]> git.sesse.net Git - nageru/blobdiff - flow.cpp
16-bit depth should be plenty.
[nageru] / flow.cpp
index feeae6b72095ffefd210093dc9d91b53e7480edf..9d04b0975c813f43b85f9b1f9a5b5ddccd51aa4a 100644 (file)
--- a/flow.cpp
+++ b/flow.cpp
@@ -48,6 +48,8 @@ float vr_alpha = 1.0f, vr_delta = 0.25f, vr_gamma = 0.25f;
 
 bool enable_timing = true;
 bool detailed_timing = false;
+bool enable_warmup = false;
+bool in_warmup = false;
 bool enable_variational_refinement = true;  // Just for debugging.
 bool enable_interpolation = false;
 
@@ -289,23 +291,23 @@ void PersistentFBOSet<num_elements>::render_to(const array<GLuint, num_elements>
 template<size_t num_elements>
 class PersistentFBOSetWithDepth {
 public:
-       void render_to(GLuint depth_tex, const array<GLuint, num_elements> &textures);
+       void render_to(GLuint depth_rb, const array<GLuint, num_elements> &textures);
 
        // Convenience wrappers.
-       void render_to(GLuint depth_tex, GLuint texture0) {
-               render_to(depth_tex, {{texture0}});
+       void render_to(GLuint depth_rb, GLuint texture0) {
+               render_to(depth_rb, {{texture0}});
        }
 
-       void render_to(GLuint depth_tex, GLuint texture0, GLuint texture1) {
-               render_to(depth_tex, {{texture0, texture1}});
+       void render_to(GLuint depth_rb, GLuint texture0, GLuint texture1) {
+               render_to(depth_rb, {{texture0, texture1}});
        }
 
-       void render_to(GLuint depth_tex, GLuint texture0, GLuint texture1, GLuint texture2) {
-               render_to(depth_tex, {{texture0, texture1, texture2}});
+       void render_to(GLuint depth_rb, GLuint texture0, GLuint texture1, GLuint texture2) {
+               render_to(depth_rb, {{texture0, texture1, texture2}});
        }
 
-       void render_to(GLuint depth_tex, GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3) {
-               render_to(depth_tex, {{texture0, texture1, texture2, texture3}});
+       void render_to(GLuint depth_rb, GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3) {
+               render_to(depth_rb, {{texture0, texture1, texture2, texture3}});
        }
 
 private:
@@ -314,9 +316,9 @@ private:
 };
 
 template<size_t num_elements>
-void PersistentFBOSetWithDepth<num_elements>::render_to(GLuint depth_tex, const array<GLuint, num_elements> &textures)
+void PersistentFBOSetWithDepth<num_elements>::render_to(GLuint depth_rb, const array<GLuint, num_elements> &textures)
 {
-       auto key = make_pair(depth_tex, textures);
+       auto key = make_pair(depth_rb, textures);
 
        auto it = fbos.find(key);
        if (it != fbos.end()) {
@@ -327,7 +329,7 @@ void PersistentFBOSetWithDepth<num_elements>::render_to(GLuint depth_tex, const
        GLuint fbo;
        glCreateFramebuffers(1, &fbo);
        GLenum bufs[num_elements];
-       glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
+       glNamedFramebufferRenderbuffer(fbo, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, depth_rb);
        for (size_t i = 0; i < num_elements; ++i) {
                glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0 + i, textures[i], 0);
                bufs[i] = GL_COLOR_ATTACHMENT0 + i;
@@ -379,7 +381,6 @@ void GrayscaleConversion::exec(GLint tex, GLint gray_tex, int width, int height)
        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);
 }
@@ -422,7 +423,6 @@ void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_he
 
        glViewport(0, 0, level_width, level_height);
        fbos.render_to(grad0_tex);
-       glUseProgram(sobel_program);
        glDisable(GL_BLEND);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -440,8 +440,8 @@ private:
        GLuint motion_fs_obj;
        GLuint motion_search_program;
 
-       GLuint uniform_inv_image_size, uniform_inv_prev_level_size;
-       GLuint uniform_image0_tex, uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
+       GLuint uniform_inv_image_size, uniform_inv_prev_level_size, uniform_out_flow_size;
+       GLuint uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
 };
 
