
        GLuint splat_program;
        GLuint splat_vao;

        GLuint uniform_invert_flow, uniform_splat_size, uniform_alpha;
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
        GLuint uniform_inv_flow_size;
};

Splat::Splat()
{
        splat_vs_obj = compile_shader(read_file("splat.vert"), GL_VERTEX_SHADER);
        splat_fs_obj = compile_shader(read_file("splat.frag"), GL_FRAGMENT_SHADER);
        splat_program = link_program(splat_vs_obj, splat_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &splat_vao);
        glBindVertexArray(splat_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(splat_program, "position");
        glEnableVertexArrayAttrib(splat_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_invert_flow = glGetUniformLocation(splat_program, "invert_flow");
        uniform_splat_size = glGetUniformLocation(splat_program, "splat_size");
        uniform_alpha = glGetUniformLocation(splat_program, "alpha");
        uniform_image0_tex = glGetUniformLocation(splat_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(splat_program, "image1_tex");
        uniform_flow_tex = glGetUniformLocation(splat_program, "flow_tex");
        uniform_inv_flow_size = glGetUniformLocation(splat_program, "inv_flow_size");
}

void Splat::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint flow_tex, GLuint depth_tex, int width, int height, float alpha)
{
        glUseProgram(splat_program);

        bind_sampler(splat_program, uniform_image0_tex, 0, tex0, linear_sampler);
        bind_sampler(splat_program, uniform_image1_tex, 1, tex1, linear_sampler);

        // FIXME: This is set to 1.0 right now so not to trigger Haswell's “PMA stall”.
        // Move to 2.0 later, or even 4.0.
        // (Since we have hole filling, it's not critical, but larger values seem to do
        // better than hole filling for large motion, blurs etc.)
        float splat_size = 1.0f;  // 4x4 splat means 16x overdraw, 2x2 splat means 4x overdraw.
        glProgramUniform2f(splat_program, uniform_splat_size, splat_size / width, splat_size / height);
        glProgramUniform1f(splat_program, uniform_alpha, alpha);
        glProgramUniform2f(splat_program, uniform_inv_flow_size, 1.0f / width, 1.0f / height);

        glViewport(0, 0, width, height);
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);  // We store the difference between I_0 and I_1, where less difference is good. (Default 1.0 is effectively +inf, which always loses.)
        glBindVertexArray(splat_vao);

        // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
        GLuint fbo;
        glCreateFramebuffers(1, &fbo);
        glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);
        glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
        glBindFramebuffer(GL_FRAMEBUFFER, fbo);

        // Do forward splatting.
        bind_sampler(splat_program, uniform_flow_tex, 2, forward_flow_tex, nearest_sampler);
        glProgramUniform1i(splat_program, uniform_invert_flow, 0);
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width * height);

        // Do backward splatting.
        bind_sampler(splat_program, uniform_flow_tex, 2, backward_flow_tex, nearest_sampler);
        glProgramUniform1i(splat_program, uniform_invert_flow, 1);
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width * height);

        glDisable(GL_DEPTH_TEST);

        glDeleteFramebuffers(1, &fbo);
}

// Doing good and fast hole-filling on a GPU is nontrivial. We choose an option
// that's fairly simple (given that most holes are really small) and also hopefully
// cheap should the holes not be so small. Conceptually, we look for the first
// non-hole to the left of us (ie., shoot a ray until we hit something), then
// the first non-hole to the right of us, then up and down, and then average them
// all together. It's going to create “stars” if the holes are big, but OK, that's
// a tradeoff.
//
// Our implementation here is efficient assuming that the hierarchical Z-buffer is
// on even for shaders that do discard (this typically kills early Z, but hopefully
// not hierarchical Z); we set up Z so that only holes are written to, which means
// that as soon as a hole is filled, the rasterizer should just skip it. Most of the
// fullscreen quads should just be discarded outright, really.
class HoleFill {
public:
        HoleFill();

        // Output will be in flow_tex, temp_tex[0, 1, 2], representing the filling
        // from the down, left, right and up, respectively. Use HoleBlend to merge
        // them into one.
        void exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height);

private:
        PersistentFBOSet<2> fbos;

