]> git.sesse.net Git - nageru/blobdiff - flow.cpp
Deal with buggy GPU timers that go backwards.
[nageru] / flow.cpp
index 47cebba7918c84471583629367192795b7aff19b..6decf73ca673739bfae79a96e3ca6e0a0b69d3df 100644 (file)
--- a/flow.cpp
+++ b/flow.cpp
@@ -1,8 +1,5 @@
 #define NO_SDL_GLEXT 1
 
-#define WIDTH 1280
-#define HEIGHT 720
-
 #include <epoxy/gl.h>
 
 #include <SDL2/SDL.h>
 
 #include <assert.h>
 #include <stdio.h>
+#include <unistd.h>
 
-#include "flow2rgb.h"
+#include "util.h"
 
 #include <algorithm>
 #include <memory>
+#include <vector>
 
 #define BUFFER_OFFSET(i) ((char *)nullptr + (i))
 
@@ -32,7 +31,7 @@ constexpr unsigned finest_level = 1;
 constexpr unsigned patch_size_pixels = 12;
 
 // Some global OpenGL objects.
-GLuint nearest_sampler, linear_sampler, mipmap_sampler;
+GLuint nearest_sampler, linear_sampler, smoothness_sampler;
 GLuint vertex_vbo;
 
 string read_file(const string &filename)
@@ -113,26 +112,41 @@ GLuint compile_shader(const string &shader_src, GLenum type)
        return obj;
 }
 
-
-GLuint load_texture(const char *filename, unsigned width, unsigned height)
+GLuint load_texture(const char *filename, unsigned *width_ret, unsigned *height_ret)
 {
-       FILE *fp = fopen(filename, "rb");
-       if (fp == nullptr) {
-               perror(filename);
+       SDL_Surface *surf = IMG_Load(filename);
+       if (surf == nullptr) {
+               fprintf(stderr, "IMG_Load(%s): %s\n", filename, IMG_GetError());
                exit(1);
        }
-       unique_ptr<uint8_t[]> pix(new uint8_t[width * height]);
-       if (fread(pix.get(), width * height, 1, fp) != 1) {
-               fprintf(stderr, "Short read from %s\n", filename);
+
+       // For whatever reason, SDL doesn't support converting to YUV surfaces
+       // nor grayscale, so we'll do it (slowly) ourselves.
+       SDL_Surface *rgb_surf = SDL_ConvertSurfaceFormat(surf, SDL_PIXELFORMAT_RGBA8888, /*flags=*/0);
+       if (rgb_surf == nullptr) {
+               fprintf(stderr, "SDL_ConvertSurfaceFormat(%s): %s\n", filename, SDL_GetError());
                exit(1);
        }
-       fclose(fp);
 
-       // Convert to bottom-left origin.
-       for (unsigned y = 0; y < height / 2; ++y) {
+       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]);
+
+       // Extract the Y component, and convert to bottom-left origin.
+       for (unsigned y = 0; y < height; ++y) {
                unsigned y2 = height - 1 - y;
-               swap_ranges(&pix[y * width], &pix[y * width + width], &pix[y2 * width]);
+               for (unsigned x = 0; x < width; ++x) {
+                       uint8_t r = sptr[(y2 * width + x) * 4 + 3];
+                       uint8_t g = sptr[(y2 * width + x) * 4 + 2];
+                       uint8_t b = sptr[(y2 * width + x) * 4 + 1];
+
+                       // Rec. 709.
+                       pix[y * width + x] = lrintf(r * 0.2126f + g * 0.7152f + b * 0.0722f);
+               }
        }
+       SDL_FreeSurface(rgb_surf);
 
        int levels = 1;
        for (int w = width, h = height; w > 1 || h > 1; ) {
@@ -147,15 +161,18 @@ GLuint load_texture(const char *filename, unsigned width, unsigned height)
        glTextureSubImage2D(tex, 0, 0, 0, width, height, GL_RED, GL_UNSIGNED_BYTE, pix.get());
        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);
+       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) {
@@ -193,9 +210,8 @@ GLuint fill_vertex_attribute(GLuint vao, GLuint glsl_program_num, const string &
        return vbo;
 }
 