 MotionSearch::MotionSearch()
@@ -452,7 +452,7 @@ MotionSearch::MotionSearch()
 
        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_out_flow_size = glGetUniformLocation(motion_search_program, "out_flow_size");
        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");
@@ -462,17 +462,16 @@ void MotionSearch::exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GL
 {
        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_grad0_tex, 2, grad0_tex, nearest_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);
+       glProgramUniform2f(motion_search_program, uniform_out_flow_size, width_patches, height_patches);
 
        glViewport(0, 0, width_patches, height_patches);
        fbos.render_to(flow_out_tex);
-       glUseProgram(motion_search_program);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
 
@@ -625,62 +624,54 @@ void Derivatives::exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, in
        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.
+// Calculate the diffusivity for each pixels, g(x,y). Smoothness (s) will
+// be calculated in the shaders on-the-fly by sampling in-between two
+// neighboring g(x,y) pixels, plus a border tweak to make sure we get
+// zero smoothness at the border.
 //
 // See variational_refinement.txt for more information.
-class ComputeSmoothness {
+class ComputeDiffusivity {
 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, bool zero_diff_flow);
+       ComputeDiffusivity();
+       void exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint diffusivity_tex, int level_width, int level_height, bool zero_diff_flow);
 
 private:
-       PersistentFBOSet<2> fbos;
+       PersistentFBOSet<1> fbos;
 
-       GLuint smoothness_vs_obj;
-       GLuint smoothness_fs_obj;
-       GLuint smoothness_program;
+       GLuint diffusivity_vs_obj;
+       GLuint diffusivity_fs_obj;
+       GLuint diffusivity_program;
 
        GLuint uniform_flow_tex, uniform_diff_flow_tex;
        GLuint uniform_alpha, uniform_zero_diff_flow;
 };
 
-ComputeSmoothness::ComputeSmoothness()
+ComputeDiffusivity::ComputeDiffusivity()
 {
-       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);
-
-       uniform_flow_tex = glGetUniformLocation(smoothness_program, "flow_tex");
-       uniform_diff_flow_tex = glGetUniformLocation(smoothness_program, "diff_flow_tex");
-       uniform_alpha = glGetUniformLocation(smoothness_program, "alpha");
-       uniform_zero_diff_flow = glGetUniformLocation(smoothness_program, "zero_diff_flow");
+       diffusivity_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
+       diffusivity_fs_obj = compile_shader(read_file("diffusivity.frag"), GL_FRAGMENT_SHADER);
+       diffusivity_program = link_program(diffusivity_vs_obj, diffusivity_fs_obj);
+
+       uniform_flow_tex = glGetUniformLocation(diffusivity_program, "flow_tex");
+       uniform_diff_flow_tex = glGetUniformLocation(diffusivity_program, "diff_flow_tex");
+       uniform_alpha = glGetUniformLocation(diffusivity_program, "alpha");
+       uniform_zero_diff_flow = glGetUniformLocation(diffusivity_program, "zero_diff_flow");
 }
 
-void ComputeSmoothness::exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height, bool zero_diff_flow)
+void ComputeDiffusivity::exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint diffusivity_tex, int level_width, int level_height, bool zero_diff_flow)
 {
-       glUseProgram(smoothness_program);
+       glUseProgram(diffusivity_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);
-       glProgramUniform1i(smoothness_program, uniform_zero_diff_flow, zero_diff_flow);
+       bind_sampler(diffusivity_program, uniform_flow_tex, 0, flow_tex, nearest_sampler);
+       bind_sampler(diffusivity_program, uniform_diff_flow_tex, 1, diff_flow_tex, nearest_sampler);
+       glProgramUniform1f(diffusivity_program, uniform_alpha, vr_alpha);
+       glProgramUniform1i(diffusivity_program, uniform_zero_diff_flow, zero_diff_flow);
 
        glViewport(0, 0, level_width, level_height);
 
