]> git.sesse.net Git - nageru/blobdiff - flow.cpp
Rename “Total” to something more descriptive.
[nageru] / flow.cpp
index bb0c096ae82be72cc9d7eb2154ff4ff357d0a78b..0cef41dcdce0b23775a17f047b6c54cffab5ad25 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;
 
@@ -222,32 +224,6 @@ GLuint link_program(GLuint vs_obj, GLuint fs_obj)
        return program;
 }
 
-GLuint generate_vbo(GLint size, GLsizeiptr data_size, const GLvoid *data)
-{
-       GLuint vbo;
-       glCreateBuffers(1, &vbo);
-       glBufferData(GL_ARRAY_BUFFER, data_size, data, GL_STATIC_DRAW);
-       glNamedBufferData(vbo, data_size, data, GL_STATIC_DRAW);
-       return vbo;
-}
-
-GLuint fill_vertex_attribute(GLuint vao, GLuint glsl_program_num, const string &attribute_name, GLint size, GLenum type, GLsizeiptr data_size, const GLvoid *data)
-{
-       int attrib = glGetAttribLocation(glsl_program_num, attribute_name.c_str());
-       if (attrib == -1) {
-               return -1;
-       }
-
-       GLuint vbo = generate_vbo(size, data_size, data);
-
-       glBindBuffer(GL_ARRAY_BUFFER, vbo);
-       glEnableVertexArrayAttrib(vao, attrib);
-       glVertexAttribPointer(attrib, size, type, GL_FALSE, 0, BUFFER_OFFSET(0));
-       glBindBuffer(GL_ARRAY_BUFFER, 0);
-
-       return vbo;
-}
-
 void bind_sampler(GLuint program, GLint location, GLuint texture_unit, GLuint tex, GLuint sampler)
 {
        if (location == -1) {
@@ -268,19 +244,19 @@ public:
        void render_to(const array<GLuint, num_elements> &textures);
 
        // Convenience wrappers.
-       void render_to(GLuint texture0, enable_if<num_elements == 1> * = nullptr) {
+       void render_to(GLuint texture0) {
                render_to({{texture0}});
        }
 
-       void render_to(GLuint texture0, GLuint texture1, enable_if<num_elements == 2> * = nullptr) {
+       void render_to(GLuint texture0, GLuint texture1) {
                render_to({{texture0, texture1}});
        }
 
-       void render_to(GLuint texture0, GLuint texture1, GLuint texture2, enable_if<num_elements == 3> * = nullptr) {
+       void render_to(GLuint texture0, GLuint texture1, GLuint texture2) {
                render_to({{texture0, texture1, texture2}});
        }
 
-       void render_to(GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3, enable_if<num_elements == 4> * = nullptr) {
+       void render_to(GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3) {
                render_to({{texture0, texture1, texture2, texture3}});
        }
 
@@ -311,6 +287,59 @@ void PersistentFBOSet<num_elements>::render_to(const array<GLuint, num_elements>
        glBindFramebuffer(GL_FRAMEBUFFER, fbo);
 }
 
+// Same, but with a depth texture.
+template<size_t num_elements>
+class PersistentFBOSetWithDepth {
+public:
+       void render_to(GLuint depth_tex, 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_tex, GLuint texture0, GLuint texture1) {
+               render_to(depth_tex, {{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_tex, GLuint texture0, GLuint texture1, GLuint texture2, GLuint texture3) {
+               render_to(depth_tex, {{texture0, texture1, texture2, texture3}});
+       }
+
+private:
+       // TODO: Delete these on destruction.
+       map<pair<GLuint, array<GLuint, num_elements>>, GLuint> fbos;
+};
+
+template<size_t num_elements>
+void PersistentFBOSetWithDepth<num_elements>::render_to(GLuint depth_tex, const array<GLuint, num_elements> &textures)
+{
+       auto key = make_pair(depth_tex, textures);
+
+       auto it = fbos.find(key);
+       if (it != fbos.end()) {
+               glBindFramebuffer(GL_FRAMEBUFFER, it->second);
+               return;
+       }
+
+       GLuint fbo;
+       glCreateFramebuffers(1, &fbo);
+       GLenum bufs[num_elements];
+       glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
+       for (size_t i = 0; i < num_elements; ++i) {
+               glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0 + i, textures[i], 0);
+               bufs[i] = GL_COLOR_ATTACHMENT0 + i;
+       }
+       glNamedFramebufferDrawBuffers(fbo, num_elements, bufs);
+
+       fbos[key] = fbo;
+       glBindFramebuffer(GL_FRAMEBUFFER, fbo);
+}
+
 // Convert RGB to grayscale, using Rec. 709 coefficients.
 class GrayscaleConversion {
 public:
@@ -352,7 +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);
 }
@@ -375,7 +403,6 @@ private:
        GLuint sobel_vs_obj;
        GLuint sobel_fs_obj;
        GLuint sobel_program;
-       GLuint sobel_vao;
 
