git.sesse.net Git - nageru/blob - flow.cpp

   1 #define NO_SDL_GLEXT 1
   2
   3 #define WIDTH 1280
   4 #define HEIGHT 720
   5
   6 #include <epoxy/gl.h>
   7
   8 #include <SDL2/SDL.h>
   9 #include <SDL2/SDL_error.h>
  10 #include <SDL2/SDL_events.h>
  11 #include <SDL2/SDL_image.h>
  12 #include <SDL2/SDL_keyboard.h>
  13 #include <SDL2/SDL_mouse.h>
  14 #include <SDL2/SDL_video.h>
  15
  16 #include <assert.h>
  17 #include <stdio.h>
  18 #include <unistd.h>
  19
  20 #include "util.h"
  21
  22 #include <algorithm>
  23 #include <memory>
  24
  25 #define BUFFER_OFFSET(i) ((char *)nullptr + (i))
  26
  27 using namespace std;
  28
  29 // Operating point 3 (10 Hz on CPU, excluding preprocessing).
  30 constexpr float patch_overlap_ratio = 0.75f;
  31 constexpr unsigned coarsest_level = 5;
  32 constexpr unsigned finest_level = 1;
  33 constexpr unsigned patch_size_pixels = 12;
  34
  35 // Some global OpenGL objects.
  36 GLuint nearest_sampler, linear_sampler, smoothness_sampler;
  37 GLuint vertex_vbo;
  38
  39 string read_file(const string &filename)
  40 {
  41         FILE *fp = fopen(filename.c_str(), "r");
  42         if (fp == nullptr) {
  43                 perror(filename.c_str());
  44                 exit(1);
  45         }
  46
  47         int ret = fseek(fp, 0, SEEK_END);
  48         if (ret == -1) {
  49                 perror("fseek(SEEK_END)");
  50                 exit(1);
  51         }
  52
  53         int size = ftell(fp);
  54
  55         ret = fseek(fp, 0, SEEK_SET);
  56         if (ret == -1) {
  57                 perror("fseek(SEEK_SET)");
  58                 exit(1);
  59         }
  60
  61         string str;
  62         str.resize(size);
  63         ret = fread(&str[0], size, 1, fp);
  64         if (ret == -1) {
  65                 perror("fread");
  66                 exit(1);
  67         }
  68         if (ret == 0) {
  69                 fprintf(stderr, "Short read when trying to read %d bytes from %s\n",
  70                                 size, filename.c_str());
  71                 exit(1);
  72         }
  73         fclose(fp);
  74
  75         return str;
  76 }
  77
  78
  79 GLuint compile_shader(const string &shader_src, GLenum type)
  80 {
  81         GLuint obj = glCreateShader(type);
  82         const GLchar* source[] = { shader_src.data() };
  83         const GLint length[] = { (GLint)shader_src.size() };
  84         glShaderSource(obj, 1, source, length);
  85         glCompileShader(obj);
  86
  87         GLchar info_log[4096];
  88         GLsizei log_length = sizeof(info_log) - 1;
  89         glGetShaderInfoLog(obj, log_length, &log_length, info_log);
  90         info_log[log_length] = 0;
  91         if (strlen(info_log) > 0) {
  92                 fprintf(stderr, "Shader compile log: %s\n", info_log);
  93         }
  94
  95         GLint status;
  96         glGetShaderiv(obj, GL_COMPILE_STATUS, &status);
  97         if (status == GL_FALSE) {
  98                 // Add some line numbers to easier identify compile errors.