-void bind_sampler(GLuint program, const char *uniform_name, GLuint texture_unit, GLuint tex, GLuint sampler)
+void bind_sampler(GLuint program, GLint location, GLuint texture_unit, GLuint tex, GLuint sampler)
 {
-       GLint location = glGetUniformLocation(program, uniform_name);
        if (location == -1) {
                return;
        }
@@ -223,6 +239,8 @@ private:
        GLuint sobel_fs_obj;
        GLuint sobel_program;
        GLuint sobel_vao;
+
+       GLuint uniform_tex, uniform_image_size;
 };
 
 Sobel::Sobel()
@@ -232,16 +250,14 @@ Sobel::Sobel()
        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);
+       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));
 
-       GLint texcoord_attrib = glGetAttribLocation(sobel_program, "texcoord");
-       glEnableVertexArrayAttrib(sobel_vao, texcoord_attrib);
-       glVertexAttribPointer(texcoord_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)
@@ -249,9 +265,7 @@ void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_he
        glUseProgram(sobel_program);
        glBindTextureUnit(0, tex0_view);
        glBindSampler(0, nearest_sampler);
-       glProgramUniform1i(sobel_program, glGetUniformLocation(sobel_program, "tex"), 0);
-       glProgramUniform2f(sobel_program, glGetUniformLocation(sobel_program, "image_size"), level_width, level_height);
-       glProgramUniform2f(sobel_program, glGetUniformLocation(sobel_program, "inv_image_size"), 1.0f / level_width, 1.0f / level_height);
+       glProgramUniform1i(sobel_program, uniform_tex, 0);
 
        GLuint grad0_fbo;  // TODO: cleanup
        glCreateFramebuffers(1, &grad0_fbo);
@@ -259,7 +273,7 @@ void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_he
 
        glViewport(0, 0, level_width, level_height);
        glBindFramebuffer(GL_FRAMEBUFFER, grad0_fbo);
-        glBindVertexArray(sobel_vao);
+       glBindVertexArray(sobel_vao);
        glUseProgram(sobel_program);
        glDisable(GL_BLEND);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
@@ -269,13 +283,16 @@ void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_he
 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 width_patches, int height_patches);
+       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:
        GLuint motion_vs_obj;
        GLuint motion_fs_obj;
        GLuint motion_search_program;
        GLuint motion_search_vao;
+
+       GLuint uniform_image_size, uniform_inv_image_size, uniform_inv_prev_level_size;
+       GLuint uniform_image0_tex, uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
 };
 
 MotionSearch::MotionSearch()
@@ -285,30 +302,35 @@ MotionSearch::MotionSearch()
        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);
+       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));
 
-       GLint texcoord_attrib = glGetAttribLocation(motion_search_program, "texcoord");
-       glEnableVertexArrayAttrib(motion_search_vao, texcoord_attrib);
-       glVertexAttribPointer(texcoord_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
+       uniform_image_size = glGetUniformLocation(motion_search_program, "image_size");
+       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 width_patches, int height_patches)
+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, "image0_tex", 0, tex0_view, nearest_sampler);
-       bind_sampler(motion_search_program, "image1_tex", 1, tex1_view, linear_sampler);
-       bind_sampler(motion_search_program, "grad0_tex", 2, grad0_tex, nearest_sampler);
-       bind_sampler(motion_search_program, "flow_tex", 3, flow_tex, linear_sampler);
+       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, nearest_sampler);
+       bind_sampler(motion_search_program, uniform_flow_tex, 3, flow_tex, linear_sampler);
 