        GLuint fill_vs_obj;
        GLuint fill_fs_obj;
        GLuint fill_program;
        GLuint fill_vao;

        GLuint uniform_tex;
        GLuint uniform_z, uniform_sample_offset;
};

HoleFill::HoleFill()
{
        fill_vs_obj = compile_shader(read_file("hole_fill.vert"), GL_VERTEX_SHADER);
        fill_fs_obj = compile_shader(read_file("hole_fill.frag"), GL_FRAGMENT_SHADER);
        fill_program = link_program(fill_vs_obj, fill_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &fill_vao);
        glBindVertexArray(fill_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(fill_program, "position");
        glEnableVertexArrayAttrib(fill_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_tex = glGetUniformLocation(fill_program, "tex");
        uniform_z = glGetUniformLocation(fill_program, "z");
        uniform_sample_offset = glGetUniformLocation(fill_program, "sample_offset");
}

void HoleFill::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height)
{
        glUseProgram(fill_program);

        bind_sampler(fill_program, uniform_tex, 0, flow_tex, nearest_sampler);

        glProgramUniform1f(fill_program, uniform_z, 1.0f - 1.0f / 1024.0f);

        glViewport(0, 0, width, height);
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);  // Only update the values > 0.999f (ie., only invalid pixels).
        glBindVertexArray(fill_vao);

        // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
        GLuint fbo;
        glCreateFramebuffers(1, &fbo);
        glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);  // NOTE: Reading and writing to the same texture.
        glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
        glBindFramebuffer(GL_FRAMEBUFFER, fbo);

        // Fill holes from the left, by shifting 1, 2, 4, 8, etc. pixels to the right.
        for (int offs = 1; offs < width; offs *= 2) {
                glProgramUniform2f(fill_program, uniform_sample_offset, -offs / float(width), 0.0f);
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                glTextureBarrier();
        }
        glCopyImageSubData(flow_tex, GL_TEXTURE_2D, 0, 0, 0, 0, temp_tex[0], GL_TEXTURE_2D, 0, 0, 0, 0, width, height, 1);

        // Similar to the right; adjust Z a bit down, so that we re-fill the pixels that
        // were overwritten in the last algorithm.
        glProgramUniform1f(fill_program, uniform_z, 1.0f - 2.0f / 1024.0f);
        for (int offs = 1; offs < width; offs *= 2) {
                glProgramUniform2f(fill_program, uniform_sample_offset, offs / float(width), 0.0f);
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                glTextureBarrier();
        }
        glCopyImageSubData(flow_tex, GL_TEXTURE_2D, 0, 0, 0, 0, temp_tex[1], GL_TEXTURE_2D, 0, 0, 0, 0, width, height, 1);

        // Up.
        glProgramUniform1f(fill_program, uniform_z, 1.0f - 3.0f / 1024.0f);
        for (int offs = 1; offs < height; offs *= 2) {
                glProgramUniform2f(fill_program, uniform_sample_offset, 0.0f, -offs / float(height));
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                glTextureBarrier();
        }
        glCopyImageSubData(flow_tex, GL_TEXTURE_2D, 0, 0, 0, 0, temp_tex[2], GL_TEXTURE_2D, 0, 0, 0, 0, width, height, 1);

        // Down.
        glProgramUniform1f(fill_program, uniform_z, 1.0f - 4.0f / 1024.0f);
        for (int offs = 1; offs < height; offs *= 2) {
                glProgramUniform2f(fill_program, uniform_sample_offset, 0.0f, offs / float(height));
                glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                glTextureBarrier();
        }

        glDisable(GL_DEPTH_TEST);

        glDeleteFramebuffers(1, &fbo);
}

// Blend the four directions from HoleFill into one pixel, so that single-pixel
// holes become the average of their four neighbors.
class HoleBlend {
public:
        HoleBlend();

        void exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height);

private:
        PersistentFBOSet<2> fbos;

        GLuint blend_vs_obj;
        GLuint blend_fs_obj;
        GLuint blend_program;
        GLuint blend_vao;

        GLuint uniform_left_tex, uniform_right_tex, uniform_up_tex, uniform_down_tex;
        GLuint uniform_z, uniform_sample_offset;
};