  99                 string src_with_lines = "/*   1 */ ";
 100                 size_t lineno = 1;
 101                 for (char ch : shader_src) {
 102                         src_with_lines.push_back(ch);
 103                         if (ch == '\n') {
 104                                 char buf[32];
 105                                 snprintf(buf, sizeof(buf), "/* %3zu */ ", ++lineno);
 106                                 src_with_lines += buf;
 107                         }
 108                 }
 109
 110                 fprintf(stderr, "Failed to compile shader:\n%s\n", src_with_lines.c_str());
 111                 exit(1);
 112         }
 113
 114         return obj;
 115 }
 116
 117
 118 GLuint load_texture(const char *filename, unsigned width, unsigned height)
 119 {
 120         FILE *fp = fopen(filename, "rb");
 121         if (fp == nullptr) {
 122                 perror(filename);
 123                 exit(1);
 124         }
 125         unique_ptr<uint8_t[]> pix(new uint8_t[width * height]);
 126         if (fread(pix.get(), width * height, 1, fp) != 1) {
 127                 fprintf(stderr, "Short read from %s\n", filename);
 128                 exit(1);
 129         }
 130         fclose(fp);
 131
 132         // Convert to bottom-left origin.
 133         for (unsigned y = 0; y < height / 2; ++y) {
 134                 unsigned y2 = height - 1 - y;
 135                 swap_ranges(&pix[y * width], &pix[y * width + width], &pix[y2 * width]);
 136         }
 137
 138         int levels = 1;
 139         for (int w = width, h = height; w > 1 || h > 1; ) {
 140                 w >>= 1;
 141                 h >>= 1;
 142                 ++levels;
 143         }
 144
 145         GLuint tex;
 146         glCreateTextures(GL_TEXTURE_2D, 1, &tex);
 147         glTextureStorage2D(tex, levels, GL_R8, width, height);
 148         glTextureSubImage2D(tex, 0, 0, 0, width, height, GL_RED, GL_UNSIGNED_BYTE, pix.get());
 149         glGenerateTextureMipmap(tex);
 150
 151         return tex;
 152 }
 153
 154 GLuint link_program(GLuint vs_obj, GLuint fs_obj)
 155 {
 156         GLuint program = glCreateProgram();
 157         glAttachShader(program, vs_obj);
 158         glAttachShader(program, fs_obj);
 159         glLinkProgram(program);
 160         GLint success;
 161         glGetProgramiv(program, GL_LINK_STATUS, &success);
 162         if (success == GL_FALSE) {
 163                 GLchar error_log[1024] = {0};
 164                 glGetProgramInfoLog(program, 1024, nullptr, error_log);
 165                 fprintf(stderr, "Error linking program: %s\n", error_log);
 166                 exit(1);
 167         }
 168         return program;
 169 }
 170
 171 GLuint generate_vbo(GLint size, GLsizeiptr data_size, const GLvoid *data)
 172 {
 173         GLuint vbo;
 174         glCreateBuffers(1, &vbo);
 175         glBufferData(GL_ARRAY_BUFFER, data_size, data, GL_STATIC_DRAW);
 176         glNamedBufferData(vbo, data_size, data, GL_STATIC_DRAW);
 177         return vbo;
 178 }
 179
 180 GLuint fill_vertex_attribute(GLuint vao, GLuint glsl_program_num, const string &attribute_name, GLint size, GLenum type, GLsizeiptr data_size, const GLvoid *data)
 181 {
 182         int attrib = glGetAttribLocation(glsl_program_num, attribute_name.c_str());
 183         if (attrib == -1) {
 184                 return -1;
 185         }
 186
 187         GLuint vbo = generate_vbo(size, data_size, data);
 188
 189         glBindBuffer(GL_ARRAY_BUFFER, vbo);
 190         glEnableVertexArrayAttrib(vao, attrib);
 191         glVertexAttribPointer(attrib, size, type, GL_FALSE, 0, BUFFER_OFFSET(0));
 192         glBindBuffer(GL_ARRAY_BUFFER, 0);
 193
 194         return vbo;
 195 }
 196
 197 void bind_sampler(GLuint program, GLint location, GLuint texture_unit, GLuint tex, GLuint sampler)
 198 {
 199         if (location == -1) {
 200                 return;
 201         }
 202
 203         glBindTextureUnit(texture_unit, tex);
 204         glBindSampler(texture_unit, sampler);
 205         glProgramUniform1i(program, location, texture_unit);
 206 }
 207
 208 // Compute gradients in every point, used for the motion search.