        glDisable(GL_BLEND);
-       fbos.render_to(smoothness_x_tex, smoothness_y_tex);
+       fbos.render_to(diffusivity_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).
@@ -692,14 +683,23 @@ void ComputeSmoothness::exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoot
 // 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.
+// The equation set is split in two; one contains only the pixels needed for
+// the red pass, and one only for the black pass (see sor.frag). This reduces
+// the amount of data the SOR shader has to pull in, at the cost of some
+// complexity when the equation texture ends up with half the size and we need
+// to adjust texture coordinates.  The contraction is done along the horizontal
+// axis, so that on even rows (0, 2, 4, ...), the “red” texture will contain
+// pixels 0, 2, 4, 6, etc., and on odd rows 1, 3, 5, etc..
+//
+// See variational_refinement.txt for more information about the actual
+// equations in use.
 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, bool zero_diff_flow);
+       void exec(GLuint I_x_y_tex, GLuint I_t_tex, GLuint diff_flow_tex, GLuint flow_tex, GLuint beta_0_tex, GLuint diffusivity_tex, GLuint equation_red_tex, GLuint equation_black_tex, int level_width, int level_height, bool zero_diff_flow);
 
 private:
-       PersistentFBOSet<1> fbos;
+       PersistentFBOSet<2> fbos;
 
        GLuint equations_vs_obj;
        GLuint equations_fs_obj;
@@ -708,13 +708,13 @@ private:
        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_diffusivity_tex;
        GLuint uniform_gamma, uniform_delta, uniform_zero_diff_flow;
 };
 
 SetupEquations::SetupEquations()
 {
-       equations_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
+       equations_vs_obj = compile_shader(read_file("equations.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);
 
@@ -723,14 +723,13 @@ SetupEquations::SetupEquations()
        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_diffusivity_tex = glGetUniformLocation(equations_program, "diffusivity_tex");
        uniform_gamma = glGetUniformLocation(equations_program, "gamma");
        uniform_delta = glGetUniformLocation(equations_program, "delta");
        uniform_zero_diff_flow = glGetUniformLocation(equations_program, "zero_diff_flow");
 }
 
-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, bool zero_diff_flow)
+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 diffusivity_tex, GLuint equation_red_tex, GLuint equation_black_tex, int level_width, int level_height, bool zero_diff_flow)
 {
        glUseProgram(equations_program);
 
@@ -739,15 +738,14 @@ void SetupEquations::exec(GLuint I_x_y_tex, GLuint I_t_tex, GLuint diff_flow_tex
        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);
+       bind_sampler(equations_program, uniform_diffusivity_tex, 5, diffusivity_tex, zero_border_sampler);
        glProgramUniform1f(equations_program, uniform_delta, vr_delta);
        glProgramUniform1f(equations_program, uniform_gamma, vr_gamma);
        glProgramUniform1i(equations_program, uniform_zero_diff_flow, zero_diff_flow);
 
-       glViewport(0, 0, level_width, level_height);
+       glViewport(0, 0, (level_width + 1) / 2, level_height);
        glDisable(GL_BLEND);
-       fbos.render_to(equation_tex);
+       fbos.render_to({equation_red_tex, equation_black_tex});
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
 
@@ -758,7 +756,7 @@ void SetupEquations::exec(GLuint I_x_y_tex, GLuint I_t_tex, GLuint diff_flow_tex
 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, bool zero_diff_flow, ScopedTimer *sor_timer);
+       void exec(GLuint diff_flow_tex, GLuint equation_red_tex, GLuint equation_black_tex, GLuint diffusivity_tex, int level_width, int level_height, int num_iterations, bool zero_diff_flow, ScopedTimer *sor_timer);
 
 private:
        PersistentFBOSet<1> fbos;
@@ -768,9 +766,9 @@ private:
        GLuint sor_program;
 
        GLuint uniform_diff_flow_tex;
-       GLuint uniform_equation_tex;
-       GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
-       GLuint uniform_phase, uniform_zero_diff_flow;
+       GLuint uniform_equation_red_tex, uniform_equation_black_tex;
+       GLuint uniform_diffusivity_tex;
+       GLuint uniform_phase, uniform_num_nonzero_phases;
 };
 
 SOR::SOR()
@@ -780,23 +778,25 @@ SOR::SOR()
        sor_program = link_program(sor_vs_obj, sor_fs_obj);
 