-       glProgramUniform2f(motion_search_program, glGetUniformLocation(motion_search_program, "image_size"), level_width, level_height);
-       glProgramUniform2f(motion_search_program, glGetUniformLocation(motion_search_program, "inv_image_size"), 1.0f / level_width, 1.0f / level_height);
+       glProgramUniform2f(motion_search_program, uniform_image_size, level_width, level_height);
+       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);
 
        GLuint flow_fbo;  // TODO: cleanup
        glCreateFramebuffers(1, &flow_fbo);
@@ -316,7 +338,7 @@ void MotionSearch::exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GL
 
        glViewport(0, 0, width_patches, height_patches);
        glBindFramebuffer(GL_FRAMEBUFFER, flow_fbo);
-        glBindVertexArray(motion_search_vao);
+       glBindVertexArray(motion_search_vao);
        glUseProgram(motion_search_program);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -339,6 +361,9 @@ private:
        GLuint densify_fs_obj;
        GLuint densify_program;
        GLuint densify_vao;
+
+       GLuint uniform_width_patches, uniform_patch_size, uniform_patch_spacing;
+       GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
 };
 
 Densify::Densify()
@@ -348,31 +373,40 @@ Densify::Densify()
        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);
+       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_width_patches = glGetUniformLocation(densify_program, "width_patches");
+       uniform_patch_size = glGetUniformLocation(densify_program, "patch_size");
+       uniform_patch_spacing = glGetUniformLocation(densify_program, "patch_spacing");
+       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, "image0_tex", 0, tex0_view, nearest_sampler);
-       bind_sampler(densify_program, "image1_tex", 1, tex1_view, linear_sampler);
-       bind_sampler(densify_program, "flow_tex", 2, flow_tex, nearest_sampler);
+       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);
 
-       glProgramUniform1i(densify_program, glGetUniformLocation(densify_program, "width_patches"), width_patches);
-       glProgramUniform2f(densify_program, glGetUniformLocation(densify_program, "patch_size"),
+       glProgramUniform1i(densify_program, uniform_width_patches, width_patches);
+       glProgramUniform2f(densify_program, uniform_patch_size,
                float(patch_size_pixels) / level_width,
                float(patch_size_pixels) / level_height);
 
        float patch_spacing_x = float(level_width - patch_size_pixels) / (width_patches - 1);
        float patch_spacing_y = float(level_height - patch_size_pixels) / (height_patches - 1);
-       glProgramUniform2f(densify_program, glGetUniformLocation(densify_program, "patch_spacing"),
+       if (width_patches == 1) patch_spacing_x = 0.0f;  // Avoid infinities.
+       if (height_patches == 1) patch_spacing_y = 0.0f;
+       glProgramUniform2f(densify_program, uniform_patch_spacing,
                patch_spacing_x / level_width,
                patch_spacing_y / level_height);
 
@@ -383,12 +417,543 @@ void Densify::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint d
        glViewport(0, 0, level_width, level_height);
        glEnable(GL_BLEND);
        glBlendFunc(GL_ONE, GL_ONE);
-        glBindVertexArray(densify_vao);
+       glBindVertexArray(densify_vao);
        glBindFramebuffer(GL_FRAMEBUFFER, dense_flow_fbo);
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width_patches * height_patches);
 }
 