        GLuint uniform_tex;
 };
@@ -386,14 +413,6 @@ Sobel::Sobel()
        sobel_fs_obj = compile_shader(read_file("sobel.frag"), GL_FRAGMENT_SHADER);
        sobel_program = link_program(sobel_vs_obj, sobel_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &sobel_vao);
-       glBindVertexArray(sobel_vao);
-
-       GLint position_attrib = glGetAttribLocation(sobel_program, "position");
-       glEnableVertexArrayAttrib(sobel_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_tex = glGetUniformLocation(sobel_program, "tex");
 }
 
@@ -404,8 +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);
-       glBindVertexArray(sobel_vao);
-       glUseProgram(sobel_program);
        glDisable(GL_BLEND);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -422,10 +439,9 @@ private:
        GLuint motion_vs_obj;
        GLuint motion_fs_obj;
        GLuint motion_search_program;
-       GLuint motion_search_vao;
 
-       GLuint uniform_inv_image_size, uniform_inv_prev_level_size;
-       GLuint uniform_image0_tex, uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
+       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()
@@ -434,18 +450,9 @@ MotionSearch::MotionSearch()
        motion_fs_obj = compile_shader(read_file("motion_search.frag"), GL_FRAGMENT_SHADER);
        motion_search_program = link_program(motion_vs_obj, motion_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &motion_search_vao);
-       glBindVertexArray(motion_search_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(motion_search_program, "position");
-       glEnableVertexArrayAttrib(motion_search_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_inv_image_size = glGetUniformLocation(motion_search_program, "inv_image_size");
        uniform_inv_prev_level_size = glGetUniformLocation(motion_search_program, "inv_prev_level_size");
-       uniform_image0_tex = glGetUniformLocation(motion_search_program, "image0_tex");
+       uniform_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");
@@ -455,18 +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);
-       glBindVertexArray(motion_search_vao);
-       glUseProgram(motion_search_program);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
 
@@ -489,7 +494,6 @@ private:
        GLuint densify_vs_obj;
        GLuint densify_fs_obj;
        GLuint densify_program;
-       GLuint densify_vao;
 
        GLuint uniform_patch_size;
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
@@ -501,15 +505,6 @@ Densify::Densify()
        densify_fs_obj = compile_shader(read_file("densify.frag"), GL_FRAGMENT_SHADER);
        densify_program = link_program(densify_vs_obj, densify_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &densify_vao);
-       glBindVertexArray(densify_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(densify_program, "position");
-       glEnableVertexArrayAttrib(densify_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_patch_size = glGetUniformLocation(densify_program, "patch_size");
        uniform_image0_tex = glGetUniformLocation(densify_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(densify_program, "image1_tex");
@@ -531,8 +526,9 @@ 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);
        fbos.render_to(dense_flow_tex);
+       glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
+       glClear(GL_COLOR_BUFFER_BIT);
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width_patches * height_patches);
 }
 
@@ -555,7 +551,6 @@ 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;
 };
@@ -566,15 +561,6 @@ Prewarp::Prewarp()
        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");
@@ -590,7 +576,6 @@ void Prewarp::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint I
 