 209 // The DIS paper doesn't actually mention how these are computed,
 210 // but seemingly, a 3x3 Sobel operator is used here (at least in
 211 // later versions of the code), while a [1 -8 0 8 -1] kernel is
 212 // used for all the derivatives in the variational refinement part
 213 // (which borrows code from DeepFlow). This is inconsistent,
 214 // but I guess we're better off with staying with the original
 215 // decisions until we actually know having different ones would be better.
 216 class Sobel {
 217 public:
 218         Sobel();
 219         void exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_height);
 220
 221 private:
 222         GLuint sobel_vs_obj;
 223         GLuint sobel_fs_obj;
 224         GLuint sobel_program;
 225         GLuint sobel_vao;
 226
 227         GLuint uniform_tex, uniform_image_size;
 228 };
 229
 230 Sobel::Sobel()
 231 {
 232         sobel_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 233         sobel_fs_obj = compile_shader(read_file("sobel.frag"), GL_FRAGMENT_SHADER);
 234         sobel_program = link_program(sobel_vs_obj, sobel_fs_obj);
 235
 236         // Set up the VAO containing all the required position/texcoord data.
 237         glCreateVertexArrays(1, &sobel_vao);
 238         glBindVertexArray(sobel_vao);
 239
 240         GLint position_attrib = glGetAttribLocation(sobel_program, "position");
 241         glEnableVertexArrayAttrib(sobel_vao, position_attrib);
 242         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 243
 244         uniform_tex = glGetUniformLocation(sobel_program, "tex");
 245 }
 246
 247 void Sobel::exec(GLint tex0_view, GLint grad0_tex, int level_width, int level_height)
 248 {
 249         glUseProgram(sobel_program);
 250         glBindTextureUnit(0, tex0_view);
 251         glBindSampler(0, nearest_sampler);
 252         glProgramUniform1i(sobel_program, uniform_tex, 0);
 253
 254         GLuint grad0_fbo;  // TODO: cleanup
 255         glCreateFramebuffers(1, &grad0_fbo);
 256         glNamedFramebufferTexture(grad0_fbo, GL_COLOR_ATTACHMENT0, grad0_tex, 0);
 257
 258         glViewport(0, 0, level_width, level_height);
 259         glBindFramebuffer(GL_FRAMEBUFFER, grad0_fbo);
 260         glBindVertexArray(sobel_vao);
 261         glUseProgram(sobel_program);
 262         glDisable(GL_BLEND);
 263         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 264 }
 265
 266 // Motion search to find the initial flow. See motion_search.frag for documentation.
 267 class MotionSearch {
 268 public:
 269         MotionSearch();
 270         void exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GLuint flow_tex, GLuint flow_out_tex, int level_width, int level_height, int width_patches, int height_patches);
 271
 272 private:
 273         GLuint motion_vs_obj;
 274         GLuint motion_fs_obj;
 275         GLuint motion_search_program;
 276         GLuint motion_search_vao;
 277
 278         GLuint uniform_image_size, uniform_inv_image_size;
 279         GLuint uniform_image0_tex, uniform_image1_tex, uniform_grad0_tex, uniform_flow_tex;
 280 };
 281
 282 MotionSearch::MotionSearch()
 283 {
 284         motion_vs_obj = compile_shader(read_file("motion_search.vert"), GL_VERTEX_SHADER);
 285         motion_fs_obj = compile_shader(read_file("motion_search.frag"), GL_FRAGMENT_SHADER);
 286         motion_search_program = link_program(motion_vs_obj, motion_fs_obj);
 287
 288         // Set up the VAO containing all the required position/texcoord data.