HoleBlend::HoleBlend()
{
        blend_vs_obj = compile_shader(read_file("hole_fill.vert"), GL_VERTEX_SHADER);  // Reuse the vertex shader from the fill.
        blend_fs_obj = compile_shader(read_file("hole_blend.frag"), GL_FRAGMENT_SHADER);
        blend_program = link_program(blend_vs_obj, blend_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &blend_vao);
        glBindVertexArray(blend_vao);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        GLint position_attrib = glGetAttribLocation(blend_program, "position");
        glEnableVertexArrayAttrib(blend_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_left_tex = glGetUniformLocation(blend_program, "left_tex");
        uniform_right_tex = glGetUniformLocation(blend_program, "right_tex");
        uniform_up_tex = glGetUniformLocation(blend_program, "up_tex");
        uniform_down_tex = glGetUniformLocation(blend_program, "down_tex");
        uniform_z = glGetUniformLocation(blend_program, "z");
        uniform_sample_offset = glGetUniformLocation(blend_program, "sample_offset");
}

void HoleBlend::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height)
{
        glUseProgram(blend_program);

        bind_sampler(blend_program, uniform_left_tex, 0, temp_tex[0], nearest_sampler);
        bind_sampler(blend_program, uniform_right_tex, 1, temp_tex[1], nearest_sampler);
        bind_sampler(blend_program, uniform_up_tex, 2, temp_tex[2], nearest_sampler);
        bind_sampler(blend_program, uniform_down_tex, 3, flow_tex, nearest_sampler);

        glProgramUniform1f(blend_program, uniform_z, 1.0f - 4.0f / 1024.0f);
        glProgramUniform2f(blend_program, uniform_sample_offset, 0.0f, 0.0f);

        glViewport(0, 0, width, height);
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LEQUAL);  // Skip over all of the pixels that were never holes to begin with.
        glBindVertexArray(blend_vao);

        // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
        GLuint fbo;
        glCreateFramebuffers(1, &fbo);
        glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);  // NOTE: Reading and writing to the same texture.
        glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
        glBindFramebuffer(GL_FRAMEBUFFER, fbo);

        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);

        glDisable(GL_DEPTH_TEST);

        glDeleteFramebuffers(1, &fbo);
}

class Blend {
public:
        Blend();
        void exec(GLuint tex0, GLuint tex1, GLuint flow_tex, GLuint output_tex, int width, int height, float alpha);

private:
        PersistentFBOSet<1> fbos;
        GLuint blend_vs_obj;
        GLuint blend_fs_obj;
        GLuint blend_program;
        GLuint blend_vao;

        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
        GLuint uniform_alpha, uniform_flow_consistency_tolerance;
};

Blend::Blend()
{
        blend_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
        blend_fs_obj = compile_shader(read_file("blend.frag"), GL_FRAGMENT_SHADER);
        blend_program = link_program(blend_vs_obj, blend_fs_obj);

        // Set up the VAO containing all the required position/texcoord data.
        glCreateVertexArrays(1, &blend_vao);
        glBindVertexArray(blend_vao);

        GLint position_attrib = glGetAttribLocation(blend_program, "position");
        glEnableVertexArrayAttrib(blend_vao, position_attrib);
        glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));

        uniform_image0_tex = glGetUniformLocation(blend_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(blend_program, "image1_tex");
        uniform_flow_tex = glGetUniformLocation(blend_program, "flow_tex");
        uniform_alpha = glGetUniformLocation(blend_program, "alpha");
        uniform_flow_consistency_tolerance = glGetUniformLocation(blend_program, "flow_consistency_tolerance");
}

void Blend::exec(GLuint tex0, GLuint tex1, GLuint flow_tex, GLuint output_tex, int level_width, int level_height, float alpha)
{
        glUseProgram(blend_program);
        bind_sampler(blend_program, uniform_image0_tex, 0, tex0, linear_sampler);
        bind_sampler(blend_program, uniform_image1_tex, 1, tex1, linear_sampler);
        bind_sampler(blend_program, uniform_flow_tex, 2, flow_tex, linear_sampler);  // May be upsampled.
        glProgramUniform1f(blend_program, uniform_alpha, alpha);
        //glProgramUniform1f(blend_program, uniform_flow_consistency_tolerance, 1.0f / 

        glViewport(0, 0, level_width, level_height);
        fbos.render_to(output_tex);
        glBindVertexArray(blend_vao);
        glUseProgram(blend_program);
        glDisable(GL_BLEND);  // A bit ironic, perhaps.
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}

class Interpolate {
public:
        Interpolate(int width, int height, int flow_level);