        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
-       glBindVertexArray(prewarp_vao);
        fbos.render_to(I_tex, I_t_tex, normalized_flow_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -614,7 +599,6 @@ private:
        GLuint derivatives_vs_obj;
        GLuint derivatives_fs_obj;
        GLuint derivatives_program;
-       GLuint derivatives_vao;
 
        GLuint uniform_tex;
 };
@@ -625,15 +609,6 @@ Derivatives::Derivatives()
        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");
 }
 
@@ -645,76 +620,58 @@ void Derivatives::exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, in
 
        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
-       glBindVertexArray(derivatives_vao);
        fbos.render_to(I_x_y_tex, beta_0_tex);
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
 
-// Calculate the smoothness constraints between neighboring pixels;
-// s_x(x,y) stores smoothness between pixel (x,y) and (x+1,y),
-// and s_y(x,y) stores between (x,y) and (x,y+1). We'll sample with
-// border color (0,0) later, so that there's zero diffusion out of
-// the border.
+// 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);
+       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 smoothness_vao;
+       GLuint diffusivity_vs_obj;
+       GLuint diffusivity_fs_obj;
+       GLuint diffusivity_program;
 
        GLuint uniform_flow_tex, uniform_diff_flow_tex;
-       GLuint uniform_alpha;
+       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);
-
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &smoothness_vao);
-       glBindVertexArray(smoothness_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(smoothness_program, "position");
-       glEnableVertexArrayAttrib(smoothness_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
-       uniform_flow_tex = glGetUniformLocation(smoothness_program, "flow_tex");
-       uniform_diff_flow_tex = glGetUniformLocation(smoothness_program, "diff_flow_tex");
-       uniform_alpha = glGetUniformLocation(smoothness_program, "alpha");
+       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)
+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);
+       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);
-       glBindVertexArray(smoothness_vao);
-       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).
@@ -726,54 +683,53 @@ 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);
+       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;
        GLuint equations_program;
-       GLuint equations_vao;
 
        GLuint uniform_I_x_y_tex, uniform_I_t_tex;
        GLuint uniform_diff_flow_tex, uniform_base_flow_tex;
        GLuint uniform_beta_0_tex;
-       GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
-       GLuint uniform_gamma, uniform_delta;
+       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);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &equations_vao);
-       glBindVertexArray(equations_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(equations_program, "position");
-       glEnableVertexArrayAttrib(equations_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_I_x_y_tex = glGetUniformLocation(equations_program, "I_x_y_tex");
        uniform_I_t_tex = glGetUniformLocation(equations_program, "I_t_tex");
        uniform_diff_flow_tex = glGetUniformLocation(equations_program, "diff_flow_tex");
        uniform_base_flow_tex = glGetUniformLocation(equations_program, "base_flow_tex");
        uniform_beta_0_tex = glGetUniformLocation(equations_program, "beta_0_tex");
-       uniform_smoothness_x_tex = glGetUniformLocation(equations_program, "smoothness_x_tex");
-       uniform_smoothness_y_tex = glGetUniformLocation(equations_program, "smoothness_y_tex");
+       uniform_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)
+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);
 
@@ -782,15 +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);
-       glBindVertexArray(equations_vao);
-       fbos.render_to(equation_tex);
+       fbos.render_to({equation_red_tex, equation_black_tex});
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
 
@@ -801,7 +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, 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;
@@ -809,12 +764,11 @@ 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;
-       GLuint uniform_phase;
+       GLuint uniform_equation_red_tex, uniform_equation_black_tex;
+       GLuint uniform_diffusivity_tex;
+       GLuint uniform_phase, uniform_num_nonzero_phases;
 };
 