        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_equation_red_tex = glGetUniformLocation(sor_program, "equation_red_tex");
+       uniform_equation_black_tex = glGetUniformLocation(sor_program, "equation_black_tex");
+       uniform_diffusivity_tex = glGetUniformLocation(sor_program, "diffusivity_tex");
        uniform_phase = glGetUniformLocation(sor_program, "phase");
-       uniform_zero_diff_flow = glGetUniformLocation(sor_program, "zero_diff_flow");
+       uniform_num_nonzero_phases = glGetUniformLocation(sor_program, "num_nonzero_phases");
 }
 
-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, bool zero_diff_flow, ScopedTimer *sor_timer)
+void SOR::exec(GLuint diff_flow_tex, GLuint equation_red_tex, GLuint equation_black_tex, GLuint diffusivity_tex, int level_width, int level_height, int num_iterations, bool zero_diff_flow, ScopedTimer *sor_timer)
 {
        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);
+       bind_sampler(sor_program, uniform_diffusivity_tex, 1, diffusivity_tex, zero_border_sampler);
+       bind_sampler(sor_program, uniform_equation_red_tex, 2, equation_red_tex, nearest_sampler);
+       bind_sampler(sor_program, uniform_equation_black_tex, 3, equation_black_tex, nearest_sampler);
 
-       glProgramUniform1i(sor_program, uniform_zero_diff_flow, zero_diff_flow);
+       if (!zero_diff_flow) {
+               glProgramUniform1i(sor_program, uniform_num_nonzero_phases, 2);
+       }
 
        // 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
@@ -809,6 +809,9 @@ void SOR::exec(GLuint diff_flow_tex, GLuint equation_tex, GLuint smoothness_x_te
        for (int i = 0; i < num_iterations; ++i) {
                {
                        ScopedTimer timer("Red pass", sor_timer);
+                       if (zero_diff_flow && i == 0) {
+                               glProgramUniform1i(sor_program, uniform_num_nonzero_phases, 0);
+                       }
                        glProgramUniform1i(sor_program, uniform_phase, 0);
                        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
                        glTextureBarrier();
@@ -816,11 +819,13 @@ void SOR::exec(GLuint diff_flow_tex, GLuint equation_tex, GLuint smoothness_x_te
                {
                        ScopedTimer timer("Black pass", sor_timer);
                        if (zero_diff_flow && i == 0) {
-                               // Not zero anymore.
-                               glProgramUniform1i(sor_program, uniform_zero_diff_flow, 0);
+                               glProgramUniform1i(sor_program, uniform_num_nonzero_phases, 1);
                        }
                        glProgramUniform1i(sor_program, uniform_phase, 1);
                        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
+                       if (zero_diff_flow && i == 0) {
+                               glProgramUniform1i(sor_program, uniform_num_nonzero_phases, 2);
+                       }
                        if (i != num_iterations - 1) {
                                glTextureBarrier();
                        }
@@ -914,6 +919,8 @@ class TexturePool {
 public:
        GLuint get_texture(GLenum format, GLuint width, GLuint height);
        void release_texture(GLuint tex_num);
+       GLuint get_renderbuffer(GLenum format, GLuint width, GLuint height);
+       void release_renderbuffer(GLuint tex_num);
 
 private:
        struct Texture {
@@ -921,6 +928,7 @@ private:
                GLenum format;
                GLuint width, height;
                bool in_use = false;
+               bool is_renderbuffer = false;
        };
        vector<Texture> textures;
 };
@@ -954,7 +962,7 @@ private:
        Densify densify;
        Prewarp prewarp;
        Derivatives derivatives;
-       ComputeSmoothness compute_smoothness;
+       ComputeDiffusivity compute_diffusivity;
        SetupEquations setup_equations;
        SOR sor;
        AddBaseFlow add_base_flow;
@@ -982,11 +990,11 @@ DISComputeFlow::DISComputeFlow(int width, int height)
        // 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_MIN_FILTER, GL_LINEAR);
+       glSamplerParameteri(zero_border_sampler, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
        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 };
+       float zero[] = { 0.0f, 0.0f, 0.0f, 0.0f };  // Note that zero alpha means we can also see whether we sampled outside the border or not.
        glSamplerParameterfv(zero_border_sampler, GL_TEXTURE_BORDER_COLOR, zero);
 