-int main(void)
+// 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:
+       GLuint prewarp_vs_obj;
+       GLuint prewarp_fs_obj;
+       GLuint prewarp_program;
+       GLuint prewarp_vao;
+
+       GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
+       GLuint uniform_image_size;
+};
+
+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");
+
+       uniform_image_size = glGetUniformLocation(prewarp_program, "image_size");
+}
+
+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);
+
+       glProgramUniform2f(prewarp_program, uniform_image_size, level_width, level_height);
+
+       GLuint prewarp_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &prewarp_fbo);
+       GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1, GL_COLOR_ATTACHMENT2 };
+       glNamedFramebufferDrawBuffers(prewarp_fbo, 3, bufs);
+       glNamedFramebufferTexture(prewarp_fbo, GL_COLOR_ATTACHMENT0, I_tex, 0);
+       glNamedFramebufferTexture(prewarp_fbo, GL_COLOR_ATTACHMENT1, I_t_tex, 0);
+       glNamedFramebufferTexture(prewarp_fbo, GL_COLOR_ATTACHMENT2, normalized_flow_tex, 0);
+
+       glViewport(0, 0, level_width, level_height);
+       glDisable(GL_BLEND);
+       glBindVertexArray(prewarp_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, prewarp_fbo);
+       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:
+       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);
+
+       GLuint derivatives_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &derivatives_fbo);
+       GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
+       glNamedFramebufferDrawBuffers(derivatives_fbo, 2, bufs);
+       glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT0, I_x_y_tex, 0);
+       glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT1, beta_0_tex, 0);
+
+       glViewport(0, 0, level_width, level_height);
+       glDisable(GL_BLEND);
+       glBindVertexArray(derivatives_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, derivatives_fbo);
+       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:
+       GLuint smoothness_vs_obj;
+       GLuint smoothness_fs_obj;
+       GLuint smoothness_program;
+       GLuint smoothness_vao;
+
+       GLuint uniform_flow_tex, uniform_diff_flow_tex;
+};
+
+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");
+}
+
+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);
+
+       GLuint smoothness_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &smoothness_fbo);
+       GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
+       glNamedFramebufferDrawBuffers(smoothness_fbo, 2, bufs);
+       glNamedFramebufferTexture(smoothness_fbo, GL_COLOR_ATTACHMENT0, smoothness_x_tex, 0);
+       glNamedFramebufferTexture(smoothness_fbo, GL_COLOR_ATTACHMENT1, smoothness_y_tex, 0);
+
+       glViewport(0, 0, level_width, level_height);
+
+       glDisable(GL_BLEND);
+       glBindVertexArray(smoothness_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, smoothness_fbo);
+       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:
+       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;
+};
+
+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");
+}
+
+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, smoothness_sampler);
+       bind_sampler(equations_program, uniform_smoothness_y_tex, 6, smoothness_y_tex, smoothness_sampler);
+
+       GLuint equations_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &equations_fbo);
+       glNamedFramebufferTexture(equations_fbo, GL_COLOR_ATTACHMENT0, equation_tex, 0);
+
+       glViewport(0, 0, level_width, level_height);
+       glDisable(GL_BLEND);
+       glBindVertexArray(equations_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, equations_fbo);
+       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 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:
+       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;
+};
+
+SOR::SOR()
+{
+       sor_vs_obj = compile_shader(read_file("vs.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");
+}
+
+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, smoothness_sampler);
+       bind_sampler(sor_program, uniform_smoothness_y_tex, 2, smoothness_y_tex, smoothness_sampler);
+       bind_sampler(sor_program, uniform_equation_tex, 3, equation_tex, nearest_sampler);
+
+       GLuint sor_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &sor_fbo);
+       glNamedFramebufferTexture(sor_fbo, GL_COLOR_ATTACHMENT0, diff_flow_tex, 0);  // NOTE: Bind to same as we render from!
+
+       glViewport(0, 0, level_width, level_height);
+       glDisable(GL_BLEND);
+       glBindVertexArray(sor_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, sor_fbo);
+
+       for (int i = 0; i < num_iterations; ++i) {
+               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:
+       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);
+
+       GLuint add_flow_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &add_flow_fbo);
+       glNamedFramebufferTexture(add_flow_fbo, GL_COLOR_ATTACHMENT0, base_flow_tex, 0);
+
+       glViewport(0, 0, level_width, level_height);
+       glEnable(GL_BLEND);
+       glBlendFunc(GL_ONE, GL_ONE);
+       glBindVertexArray(add_flow_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, add_flow_fbo);
+
+       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)
+{
+       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;
+}
+
+// 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:
+       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);
+
+       GLuint resize_flow_fbo;  // TODO: cleanup
+       glCreateFramebuffers(1, &resize_flow_fbo);
+       glNamedFramebufferTexture(resize_flow_fbo, GL_COLOR_ATTACHMENT0, out_tex, 0);
+
+       glViewport(0, 0, output_width, output_height);
+       glDisable(GL_BLEND);
+       glBindVertexArray(resize_flow_vao);
+       glBindFramebuffer(GL_FRAMEBUFFER, resize_flow_fbo);
+
+       glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
+}
+
+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 (!ended) {
+                       glQueryCounter(query.second, GL_TIMESTAMP);
+                       ended = true;
+               }
+       }
+
+private:
+       GPUTimers *timers;
+       int level;
+       pair<GLuint, GLuint> query;
+       bool ended = false;
+};
+
+int main(int argc, char **argv)
 {
        if (SDL_Init(SDL_INIT_EVERYTHING) == -1) {
                fprintf(stderr, "SDL_Init failed: %s\n", SDL_GetError());
@@ -412,8 +977,15 @@ int main(void)
        assert(context != nullptr);
 