 289         glCreateVertexArrays(1, &motion_search_vao);
 290         glBindVertexArray(motion_search_vao);
 291         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 292
 293         GLint position_attrib = glGetAttribLocation(motion_search_program, "position");
 294         glEnableVertexArrayAttrib(motion_search_vao, position_attrib);
 295         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 296
 297         uniform_image_size = glGetUniformLocation(motion_search_program, "image_size");
 298         uniform_inv_image_size = glGetUniformLocation(motion_search_program, "inv_image_size");
 299         uniform_image0_tex = glGetUniformLocation(motion_search_program, "image0_tex");
 300         uniform_image1_tex = glGetUniformLocation(motion_search_program, "image1_tex");
 301         uniform_grad0_tex = glGetUniformLocation(motion_search_program, "grad0_tex");
 302         uniform_flow_tex = glGetUniformLocation(motion_search_program, "flow_tex");
 303 }
 304
 305 void MotionSearch::exec(GLuint tex0_view, GLuint tex1_view, GLuint grad0_tex, GLuint flow_tex, GLuint flow_out_tex, int level_width, int level_height, int width_patches, int height_patches)
 306 {
 307         glUseProgram(motion_search_program);
 308
 309         bind_sampler(motion_search_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
 310         bind_sampler(motion_search_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
 311         bind_sampler(motion_search_program, uniform_grad0_tex, 2, grad0_tex, nearest_sampler);
 312         bind_sampler(motion_search_program, uniform_flow_tex, 3, flow_tex, linear_sampler);
 313
 314         glProgramUniform2f(motion_search_program, uniform_image_size, level_width, level_height);
 315         glProgramUniform2f(motion_search_program, uniform_inv_image_size, 1.0f / level_width, 1.0f / level_height);
 316
 317         GLuint flow_fbo;  // TODO: cleanup
 318         glCreateFramebuffers(1, &flow_fbo);
 319         glNamedFramebufferTexture(flow_fbo, GL_COLOR_ATTACHMENT0, flow_out_tex, 0);
 320
 321         glViewport(0, 0, width_patches, height_patches);
 322         glBindFramebuffer(GL_FRAMEBUFFER, flow_fbo);
 323         glBindVertexArray(motion_search_vao);
 324         glUseProgram(motion_search_program);
 325         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 326 }
 327
 328 // Do “densification”, ie., upsampling of the flow patches to the flow field
 329 // (the same size as the image at this level). We draw one quad per patch
 330 // over its entire covered area (using instancing in the vertex shader),
 331 // and then weight the contributions in the pixel shader by post-warp difference.
 332 // This is equation (3) in the paper.
 333 //
 334 // We accumulate the flow vectors in the R/G channels (for u/v) and the total
 335 // weight in the B channel. Dividing R and G by B gives the normalized values.
 336 class Densify {
 337 public:
 338         Densify();
 339         void exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint dense_flow_tex, int level_width, int level_height, int width_patches, int height_patches);
 340
 341 private:
 342         GLuint densify_vs_obj;
 343         GLuint densify_fs_obj;
 344         GLuint densify_program;
 345         GLuint densify_vao;
 346
 347         GLuint uniform_width_patches, uniform_patch_size, uniform_patch_spacing;
 348         GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
 349 };
 350
 351 Densify::Densify()
 352 {
 353         densify_vs_obj = compile_shader(read_file("densify.vert"), GL_VERTEX_SHADER);
 354         densify_fs_obj = compile_shader(read_file("densify.frag"), GL_FRAGMENT_SHADER);
 355         densify_program = link_program(densify_vs_obj, densify_fs_obj);
 356
 357         // Set up the VAO containing all the required position/texcoord data.
 358         glCreateVertexArrays(1, &densify_vao);
 359         glBindVertexArray(densify_vao);
 360         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 361
 362         GLint position_attrib = glGetAttribLocation(densify_program, "position");
 363         glEnableVertexArrayAttrib(densify_vao, position_attrib);
 364         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 365
 366         uniform_width_patches = glGetUniformLocation(densify_program, "width_patches");
 367         uniform_patch_size = glGetUniformLocation(densify_program, "patch_size");
 368         uniform_patch_spacing = glGetUniformLocation(densify_program, "patch_spacing");
 369         uniform_image0_tex = glGetUniformLocation(densify_program, "image0_tex");
 370         uniform_image1_tex = glGetUniformLocation(densify_program, "image1_tex");
 371         uniform_flow_tex = glGetUniformLocation(densify_program, "flow_tex");
 372 }
 373
 374 void Densify::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint dense_flow_tex, int level_width, int level_height, int width_patches, int height_patches)
 375 {
 376         glUseProgram(densify_program);
 377
 378         bind_sampler(densify_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
 379         bind_sampler(densify_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
 380         bind_sampler(densify_program, uniform_flow_tex, 2, flow_tex, nearest_sampler);
 381
 382         glProgramUniform1i(densify_program, uniform_width_patches, width_patches);
 383         glProgramUniform2f(densify_program, uniform_patch_size,
 384                 float(patch_size_pixels) / level_width,
 385                 float(patch_size_pixels) / level_height);
 386
 387         float patch_spacing_x = float(level_width - patch_size_pixels) / (width_patches - 1);
 388         float patch_spacing_y = float(level_height - patch_size_pixels) / (height_patches - 1);
 389         if (width_patches == 1) patch_spacing_x = 0.0f;  // Avoid infinities.