        // Returns a texture that must be released with release_texture()
        // after use. tex0 and tex1 must be RGBA8 textures with mipmaps
        // (unless flow_level == 0).
        GLuint exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint width, GLuint height, float alpha);

        void release_texture(GLuint tex) {
                pool.release_texture(tex);
        }

private:
        int width, height, flow_level;
        TexturePool pool;
        Splat splat;
        HoleFill hole_fill;
        HoleBlend hole_blend;
        Blend blend;
};

Interpolate::Interpolate(int width, int height, int flow_level)
        : width(width), height(height), flow_level(flow_level) {}

GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint width, GLuint height, float alpha)
{
        GPUTimers timers;

        ScopedTimer total_timer("Total", &timers);

        // Pick out the right level to test splatting results on.
        GLuint tex0_view, tex1_view;
        glGenTextures(1, &tex0_view);
        glTextureView(tex0_view, GL_TEXTURE_2D, tex0, GL_RGBA8, flow_level, 1, 0, 1);
        glGenTextures(1, &tex1_view);
        glTextureView(tex1_view, GL_TEXTURE_2D, tex1, GL_RGBA8, flow_level, 1, 0, 1);

        int flow_width = width >> flow_level;
        int flow_height = height >> flow_level;

        GLuint flow_tex = pool.get_texture(GL_RG16F, flow_width, flow_height);
        GLuint depth_tex = pool.get_texture(GL_DEPTH_COMPONENT32F, flow_width, flow_height);  // Used for ranking flows.
        {
                ScopedTimer timer("Clear", &total_timer);
                float invalid_flow[] = { 1000.0f, 1000.0f };
                glClearTexImage(flow_tex, 0, GL_RG, GL_FLOAT, invalid_flow);
                float infinity = 1.0f;
                glClearTexImage(depth_tex, 0, GL_DEPTH_COMPONENT, GL_FLOAT, &infinity);
        }

        {
                ScopedTimer timer("Splat", &total_timer);
                splat.exec(tex0_view, tex1_view, forward_flow_tex, backward_flow_tex, flow_tex, depth_tex, flow_width, flow_height, alpha);
        }
        glDeleteTextures(1, &tex0_view);
        glDeleteTextures(1, &tex1_view);

        GLuint temp_tex[3];
        temp_tex[0] = pool.get_texture(GL_RG16F, flow_width, flow_height);
        temp_tex[1] = pool.get_texture(GL_RG16F, flow_width, flow_height);
        temp_tex[2] = pool.get_texture(GL_RG16F, flow_width, flow_height);

        {
                ScopedTimer timer("Fill holes", &total_timer);
                hole_fill.exec(flow_tex, depth_tex, temp_tex, flow_width, flow_height);
                hole_blend.exec(flow_tex, depth_tex, temp_tex, flow_width, flow_height);
        }

        pool.release_texture(temp_tex[0]);
        pool.release_texture(temp_tex[1]);
        pool.release_texture(temp_tex[2]);
        pool.release_texture(depth_tex);

        GLuint output_tex = pool.get_texture(GL_RGBA8, width, height);
        {
                ScopedTimer timer("Blend", &total_timer);
                blend.exec(tex0, tex1, flow_tex, output_tex, width, height, alpha);
        }
        total_timer.end();
        timers.print();

        return output_tex;
}

GLuint TexturePool::get_texture(GLenum format, GLuint width, GLuint height)
{
        for (Texture &tex : textures) {
                if (!tex.in_use && tex.format == format &&
                    tex.width == width && tex.height == height) {
                        tex.in_use = true;
                        return tex.tex_num;
                }
        }