        // Initial flow is zero, 1x1.
@@ -1022,7 +1030,7 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
 
        glBindVertexArray(vao);
 
-       ScopedTimer total_timer("Total", &timers);
+       ScopedTimer total_timer("Compute flow", &timers);
        for (int level = coarsest_level; level >= int(finest_level); --level) {
                char timer_name[256];
                snprintf(timer_name, sizeof(timer_name), "Level %d (%d x %d)", level, width >> level, height >> level);
@@ -1050,7 +1058,7 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
 
                // 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);
+               GLuint grad0_tex = pool.get_texture(GL_R32UI, level_width, level_height);
 
                // Find the derivative.
                {
@@ -1120,44 +1128,42 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
                // We need somewhere to store du and dv (the flow increment, relative
                // to the non-refined base flow u0 and v0). It's initially garbage,
                // but not read until we've written something sane to it.
-               GLuint du_dv_tex = pool.get_texture(GL_RG16F, level_width, level_height);
+               GLuint diff_flow_tex = pool.get_texture(GL_RG16F, level_width, level_height);
 
-               // 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 for diffusivity.
+               GLuint diffusivity_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);
+               GLuint equation_red_tex = pool.get_texture(GL_RGBA32UI, (level_width + 1) / 2, level_height);
+               GLuint equation_black_tex = pool.get_texture(GL_RGBA32UI, (level_width + 1) / 2, 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.
+                       // Calculate the diffusivity term for each pixel.
                        {
-                               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, outer_idx == 0);
+                               ScopedTimer timer("Compute diffusivity", &varref_timer);
+                               compute_diffusivity.exec(base_flow_tex, diff_flow_tex, diffusivity_tex, level_width, level_height, outer_idx == 0);
                        }
 
                        // 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, outer_idx == 0);
+                               setup_equations.exec(I_x_y_tex, I_t_tex, diff_flow_tex, base_flow_tex, beta_0_tex, diffusivity_tex, equation_red_tex, equation_black_tex, level_width, level_height, outer_idx == 0);
                        }
 
-                       // Run a few SOR (or quasi-SOR, since we're not really Jacobi) iterations.
-                       // Note that these are to/from the same texture.
+                       // Run a few SOR 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, outer_idx == 0, &timer);
+                               sor.exec(diff_flow_tex, equation_red_tex, equation_black_tex, diffusivity_tex, level_width, level_height, 5, outer_idx == 0, &timer);
                        }
                }
 
                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);
+               pool.release_texture(diffusivity_tex);
+               pool.release_texture(equation_red_tex);
+               pool.release_texture(equation_black_tex);
 
                // Add the differential flow found by the variational refinement to the base flow,
                // giving the final flow estimate for this level.
@@ -1167,9 +1173,9 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
                // 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);
+                       add_base_flow.exec(base_flow_tex, diff_flow_tex, level_width, level_height);
                }
-               pool.release_texture(du_dv_tex);
+               pool.release_texture(diff_flow_tex);
 
                if (prev_level_flow_tex != initial_flow_tex) {
                        pool.release_texture(prev_level_flow_tex);
@@ -1180,7 +1186,9 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
        }
        total_timer.end();
 
-       timers.print();
+       if (!in_warmup) {
+               timers.print();
+       }
 
        // Scale up the flow to the final size (if needed).
        if (finest_level == 0 || resize_strategy == DO_NOT_RESIZE_FLOW) {
@@ -1200,7 +1208,7 @@ 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);
+       void exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint flow_tex, GLuint depth_rb, int width, int height, float alpha);
 
 private:
        PersistentFBOSetWithDepth<1> fbos;
@@ -1229,7 +1237,7 @@ Splat::Splat()
        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)
+void Splat::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint flow_tex, GLuint depth_rb, int width, int height, float alpha)
 {
        glUseProgram(splat_program);
 
@@ -1250,7 +1258,7 @@ void Splat::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backw
        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.)
 