 390         if (height_patches == 1) patch_spacing_y = 0.0f;
 391         glProgramUniform2f(densify_program, uniform_patch_spacing,
 392                 patch_spacing_x / level_width,
 393                 patch_spacing_y / level_height);
 394
 395         GLuint dense_flow_fbo;  // TODO: cleanup
 396         glCreateFramebuffers(1, &dense_flow_fbo);
 397         glNamedFramebufferTexture(dense_flow_fbo, GL_COLOR_ATTACHMENT0, dense_flow_tex, 0);
 398
 399         glViewport(0, 0, level_width, level_height);
 400         glEnable(GL_BLEND);
 401         glBlendFunc(GL_ONE, GL_ONE);
 402         glBindVertexArray(densify_vao);
 403         glBindFramebuffer(GL_FRAMEBUFFER, dense_flow_fbo);
 404         glDrawArraysInstanced(GL_TRIANGLE_STRIP, 0, 4, width_patches * height_patches);
 405 }
 406
 407 // Warp I_1 to I_w, and then compute the mean (I) and difference (I_t) of
 408 // I_0 and I_w. The prewarping is what enables us to solve the variational
 409 // flow for du,dv instead of u,v.
 410 //
 411 // See variational_refinement.txt for more information.
 412 class Prewarp {
 413 public:
 414         Prewarp();
 415         void exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint I_tex, GLuint I_t_tex, int level_width, int level_height);
 416
 417 private:
 418         GLuint prewarp_vs_obj;
 419         GLuint prewarp_fs_obj;
 420         GLuint prewarp_program;
 421         GLuint prewarp_vao;
 422
 423         GLuint uniform_image0_tex, uniform_image1_tex, uniform_flow_tex;
 424 };
 425
 426 Prewarp::Prewarp()
 427 {
 428         prewarp_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 429         prewarp_fs_obj = compile_shader(read_file("prewarp.frag"), GL_FRAGMENT_SHADER);
 430         prewarp_program = link_program(prewarp_vs_obj, prewarp_fs_obj);
 431
 432         // Set up the VAO containing all the required position/texcoord data.
 433         glCreateVertexArrays(1, &prewarp_vao);
 434         glBindVertexArray(prewarp_vao);
 435         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 436
 437         GLint position_attrib = glGetAttribLocation(prewarp_program, "position");
 438         glEnableVertexArrayAttrib(prewarp_vao, position_attrib);
 439         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 440
 441         uniform_image0_tex = glGetUniformLocation(prewarp_program, "image0_tex");
 442         uniform_image1_tex = glGetUniformLocation(prewarp_program, "image1_tex");
 443         uniform_flow_tex = glGetUniformLocation(prewarp_program, "flow_tex");
 444 }
 445
 446 void Prewarp::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint I_tex, GLuint I_t_tex, int level_width, int level_height)
 447 {
 448         glUseProgram(prewarp_program);
 449
 450         bind_sampler(prewarp_program, uniform_image0_tex, 0, tex0_view, nearest_sampler);
 451         bind_sampler(prewarp_program, uniform_image1_tex, 1, tex1_view, linear_sampler);
 452         bind_sampler(prewarp_program, uniform_flow_tex, 2, flow_tex, nearest_sampler);
 453
 454         GLuint prewarp_fbo;  // TODO: cleanup
 455         glCreateFramebuffers(1, &prewarp_fbo);
 456         GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
 457         glNamedFramebufferDrawBuffers(prewarp_fbo, 2, bufs);
 458         glNamedFramebufferTexture(prewarp_fbo, GL_COLOR_ATTACHMENT0, I_tex, 0);
 459         glNamedFramebufferTexture(prewarp_fbo, GL_COLOR_ATTACHMENT1, I_t_tex, 0);
 460
 461         glViewport(0, 0, level_width, level_height);
 462         glDisable(GL_BLEND);
 463         glBindVertexArray(prewarp_vao);
 464         glBindFramebuffer(GL_FRAMEBUFFER, prewarp_fbo);
 465         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 466 }
 467
 468 // From I, calculate the partial derivatives I_x and I_y. We use a four-tap
 469 // central difference filter, since apparently, that's tradition (I haven't
 470 // measured quality versus a more normal 0.5 (I[x+1] - I[x-1]).)