 SOR::SOR()
@@ -823,30 +777,26 @@ SOR::SOR()
        sor_fs_obj = compile_shader(read_file("sor.frag"), GL_FRAGMENT_SHADER);
        sor_program = link_program(sor_vs_obj, sor_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &sor_vao);
-       glBindVertexArray(sor_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(sor_program, "position");
-       glEnableVertexArrayAttrib(sor_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_diff_flow_tex = glGetUniformLocation(sor_program, "diff_flow_tex");
-       uniform_equation_tex = glGetUniformLocation(sor_program, "equation_tex");
-       uniform_smoothness_x_tex = glGetUniformLocation(sor_program, "smoothness_x_tex");
-       uniform_smoothness_y_tex = glGetUniformLocation(sor_program, "smoothness_y_tex");
+       uniform_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_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, 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);
+
+       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
@@ -854,20 +804,28 @@ void SOR::exec(GLuint diff_flow_tex, GLuint equation_tex, GLuint smoothness_x_te
        // as per the spec.
        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
-       glBindVertexArray(sor_vao);
        fbos.render_to(diff_flow_tex);
 
        for (int i = 0; i < num_iterations; ++i) {
                {
                        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();
                }
                {
                        ScopedTimer timer("Black pass", sor_timer);
+                       if (zero_diff_flow && i == 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();
                        }
@@ -888,7 +846,6 @@ private:
        GLuint add_flow_vs_obj;
        GLuint add_flow_fs_obj;
        GLuint add_flow_program;
-       GLuint add_flow_vao;
 
        GLuint uniform_diff_flow_tex;
 };
@@ -899,15 +856,6 @@ AddBaseFlow::AddBaseFlow()
        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");
 }
 
@@ -920,7 +868,6 @@ void AddBaseFlow::exec(GLuint base_flow_tex, GLuint diff_flow_tex, int level_wid
        glViewport(0, 0, level_width, level_height);
        glEnable(GL_BLEND);
        glBlendFunc(GL_ONE, GL_ONE);
-       glBindVertexArray(add_flow_vao);
        fbos.render_to(base_flow_tex);
 
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
@@ -938,7 +885,6 @@ 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;
@@ -950,15 +896,6 @@ ResizeFlow::ResizeFlow()
        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");
 }
@@ -973,7 +910,6 @@ void ResizeFlow::exec(GLuint flow_tex, GLuint out_tex, int input_width, int inpu
 
        glViewport(0, 0, output_width, output_height);
        glDisable(GL_BLEND);
-       glBindVertexArray(resize_flow_vao);
        fbos.render_to(out_tex);
 
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
@@ -1014,6 +950,7 @@ public:
 private:
        int width, height;
        GLuint initial_flow_tex;
+       GLuint vertex_vbo, vao;
        TexturePool pool;
 
        // The various passes.
@@ -1022,7 +959,7 @@ private:
        Densify densify;
        Prewarp prewarp;
        Derivatives derivatives;
-       ComputeSmoothness compute_smoothness;
+       ComputeDiffusivity compute_diffusivity;
        SetupEquations setup_equations;
        SOR sor;
        AddBaseFlow add_base_flow;
@@ -1050,17 +987,35 @@ 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.
        glCreateTextures(GL_TEXTURE_2D, 1, &initial_flow_tex);
        glTextureStorage2D(initial_flow_tex, 1, GL_RG16F, 1, 1);
        glClearTexImage(initial_flow_tex, 0, GL_RG, GL_FLOAT, nullptr);
+
+       // Set up the vertex data that will be shared between all passes.
+       float vertices[] = {
+               0.0f, 1.0f,
+               0.0f, 0.0f,
+               1.0f, 1.0f,
+               1.0f, 0.0f,
+       };
+       glCreateBuffers(1, &vertex_vbo);
+       glNamedBufferData(vertex_vbo, sizeof(vertices), vertices, GL_STATIC_DRAW);
+
+       glCreateVertexArrays(1, &vao);
+       glBindVertexArray(vao);
+       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
+
+       GLint position_attrib = 0;  // Hard-coded in every vertex shader.
+       glEnableVertexArrayAttrib(vao, position_attrib);
+       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 }
 
 GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_strategy)
@@ -1070,7 +1025,9 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
 
        GPUTimers timers;
 
-       ScopedTimer total_timer("Total", &timers);
+       glBindVertexArray(vao);
+
+       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);
@@ -1098,7 +1055,7 @@ 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.
                {
@@ -1121,9 +1078,8 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
 
                // Densification.
 