        Texture tex;
        glCreateTextures(GL_TEXTURE_2D, 1, &tex.tex_num);
        glTextureStorage2D(tex.tex_num, 1, format, width, height);
        tex.format = format;
        tex.width = width;
        tex.height = height;
        tex.in_use = true;
        textures.push_back(tex);
        return tex.tex_num;
}

void TexturePool::release_texture(GLuint tex_num)
{
        for (Texture &tex : textures) {
                if (tex.tex_num == tex_num) {
                        assert(tex.in_use);
                        tex.in_use = false;
                        return;
                }
        }
        assert(false);
}

// OpenGL uses a bottom-left coordinate system, .flo files use a top-left coordinate system.
void flip_coordinate_system(float *dense_flow, unsigned width, unsigned height)
{
        for (unsigned i = 0; i < width * height; ++i) {
                dense_flow[i * 2 + 1] = -dense_flow[i * 2 + 1];
        }
}

// Not relevant for RGB.
void flip_coordinate_system(uint8_t *dense_flow, unsigned width, unsigned height)
{
}

void write_flow(const char *filename, const float *dense_flow, unsigned width, unsigned height)
{
        FILE *flowfp = fopen(filename, "wb");
        fprintf(flowfp, "FEIH");
        fwrite(&width, 4, 1, flowfp);
        fwrite(&height, 4, 1, flowfp);
        for (unsigned y = 0; y < height; ++y) {
                int yy = height - y - 1;
                fwrite(&dense_flow[yy * width * 2], width * 2 * sizeof(float), 1, flowfp);
        }
        fclose(flowfp);
}

// Not relevant for RGB.
void write_flow(const char *filename, const uint8_t *dense_flow, unsigned width, unsigned height)
{
        assert(false);
}

void write_ppm(const char *filename, const float *dense_flow, unsigned width, unsigned height)
{
        FILE *fp = fopen(filename, "wb");
        fprintf(fp, "P6\n%d %d\n255\n", width, height);
        for (unsigned y = 0; y < unsigned(height); ++y) {
                int yy = height - y - 1;
                for (unsigned x = 0; x < unsigned(width); ++x) {
                        float du = dense_flow[(yy * width + x) * 2 + 0];
                        float dv = dense_flow[(yy * width + x) * 2 + 1];

                        uint8_t r, g, b;
                        flow2rgb(du, dv, &r, &g, &b);
                        putc(r, fp);
                        putc(g, fp);
                        putc(b, fp);
                }
        }
        fclose(fp);
}

void write_ppm(const char *filename, const uint8_t *rgba, unsigned width, unsigned height)
{
        unique_ptr<uint8_t[]> rgb_line(new uint8_t[width * 3 + 1]);

        FILE *fp = fopen(filename, "wb");
        fprintf(fp, "P6\n%d %d\n255\n", width, height);
        for (unsigned y = 0; y < height; ++y) {
                unsigned y2 = height - 1 - y;
                for (size_t x = 0; x < width; ++x) {
                        memcpy(&rgb_line[x * 3], &rgba[(y2 * width + x) * 4], 4);
                }
                fwrite(rgb_line.get(), width * 3, 1, fp);
        }
        fclose(fp);
}

struct FlowType {
        using type = float;
        static constexpr GLenum gl_format = GL_RG;
        static constexpr GLenum gl_type = GL_FLOAT;
        static constexpr int num_channels = 2;
};

struct RGBAType {
        using type = uint8_t;
        static constexpr GLenum gl_format = GL_RGBA;
        static constexpr GLenum gl_type = GL_UNSIGNED_BYTE;
        static constexpr int num_channels = 4;
};

template <class Type>
void finish_one_read(GLuint width, GLuint height)
{
        using T = typename Type::type;
        constexpr int bytes_per_pixel = Type::num_channels * sizeof(T);

        assert(!reads_in_progress.empty());
        ReadInProgress read = reads_in_progress.front();
        reads_in_progress.pop_front();

        unique_ptr<T[]> flow(new typename Type::type[width * height * Type::num_channels]);
        void *buf = glMapNamedBufferRange(read.pbo, 0, width * height * bytes_per_pixel, GL_MAP_READ_BIT);  // Blocks if the read isn't done yet.
        memcpy(flow.get(), buf, width * height * bytes_per_pixel);  // TODO: Unneeded for RGBType, since flip_coordinate_system() does nothing.:
        glUnmapNamedBuffer(read.pbo);
        spare_pbos.push(read.pbo);