        // Load pictures.
-       GLuint tex0 = load_texture("test1499.pgm", WIDTH, HEIGHT);
-       GLuint tex1 = load_texture("test1500.pgm", WIDTH, HEIGHT);
+       unsigned width1, height1, width2, height2;
+       GLuint tex0 = load_texture(argc >= 2 ? argv[1] : "test1499.png", &width1, &height1);
+       GLuint tex1 = load_texture(argc >= 3 ? argv[2] : "test1500.png", &width2, &height2);
+
+       if (width1 != width2 || height1 != height2) {
+               fprintf(stderr, "Image dimensions don't match (%dx%d versus %dx%d)\n",
+                       width1, height1, width2, height2);
+               exit(1);
+       }
 
        // Make some samplers.
        glCreateSamplers(1, &nearest_sampler);
@@ -428,11 +1000,15 @@ int main(void)
        glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
        glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
 
-       glCreateSamplers(1, &mipmap_sampler);
-       glSamplerParameteri(mipmap_sampler, GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_NEAREST);
-       glSamplerParameteri(mipmap_sampler, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
-       glSamplerParameteri(mipmap_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
-       glSamplerParameteri(mipmap_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.
+       glCreateSamplers(1, &smoothness_sampler);
+       glSamplerParameteri(smoothness_sampler, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
+       glSamplerParameteri(smoothness_sampler, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
+       glSamplerParameteri(smoothness_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);
+       glSamplerParameteri(smoothness_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);
+       float zero[] = { 0.0f, 0.0f, 0.0f, 0.0f };
+       glSamplerParameterfv(smoothness_sampler, GL_TEXTURE_BORDER_COLOR, zero);
 
        float vertices[] = {
                0.0f, 1.0f,
@@ -447,17 +1023,36 @@ int main(void)
        // Initial flow is zero, 1x1.
        GLuint initial_flow_tex;
        glCreateTextures(GL_TEXTURE_2D, 1, &initial_flow_tex);
-       glTextureStorage2D(initial_flow_tex, 1, GL_RGB32F, 1, 1);
+       glTextureStorage2D(initial_flow_tex, 1, GL_RG16F, 1, 1);
+       int prev_level_width = 1, prev_level_height = 1;
 
        GLuint prev_level_flow_tex = initial_flow_tex;
 
        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;
+
+       GLuint query;
+       glGenQueries(1, &query);
+       glBeginQuery(GL_TIME_ELAPSED, query);
 