-               // Set up an output texture (initially zero).
+               // Set up an output texture (cleared in Densify).
                GLuint dense_flow_tex = pool.get_texture(GL_RGB16F, level_width, level_height);
-               glClearTexImage(dense_flow_tex, 0, GL_RGB, GL_FLOAT, nullptr);
 
                // And draw.
                {
@@ -1167,46 +1123,44 @@ GLuint DISComputeFlow::exec(GLuint tex0, GLuint tex1, ResizeStrategy resize_stra
                pool.release_texture(I_tex);
 
                // We need somewhere to store du and dv (the flow increment, relative
-               // to the non-refined base flow u0 and v0). It starts at zero.
-               GLuint du_dv_tex = pool.get_texture(GL_RG16F, level_width, level_height);
-               glClearTexImage(du_dv_tex, 0, GL_RG, GL_FLOAT, nullptr);
+               // 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 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);
+                               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);
+                               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, &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.
@@ -1216,9 +1170,9 @@ 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);
@@ -1229,7 +1183,9 @@ 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) {
@@ -1252,12 +1208,11 @@ public:
        void exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint flow_tex, GLuint depth_tex, int width, int height, float alpha);
 
 private:
-       PersistentFBOSet<2> fbos;
+       PersistentFBOSetWithDepth<1> fbos;
 
        GLuint splat_vs_obj;
        GLuint splat_fs_obj;
        GLuint splat_program;
-       GLuint splat_vao;
 
        GLuint uniform_invert_flow, uniform_splat_size, uniform_alpha;
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
@@ -1270,15 +1225,6 @@ Splat::Splat()
        splat_fs_obj = compile_shader(read_file("splat.frag"), GL_FRAGMENT_SHADER);
        splat_program = link_program(splat_vs_obj, splat_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &splat_vao);
-       glBindVertexArray(splat_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(splat_program, "position");
-       glEnableVertexArrayAttrib(splat_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_invert_flow = glGetUniformLocation(splat_program, "invert_flow");
        uniform_splat_size = glGetUniformLocation(splat_program, "splat_size");
        uniform_alpha = glGetUniformLocation(splat_program, "alpha");
@@ -1308,14 +1254,14 @@ void Splat::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backw
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);  // We store the difference between I_0 and I_1, where less difference is good. (Default 1.0 is effectively +inf, which always loses.)
-       glBindVertexArray(splat_vao);
 
-       // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
-       GLuint fbo;
-       glCreateFramebuffers(1, &fbo);
-       glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);
-       glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
-       glBindFramebuffer(GL_FRAMEBUFFER, fbo);
+       fbos.render_to(depth_tex, flow_tex);
+
+       // Evidently NVIDIA doesn't use fast clears for glClearTexImage, so clear now that
+       // we've got it bound.
+       glClearColor(1000.0f, 1000.0f, 0.0f, 1.0f);  // Invalid flow.
+       glClearDepth(1.0f);  // Effectively infinity.
+       glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
 
        // Do forward splatting.
        bind_sampler(splat_program, uniform_flow_tex, 2, forward_flow_tex, nearest_sampler);
@@ -1328,8 +1274,6 @@ void Splat::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backw
        glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width * height);
 
        glDisable(GL_DEPTH_TEST);
-
-       glDeleteFramebuffers(1, &fbo);
 }
 
 // Doing good and fast hole-filling on a GPU is nontrivial. We choose an option
@@ -1355,12 +1299,11 @@ public:
        void exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height);
 
 private:
-       PersistentFBOSet<2> fbos;
+       PersistentFBOSetWithDepth<1> fbos;
 
        GLuint fill_vs_obj;
        GLuint fill_fs_obj;
        GLuint fill_program;
-       GLuint fill_vao;
 