        flip_coordinate_system(flow.get(), width, height);
        if (!read.flow_filename.empty()) {
                write_flow(read.flow_filename.c_str(), flow.get(), width, height);
                fprintf(stderr, "%s %s -> %s\n", read.filename0.c_str(), read.filename1.c_str(), read.flow_filename.c_str());
        }
        if (!read.ppm_filename.empty()) {
                write_ppm(read.ppm_filename.c_str(), flow.get(), width, height);
        }
}

template <class Type>
void schedule_read(GLuint tex, GLuint width, GLuint height, const char *filename0, const char *filename1, const char *flow_filename, const char *ppm_filename)
{
        using T = typename Type::type;
        constexpr int bytes_per_pixel = Type::num_channels * sizeof(T);

        if (spare_pbos.empty()) {
                finish_one_read<Type>(width, height);
        }
        assert(!spare_pbos.empty());
        reads_in_progress.emplace_back(ReadInProgress{ spare_pbos.top(), filename0, filename1, flow_filename, ppm_filename });
        glBindBuffer(GL_PIXEL_PACK_BUFFER, spare_pbos.top());
        spare_pbos.pop();
        glGetTextureImage(tex, 0, Type::gl_format, Type::gl_type, width * height * bytes_per_pixel, nullptr);
        glBindBuffer(GL_PIXEL_PACK_BUFFER, 0);
}

void compute_flow_only(int argc, char **argv, int optind)
{
        const char *filename0 = argc >= (optind + 1) ? argv[optind] : "test1499.png";
        const char *filename1 = argc >= (optind + 2) ? argv[optind + 1] : "test1500.png";
        const char *flow_filename = argc >= (optind + 3) ? argv[optind + 2] : "flow.flo";

        // Load pictures.
        unsigned width1, height1, width2, height2;
        GLuint tex0 = load_texture(filename0, &width1, &height1, WITHOUT_MIPMAPS);
        GLuint tex1 = load_texture(filename1, &width2, &height2, WITHOUT_MIPMAPS);

        if (width1 != width2 || height1 != height2) {
                fprintf(stderr, "Image dimensions don't match (%dx%d versus %dx%d)\n",
                        width1, height1, width2, height2);
                exit(1);
        }

        // Set up some PBOs to do asynchronous readback.
        GLuint pbos[5];
        glCreateBuffers(5, pbos);
        for (int i = 0; i < 5; ++i) {
                glNamedBufferData(pbos[i], width1 * height1 * 2 * sizeof(float), nullptr, GL_STREAM_READ);
                spare_pbos.push(pbos[i]);
        }

        int levels = find_num_levels(width1, height1);
        GLuint tex0_gray, tex1_gray;
        glCreateTextures(GL_TEXTURE_2D, 1, &tex0_gray);
        glCreateTextures(GL_TEXTURE_2D, 1, &tex1_gray);
        glTextureStorage2D(tex0_gray, levels, GL_R8, width1, height1);
        glTextureStorage2D(tex1_gray, levels, GL_R8, width1, height1);

        GrayscaleConversion gray;
        gray.exec(tex0, tex0_gray, width1, height1);
        glDeleteTextures(1, &tex0);
        glGenerateTextureMipmap(tex0_gray);

        gray.exec(tex1, tex1_gray, width1, height1);
        glDeleteTextures(1, &tex1);
        glGenerateTextureMipmap(tex1_gray);

        DISComputeFlow compute_flow(width1, height1);
        GLuint final_tex = compute_flow.exec(tex0_gray, tex1_gray, DISComputeFlow::RESIZE_FLOW_TO_FULL_SIZE);

        schedule_read<FlowType>(final_tex, width1, height1, filename0, filename1, flow_filename, "flow.ppm");
        compute_flow.release_texture(final_tex);