+       GPUTimers timers;
+
+       ScopedTimer total_timer("Total", &timers);
        for (int level = coarsest_level; level >= int(finest_level); --level) {
-               int level_width = WIDTH >> level;
-               int level_height = HEIGHT >> level;
+               char timer_name[256];
+               snprintf(timer_name, sizeof(timer_name), "Level %d", level);
+               ScopedTimer level_timer(timer_name, &total_timer);
+
+               int level_width = width1 >> level;
+               int level_height = height1 >> level;
                float patch_spacing_pixels = patch_size_pixels * (1.0f - patch_overlap_ratio);
                int width_patches = 1 + lrintf((level_width - patch_size_pixels) / patch_spacing_pixels);
                int height_patches = 1 + lrintf((level_height - patch_size_pixels) / patch_spacing_pixels);
@@ -479,7 +1074,10 @@ int main(void)
                glTextureStorage2D(grad0_tex, 1, GL_RG16F, level_width, level_height);
 
                // Find the derivative.
-               sobel.exec(tex0_view, grad0_tex, level_width, level_height);
+               {
+                       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.
@@ -487,43 +1085,153 @@ int main(void)
                // Create an output flow texture.
                GLuint flow_out_tex;
                glCreateTextures(GL_TEXTURE_2D, 1, &flow_out_tex);
-               glTextureStorage2D(flow_out_tex, 1, GL_RG16F, width_patches, height_patches);
+               glTextureStorage2D(flow_out_tex, 1, GL_RGB16F, width_patches, height_patches);
 
                // And draw.
-               motion_search.exec(tex0_view, tex1_view, grad0_tex, prev_level_flow_tex, flow_out_tex, level_width, level_height, width_patches, height_patches);
+               {
+                       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);
+               }
 
                // Densification.
 
-               // Set up an output texture.
+               // Set up an output texture (initially zero).
                GLuint dense_flow_tex;
                glCreateTextures(GL_TEXTURE_2D, 1, &dense_flow_tex);
-               //glTextureStorage2D(dense_flow_tex, 1, GL_RGB16F, level_width, level_height);
-               glTextureStorage2D(dense_flow_tex, 1, GL_RGBA32F, level_width, level_height);
+               glTextureStorage2D(dense_flow_tex, 1, GL_RGB16F, level_width, level_height);
+               glClearTexImage(dense_flow_tex, 0, GL_RGB, GL_FLOAT, nullptr);
 
                // And draw.
-               densify.exec(tex0_view, tex1_view, flow_out_tex, dense_flow_tex, level_width, level_height, width_patches, height_patches);
+               {
+                       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);
+               }
+
+               // 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, I_t_tex, base_flow_tex;
+               glCreateTextures(GL_TEXTURE_2D, 1, &I_tex);
+               glCreateTextures(GL_TEXTURE_2D, 1, &I_t_tex);
+               glCreateTextures(GL_TEXTURE_2D, 1, &base_flow_tex);
+               glTextureStorage2D(I_tex, 1, GL_R16F, level_width, level_height);
+               glTextureStorage2D(I_t_tex, 1, GL_R16F, level_width, level_height);
+               glTextureStorage2D(base_flow_tex, 1, 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);
+               }
+
+               // 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, beta_0_tex;
+               glCreateTextures(GL_TEXTURE_2D, 1, &I_x_y_tex);
+               glCreateTextures(GL_TEXTURE_2D, 1, &beta_0_tex);
+               glTextureStorage2D(I_x_y_tex, 1, GL_RG16F, level_width, level_height);
+               glTextureStorage2D(beta_0_tex, 1, 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);
+               }
+
+               // 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;
+               glCreateTextures(GL_TEXTURE_2D, 1, &du_dv_tex);
+               glTextureStorage2D(du_dv_tex, 1, GL_RG16F, level_width, level_height);
+               glClearTexImage(du_dv_tex, 0, GL_RG, GL_FLOAT, nullptr);
+
+               // And for smoothness.
+               GLuint smoothness_x_tex, smoothness_y_tex;
+               glCreateTextures(GL_TEXTURE_2D, 1, &smoothness_x_tex);
+               glCreateTextures(GL_TEXTURE_2D, 1, &smoothness_y_tex);
+               glTextureStorage2D(smoothness_x_tex, 1, GL_R16F, level_width, level_height);
+               glTextureStorage2D(smoothness_y_tex, 1, GL_R16F, level_width, level_height);
+
+               // And finally for the equation set. See SetupEquations for
+               // the storage format.
+               GLuint equation_tex;
+               glCreateTextures(GL_TEXTURE_2D, 1, &equation_tex);
+               glTextureStorage2D(equation_tex, 1, 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);
+                       }
 