        GLuint uniform_tex;
        GLuint uniform_z, uniform_sample_offset;
@@ -1372,15 +1315,6 @@ HoleFill::HoleFill()
        fill_fs_obj = compile_shader(read_file("hole_fill.frag"), GL_FRAGMENT_SHADER);
        fill_program = link_program(fill_vs_obj, fill_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &fill_vao);
-       glBindVertexArray(fill_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(fill_program, "position");
-       glEnableVertexArrayAttrib(fill_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_tex = glGetUniformLocation(fill_program, "tex");
        uniform_z = glGetUniformLocation(fill_program, "z");
        uniform_sample_offset = glGetUniformLocation(fill_program, "sample_offset");
@@ -1398,14 +1332,8 @@ void HoleFill::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int w
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);  // Only update the values > 0.999f (ie., only invalid pixels).
-       glBindVertexArray(fill_vao);
 
-       // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
-       GLuint fbo;
-       glCreateFramebuffers(1, &fbo);
-       glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);  // NOTE: Reading and writing to the same texture.
-       glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
-       glBindFramebuffer(GL_FRAMEBUFFER, fbo);
+       fbos.render_to(depth_tex, 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) {
@@ -1443,8 +1371,6 @@ void HoleFill::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int w
        }
 
        glDisable(GL_DEPTH_TEST);
-
-       glDeleteFramebuffers(1, &fbo);
 }
 
 // Blend the four directions from HoleFill into one pixel, so that single-pixel
@@ -1456,12 +1382,11 @@ public:
        void exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int width, int height);
 
 private:
-       PersistentFBOSet<2> fbos;
+       PersistentFBOSetWithDepth<1> fbos;
 
        GLuint blend_vs_obj;
        GLuint blend_fs_obj;
        GLuint blend_program;
-       GLuint blend_vao;
 
        GLuint uniform_left_tex, uniform_right_tex, uniform_up_tex, uniform_down_tex;
        GLuint uniform_z, uniform_sample_offset;
@@ -1473,15 +1398,6 @@ HoleBlend::HoleBlend()
        blend_fs_obj = compile_shader(read_file("hole_blend.frag"), GL_FRAGMENT_SHADER);
        blend_program = link_program(blend_vs_obj, blend_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &blend_vao);
-       glBindVertexArray(blend_vao);
-       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
-
-       GLint position_attrib = glGetAttribLocation(blend_program, "position");
-       glEnableVertexArrayAttrib(blend_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_left_tex = glGetUniformLocation(blend_program, "left_tex");
        uniform_right_tex = glGetUniformLocation(blend_program, "right_tex");
        uniform_up_tex = glGetUniformLocation(blend_program, "up_tex");
@@ -1506,20 +1422,12 @@ void HoleBlend::exec(GLuint flow_tex, GLuint depth_tex, GLuint temp_tex[3], int
        glDisable(GL_BLEND);
        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LEQUAL);  // Skip over all of the pixels that were never holes to begin with.
-       glBindVertexArray(blend_vao);
 
-       // FIXME: Get this into FBOSet, so we can reuse FBOs across frames.
-       GLuint fbo;
-       glCreateFramebuffers(1, &fbo);
-       glNamedFramebufferTexture(fbo, GL_COLOR_ATTACHMENT0, flow_tex, 0);  // NOTE: Reading and writing to the same texture.
-       glNamedFramebufferTexture(fbo, GL_DEPTH_ATTACHMENT, depth_tex, 0);
-       glBindFramebuffer(GL_FRAMEBUFFER, fbo);
+       fbos.render_to(depth_tex, flow_tex);  // NOTE: Reading and writing to the same texture.
 
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 
        glDisable(GL_DEPTH_TEST);
-
-       glDeleteFramebuffers(1, &fbo);
 }
 
 class Blend {
@@ -1532,7 +1440,6 @@ private:
        GLuint blend_vs_obj;
        GLuint blend_fs_obj;
        GLuint blend_program;
-       GLuint blend_vao;
 
        GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
        GLuint uniform_alpha, uniform_flow_consistency_tolerance;
@@ -1544,14 +1451,6 @@ Blend::Blend()
        blend_fs_obj = compile_shader(read_file("blend.frag"), GL_FRAGMENT_SHADER);
        blend_program = link_program(blend_vs_obj, blend_fs_obj);
 