        // See if there are more flows on the command line (ie., more than three arguments),
        // and if so, process them.
        int num_flows = (argc - optind) / 3;
        for (int i = 1; i < num_flows; ++i) {
                const char *filename0 = argv[optind + i * 3 + 0];
                const char *filename1 = argv[optind + i * 3 + 1];
                const char *flow_filename = argv[optind + i * 3 + 2];
                GLuint width, height;
                GLuint tex0 = load_texture(filename0, &width, &height, WITHOUT_MIPMAPS);
                if (width != width1 || height != height1) {
                        fprintf(stderr, "%s: Image dimensions don't match (%dx%d versus %dx%d)\n",
                                filename0, width, height, width1, height1);
                        exit(1);
                }
                gray.exec(tex0, tex0_gray, width, height);
                glGenerateTextureMipmap(tex0_gray);
                glDeleteTextures(1, &tex0);

                GLuint tex1 = load_texture(filename1, &width, &height, WITHOUT_MIPMAPS);
                if (width != width1 || height != height1) {
                        fprintf(stderr, "%s: Image dimensions don't match (%dx%d versus %dx%d)\n",
                                filename1, width, height, width1, height1);
                        exit(1);
                }
                gray.exec(tex1, tex1_gray, width, height);
                glGenerateTextureMipmap(tex1_gray);
                glDeleteTextures(1, &tex1);

                GLuint final_tex = compute_flow.exec(tex0_gray, tex1_gray, DISComputeFlow::RESIZE_FLOW_TO_FULL_SIZE);

                schedule_read<FlowType>(final_tex, width1, height1, filename0, filename1, flow_filename, "");
                compute_flow.release_texture(final_tex);
        }
        glDeleteTextures(1, &tex0_gray);
        glDeleteTextures(1, &tex1_gray);

        while (!reads_in_progress.empty()) {
                finish_one_read<FlowType>(width1, height1);
        }
}

// Interpolate images based on
//
//   Herbst, Seitz, Baker: “Occlusion Reasoning for Temporal Interpolation
//   Using Optical Flow”
//
// or at least a reasonable subset thereof. Unfinished.
void interpolate_image(int argc, char **argv, int optind)
{
        const char *filename0 = argc >= (optind + 1) ? argv[optind] : "test1499.png";
        const char *filename1 = argc >= (optind + 2) ? argv[optind + 1] : "test1500.png";
        //const char *out_filename = argc >= (optind + 3) ? argv[optind + 2] : "interpolated.png";

        // Load pictures.
        unsigned width1, height1, width2, height2;
        GLuint tex0 = load_texture(filename0, &width1, &height1, WITH_MIPMAPS);
        GLuint tex1 = load_texture(filename1, &width2, &height2, WITH_MIPMAPS);

        if (width1 != width2 || height1 != height2) {
                fprintf(stderr, "Image dimensions don't match (%dx%d versus %dx%d)\n",
                        width1, height1, width2, height2);
                exit(1);
        }

        // Set up some PBOs to do asynchronous readback.
        GLuint pbos[5];
        glCreateBuffers(5, pbos);
        for (int i = 0; i < 5; ++i) {
                glNamedBufferData(pbos[i], width1 * height1 * 4 * sizeof(uint8_t), nullptr, GL_STREAM_READ);
                spare_pbos.push(pbos[i]);
        }

        DISComputeFlow compute_flow(width1, height1);
        GrayscaleConversion gray;
        Interpolate interpolate(width1, height1, finest_level);

        int levels = find_num_levels(width1, height1);
        GLuint tex0_gray, tex1_gray;
        glCreateTextures(GL_TEXTURE_2D, 1, &tex0_gray);
        glCreateTextures(GL_TEXTURE_2D, 1, &tex1_gray);
        glTextureStorage2D(tex0_gray, levels, GL_R8, width1, height1);
        glTextureStorage2D(tex1_gray, levels, GL_R8, width1, height1);

        gray.exec(tex0, tex0_gray, width1, height1);
        glGenerateTextureMipmap(tex0_gray);

        gray.exec(tex1, tex1_gray, width1, height1);
        glGenerateTextureMipmap(tex1_gray);