-       fbos.render_to(depth_tex, flow_tex);
+       fbos.render_to(depth_rb, flow_tex);
 
        // Evidently NVIDIA doesn't use fast clears for glClearTexImage, so clear now that
        // we've got it bound.
@@ -1291,7 +1299,7 @@ public:
        // 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);
+       void exec(GLuint flow_tex, GLuint depth_rb, GLuint temp_tex[3], int width, int height);
 
 private:
        PersistentFBOSetWithDepth<1> fbos;
@@ -1315,7 +1323,7 @@ HoleFill::HoleFill()
        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)
+void HoleFill::exec(GLuint flow_tex, GLuint depth_rb, GLuint temp_tex[3], int width, int height)
 {
        glUseProgram(fill_program);
 
@@ -1328,7 +1336,7 @@ void HoleFill::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int w
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);  // Only update the values > 0.999f (ie., only invalid pixels).
 
-       fbos.render_to(depth_tex, flow_tex);  // NOTE: Reading and writing to the same texture.
+       fbos.render_to(depth_rb, flow_tex);  // NOTE: Reading and writing to the same texture.
 
        // Fill holes from the left, by shifting 1, 2, 4, 8, etc. pixels to the right.
        for (int offs = 1; offs < width; offs *= 2) {
@@ -1374,7 +1382,7 @@ class HoleBlend {
 public:
        HoleBlend();
 
-       void exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height);
+       void exec(GLuint flow_tex, GLuint depth_rb, GLuint temp_tex[3], int width, int height);
 
 private:
        PersistentFBOSetWithDepth<1> fbos;
@@ -1401,7 +1409,7 @@ HoleBlend::HoleBlend()
        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)
+void HoleBlend::exec(GLuint flow_tex, GLuint depth_rb, GLuint temp_tex[3], int width, int height)
 {
        glUseProgram(blend_program);
 
@@ -1418,7 +1426,7 @@ void HoleBlend::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LEQUAL);  // Skip over all of the pixels that were never holes to begin with.
 
-       fbos.render_to(depth_tex, flow_tex);  // NOTE: Reading and writing to the same texture.
+       fbos.render_to(depth_rb, flow_tex);  // NOTE: Reading and writing to the same texture.
 
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 
@@ -1463,7 +1471,6 @@ void Blend::exec(GLuint tex0, GLuint tex1, GLuint flow_tex, GLuint output_tex, i
 
        glViewport(0, 0, level_width, level_height);
        fbos.render_to(output_tex);
-       glUseProgram(blend_program);
        glDisable(GL_BLEND);  // A bit ironic, perhaps.
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -1517,7 +1524,7 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
 {
        GPUTimers timers;
 
-       ScopedTimer total_timer("Total", &timers);
+       ScopedTimer total_timer("Interpolate", &timers);
 
        glBindVertexArray(vao);
 
@@ -1532,11 +1539,11 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
        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.
+       GLuint depth_rb = pool.get_renderbuffer(GL_DEPTH_COMPONENT16, flow_width, flow_height);  // Used for ranking flows.
 
        {
                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);
+               splat.exec(tex0_view, tex1_view, forward_flow_tex, backward_flow_tex, flow_tex, depth_rb, flow_width, flow_height, alpha);
        }
        glDeleteTextures(1, &tex0_view);
        glDeleteTextures(1, &tex1_view);
@@ -1548,22 +1555,25 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
 
        {
                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);
+               hole_fill.exec(flow_tex, depth_rb, temp_tex, flow_width, flow_height);
+               hole_blend.exec(flow_tex, depth_rb, 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);
+       pool.release_renderbuffer(depth_rb);
 