-               // TODO: Variational refinement.
+                       // 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);
+                       }
 
-               prev_level_flow_tex = dense_flow_tex;
+                       // 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);
+                       }
+               }
+
+               // 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.
+               // You can comment out this part if you wish to test disabling of the variational refinement.
+               {
+                       ScopedTimer timer("Add differential flow", &varref_timer);
+                       add_base_flow.exec(base_flow_tex, du_dv_tex, level_width, level_height);
+               }
+
+               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).
+       GLuint final_tex;
+       if (finest_level == 0) {
+               final_tex = prev_level_flow_tex;
+       } else {
+               glCreateTextures(GL_TEXTURE_2D, 1, &final_tex);
+               glTextureStorage2D(final_tex, 1, GL_RG16F, width1, height1);
+               resize_flow.exec(prev_level_flow_tex, final_tex, prev_level_width, prev_level_height, width1, height1);
        }
 
-       int level_width = WIDTH >> finest_level;
-       int level_height = HEIGHT >> finest_level;
-       unique_ptr<float[]> dense_flow(new float[level_width * level_height * 3]);
-       glGetTextureImage(prev_level_flow_tex, 0, GL_RGB, GL_FLOAT, level_width * level_height * 3 * sizeof(float), dense_flow.get());
+       unique_ptr<float[]> dense_flow(new float[width1 * height1 * 2]);
+       glGetTextureImage(final_tex, 0, GL_RG, GL_FLOAT, width1 * height1 * 2 * sizeof(float), dense_flow.get());
 
        FILE *fp = fopen("flow.ppm", "wb");
-       fprintf(fp, "P6\n%d %d\n255\n", level_width, level_height);
-       for (unsigned y = 0; y < unsigned(level_height); ++y) {
-               int yy = level_height - y - 1;
-               for (unsigned x = 0; x < unsigned(level_width); ++x) {
-                       float du = dense_flow[(yy * level_width + x) * 3 + 0];
-                       float dv = dense_flow[(yy * level_width + x) * 3 + 1];
-                       float w = dense_flow[(yy * level_width + x) * 3 + 2];
-
-                       du = (du / w) * level_width;
-                       dv = (dv / w) * level_height;
+       FILE *flowfp = fopen("flow.flo", "wb");
+       fprintf(fp, "P6\n%d %d\n255\n", width1, height1);
+       fprintf(flowfp, "FEIH");
+       fwrite(&width1, 4, 1, flowfp);
+       fwrite(&height1, 4, 1, flowfp);
+       for (unsigned y = 0; y < unsigned(height1); ++y) {
+               int yy = height1 - y - 1;
+               for (unsigned x = 0; x < unsigned(width1); ++x) {
+                       float du = dense_flow[(yy * width1 + x) * 2 + 0];
+                       float dv = dense_flow[(yy * width1 + x) * 2 + 1];
+
+                       dv = -dv;
+
+                       fwrite(&du, 4, 1, flowfp);
+                       fwrite(&dv, 4, 1, flowfp);
 
                        uint8_t r, g, b;
                        flow2rgb(du, dv, &r, &g, &b);
@@ -533,6 +1241,7 @@ int main(void)
                }
        }
        fclose(fp);
+       fclose(flowfp);
 
        fprintf(stderr, "err = %d\n", glGetError());
 }