-       // Set up the VAO containing all the required position/texcoord data.
-       glCreateVertexArrays(1, &blend_vao);
-       glBindVertexArray(blend_vao);
-
-       GLint position_attrib = glGetAttribLocation(blend_program, "position");
-       glEnableVertexArrayAttrib(blend_vao, position_attrib);
-       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
-
        uniform_image0_tex = glGetUniformLocation(blend_program, "image0_tex");
        uniform_image1_tex = glGetUniformLocation(blend_program, "image1_tex");
        uniform_flow_tex = glGetUniformLocation(blend_program, "flow_tex");
@@ -1566,12 +1465,9 @@ void Blend::exec(GLuint tex0, GLuint tex1, GLuint flow_tex, GLuint output_tex, i
        bind_sampler(blend_program, uniform_image1_tex, 1, tex1, linear_sampler);
        bind_sampler(blend_program, uniform_flow_tex, 2, flow_tex, linear_sampler);  // May be upsampled.
        glProgramUniform1f(blend_program, uniform_alpha, alpha);
-       //glProgramUniform1f(blend_program, uniform_flow_consistency_tolerance, 1.0f / 
 
        glViewport(0, 0, level_width, level_height);
        fbos.render_to(output_tex);
-       glBindVertexArray(blend_vao);
-       glUseProgram(blend_program);
        glDisable(GL_BLEND);  // A bit ironic, perhaps.
        glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 }
@@ -1591,7 +1487,9 @@ public:
 
 private:
        int width, height, flow_level;
+       GLuint vertex_vbo, vao;
        TexturePool pool;
+
        Splat splat;
        HoleFill hole_fill;
        HoleBlend hole_blend;
@@ -1599,13 +1497,33 @@ private:
 };
 
 Interpolate::Interpolate(int width, int height, int flow_level)
-       : width(width), height(height), flow_level(flow_level) {}
+       : width(width), height(height), flow_level(flow_level) {
+       // Set up the vertex data that will be shared between all passes.
+       float vertices[] = {
+               0.0f, 1.0f,
+               0.0f, 0.0f,
+               1.0f, 1.0f,
+               1.0f, 0.0f,
+       };
+       glCreateBuffers(1, &vertex_vbo);
+       glNamedBufferData(vertex_vbo, sizeof(vertices), vertices, GL_STATIC_DRAW);
+
+       glCreateVertexArrays(1, &vao);
+       glBindVertexArray(vao);
+       glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
+
+       GLint position_attrib = 0;  // Hard-coded in every vertex shader.
+       glEnableVertexArrayAttrib(vao, position_attrib);
+       glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
+}
 
 GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLuint backward_flow_tex, GLuint width, GLuint height, float alpha)
 {
        GPUTimers timers;
 
-       ScopedTimer total_timer("Total", &timers);
+       ScopedTimer total_timer("Interpolate", &timers);
+
+       glBindVertexArray(vao);
 
        // Pick out the right level to test splatting results on.
        GLuint tex0_view, tex1_view;
@@ -1619,13 +1537,6 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
 
        GLuint flow_tex = pool.get_texture(GL_RG16F, flow_width, flow_height);
        GLuint depth_tex = pool.get_texture(GL_DEPTH_COMPONENT32F, flow_width, flow_height);  // Used for ranking flows.
-       {
-               ScopedTimer timer("Clear", &total_timer);
-               float invalid_flow[] = { 1000.0f, 1000.0f };
-               glClearTexImage(flow_tex, 0, GL_RG, GL_FLOAT, invalid_flow);
-               float infinity = 1.0f;
-               glClearTexImage(depth_tex, 0, GL_DEPTH_COMPONENT, GL_FLOAT, &infinity);
-       }
 
        {
                ScopedTimer timer("Splat", &total_timer);
@@ -1655,8 +1566,11 @@ GLuint Interpolate::exec(GLuint tex0, GLuint tex1, GLuint forward_flow_tex, GLui
                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;
 }
@@ -1861,6 +1775,16 @@ 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");
@@ -1955,6 +1879,19 @@ 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);
 
@@ -1983,7 +1920,8 @@ 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 ( ;; ) {
@@ -2015,6 +1953,9 @@ 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);