        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);
        }
+       pool.release_texture(flow_tex);
        total_timer.end();
-       timers.print();
+       if (!in_warmup) {
+               timers.print();
+       }
 
        return output_tex;
 }
@@ -1571,7 +1581,7 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
 GLuint TexturePool::get_texture(GLenum format, GLuint width, GLuint height)
 {
        for (Texture &tex : textures) {
-               if (!tex.in_use && tex.format == format &&
+               if (!tex.in_use && !tex.is_renderbuffer && tex.format == format &&
                    tex.width == width && tex.height == height) {
                        tex.in_use = true;
                        return tex.tex_num;
@@ -1585,6 +1595,30 @@ GLuint TexturePool::get_texture(GLenum format, GLuint width, GLuint height)
        tex.width = width;
        tex.height = height;
        tex.in_use = true;
+       tex.is_renderbuffer = false;
+       textures.push_back(tex);
+       return tex.tex_num;
+}
+
+GLuint TexturePool::get_renderbuffer(GLenum format, GLuint width, GLuint height)
+{
+       for (Texture &tex : textures) {
+               if (!tex.in_use && tex.is_renderbuffer && tex.format == format &&
+                   tex.width == width && tex.height == height) {
+                       tex.in_use = true;
+                       return tex.tex_num;
+               }
+       }
+
+       Texture tex;
+       glCreateRenderbuffers(1, &tex.tex_num);
+       glNamedRenderbufferStorage(tex.tex_num, format, width, height);
+
+       tex.format = format;
+       tex.width = width;
+       tex.height = height;
+       tex.in_use = true;
+       tex.is_renderbuffer = true;
        textures.push_back(tex);
        return tex.tex_num;
 }
@@ -1592,7 +1626,19 @@ GLuint TexturePool::get_texture(GLenum format, GLuint width, GLuint height)
 void TexturePool::release_texture(GLuint tex_num)
 {
        for (Texture &tex : textures) {
-               if (tex.tex_num == tex_num) {
+               if (!tex.is_renderbuffer && tex.tex_num == tex_num) {
+                       assert(tex.in_use);
+                       tex.in_use = false;
+                       return;
+               }
+       }
+       assert(false);
+}
+
+void TexturePool::release_renderbuffer(GLuint tex_num)
+{
+       for (Texture &tex : textures) {
+               if (tex.is_renderbuffer && tex.tex_num == tex_num) {
                        assert(tex.in_use);
                        tex.in_use = false;
                        return;
@@ -1768,6 +1814,16 @@ void compute_flow_only(int argc, char **argv, int optind)
        glGenerateTextureMipmap(tex1_gray);
 
        DISComputeFlow compute_flow(width1, height1);
+
+       if (enable_warmup) {
+               in_warmup = true;
+               for (int i = 0; i < 10; ++i) {
+                       GLuint final_tex = compute_flow.exec(tex0_gray, tex1_gray, DISComputeFlow::RESIZE_FLOW_TO_FULL_SIZE);
+                       compute_flow.release_texture(final_tex);
+               }
+               in_warmup = false;
+       }
+
        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");
@@ -1862,6 +1918,19 @@ void interpolate_image(int argc, char **argv, int optind)
        gray.exec(tex1, tex1_gray, width1, height1);
        glGenerateTextureMipmap(tex1_gray);
 
+       if (enable_warmup) {
+               in_warmup = true;
+               for (int i = 0; i < 10; ++i) {
+                       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);
+                       GLuint interpolated_tex = interpolate.exec(tex0, tex1, forward_flow_tex, backward_flow_tex, width1, height1, 0.5f);
+                       compute_flow.release_texture(forward_flow_tex);
+                       compute_flow.release_texture(backward_flow_tex);
+                       interpolate.release_texture(interpolated_tex);
+               }
+               in_warmup = false;
+       }
+
        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);
 
@@ -1890,7 +1959,8 @@ int main(int argc, char **argv)
                { "disable-timing", no_argument, 0, 1000 },
                { "detailed-timing", no_argument, 0, 1003 },
                { "ignore-variational-refinement", no_argument, 0, 1001 },  // Still calculates it, just doesn't apply it.
-               { "interpolate", no_argument, 0, 1002 }
+               { "interpolate", no_argument, 0, 1002 },
+               { "warmup", no_argument, 0, 1004 }
        };
 
        for ( ;; ) {
@@ -1922,6 +1992,9 @@ int main(int argc, char **argv)
                case 1003:
                        detailed_timing = true;
                        break;
+               case 1004:
+                       enable_warmup = true;
+                       break;
                default:
                        fprintf(stderr, "Unknown option '%s'\n", argv[option_index]);
                        exit(1);