        GLuint forward_flow_tex = compute_flow.exec(tex0_gray, tex1_gray, DISComputeFlow::DO_NOT_RESIZE_FLOW);
        GLuint backward_flow_tex = compute_flow.exec(tex1_gray, tex0_gray, DISComputeFlow::DO_NOT_RESIZE_FLOW);

        for (int frameno = 1; frameno < 60; ++frameno) {
                char ppm_filename[256];
                snprintf(ppm_filename, sizeof(ppm_filename), "interp%04d.ppm", frameno);

                float alpha = frameno / 60.0f;
                GLuint interpolated_tex = interpolate.exec(tex0, tex1, forward_flow_tex, backward_flow_tex, width1, height1, alpha);

                schedule_read<RGBAType>(interpolated_tex, width1, height1, filename0, filename1, "", ppm_filename);
                interpolate.release_texture(interpolated_tex);
        }

        while (!reads_in_progress.empty()) {
                finish_one_read<RGBAType>(width1, height1);
        }
}

int main(int argc, char **argv)
{
        static const option long_options[] = {
                { "smoothness-relative-weight", required_argument, 0, 's' },  // alpha.
                { "intensity-relative-weight", required_argument, 0, 'i' },  // delta.
                { "gradient-relative-weight", required_argument, 0, 'g' },  // gamma.
                { "disable-timing", no_argument, 0, 1000 },
                { "ignore-variational-refinement", no_argument, 0, 1001 },  // Still calculates it, just doesn't apply it.
                { "interpolate", no_argument, 0, 1002 }
        };

        for ( ;; ) {
                int option_index = 0;
                int c = getopt_long(argc, argv, "s:i:g:", long_options, &option_index);

                if (c == -1) {
                        break;
                }
                switch (c) {
                case 's':
                        vr_alpha = atof(optarg);
                        break;
                case 'i':
                        vr_delta = atof(optarg);
                        break;
                case 'g':
                        vr_gamma = atof(optarg);
                        break;
                case 1000:
                        enable_timing = false;
                        break;
                case 1001:
                        enable_variational_refinement = false;
                        break;
                case 1002:
                        enable_interpolation = true;
                        break;
                default:
                        fprintf(stderr, "Unknown option '%s'\n", argv[option_index]);
                        exit(1);
                };
        }

        if (SDL_Init(SDL_INIT_EVERYTHING) == -1) {
                fprintf(stderr, "SDL_Init failed: %s\n", SDL_GetError());
                exit(1);
        }
        SDL_GL_SetAttribute(SDL_GL_ALPHA_SIZE, 8);
        SDL_GL_SetAttribute(SDL_GL_DEPTH_SIZE, 0);
        SDL_GL_SetAttribute(SDL_GL_STENCIL_SIZE, 0);
        SDL_GL_SetAttribute(SDL_GL_DOUBLEBUFFER, 1);

        SDL_GL_SetAttribute(SDL_GL_CONTEXT_PROFILE_MASK, SDL_GL_CONTEXT_PROFILE_CORE);
        SDL_GL_SetAttribute(SDL_GL_CONTEXT_MAJOR_VERSION, 4);
        SDL_GL_SetAttribute(SDL_GL_CONTEXT_MINOR_VERSION, 5);
        // SDL_GL_SetAttribute(SDL_GL_CONTEXT_FLAGS, SDL_GL_CONTEXT_DEBUG_FLAG);
        window = SDL_CreateWindow("OpenGL window",
                SDL_WINDOWPOS_UNDEFINED,
                SDL_WINDOWPOS_UNDEFINED,
                64, 64,
                SDL_WINDOW_OPENGL | SDL_WINDOW_HIDDEN);
        SDL_GLContext context = SDL_GL_CreateContext(window);
        assert(context != nullptr);

        // FIXME: Should be part of DISComputeFlow (but needs to be initialized
        // before all the render passes).
        float vertices[] = {
                0.0f, 1.0f,
                0.0f, 0.0f,
                1.0f, 1.0f,
                1.0f, 0.0f,
        };
        glCreateBuffers(1, &vertex_vbo);
        glNamedBufferData(vertex_vbo, sizeof(vertices), vertices, GL_STATIC_DRAW);
        glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);

        if (enable_interpolation) {
                interpolate_image(argc, argv, optind);
        } else {
                compute_flow_only(argc, argv, optind);
        }
}