 471 // The coefficients come from
 472 //
 473 //   https://en.wikipedia.org/wiki/Finite_difference_coefficient
 474 //
 475 // Also computes β_0, since it depends only on I_x and I_y.
 476 class Derivatives {
 477 public:
 478         Derivatives();
 479         void exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height);
 480
 481 private:
 482         GLuint derivatives_vs_obj;
 483         GLuint derivatives_fs_obj;
 484         GLuint derivatives_program;
 485         GLuint derivatives_vao;
 486
 487         GLuint uniform_tex;
 488 };
 489
 490 Derivatives::Derivatives()
 491 {
 492         derivatives_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 493         derivatives_fs_obj = compile_shader(read_file("derivatives.frag"), GL_FRAGMENT_SHADER);
 494         derivatives_program = link_program(derivatives_vs_obj, derivatives_fs_obj);
 495
 496         // Set up the VAO containing all the required position/texcoord data.
 497         glCreateVertexArrays(1, &derivatives_vao);
 498         glBindVertexArray(derivatives_vao);
 499         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 500
 501         GLint position_attrib = glGetAttribLocation(derivatives_program, "position");
 502         glEnableVertexArrayAttrib(derivatives_vao, position_attrib);
 503         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 504
 505         uniform_tex = glGetUniformLocation(derivatives_program, "tex");
 506 }
 507
 508 void Derivatives::exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height)
 509 {
 510         glUseProgram(derivatives_program);
 511
 512         bind_sampler(derivatives_program, uniform_tex, 0, input_tex, nearest_sampler);
 513
 514         GLuint derivatives_fbo;  // TODO: cleanup
 515         glCreateFramebuffers(1, &derivatives_fbo);
 516         GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
 517         glNamedFramebufferDrawBuffers(derivatives_fbo, 2, bufs);
 518         glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT0, I_x_y_tex, 0);
 519         glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT1, beta_0_tex, 0);
 520
 521         glViewport(0, 0, level_width, level_height);
 522         glDisable(GL_BLEND);
 523         glBindVertexArray(derivatives_vao);
 524         glBindFramebuffer(GL_FRAMEBUFFER, derivatives_fbo);
 525         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 526 }
 527
 528 // Calculate the smoothness constraints between neighboring pixels;
 529 // s_x(x,y) stores smoothness between pixel (x,y) and (x+1,y),
 530 // and s_y(x,y) stores between (x,y) and (x,y+1). We'll sample with
 531 // border color (0,0) later, so that there's zero diffusion out of
 532 // the border.
 533 //
 534 // See variational_refinement.txt for more information.
 535 class ComputeSmoothness {
 536 public:
 537         ComputeSmoothness();
 538         void exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height);
 539
 540 private:
 541         GLuint smoothness_vs_obj;
 542         GLuint smoothness_fs_obj;
 543         GLuint smoothness_program;
 544         GLuint smoothness_vao;
 545
 546         GLuint uniform_flow_tex, uniform_diff_flow_tex;
 547 };
 548
 549 ComputeSmoothness::ComputeSmoothness()
 550 {
 551         smoothness_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 552         smoothness_fs_obj = compile_shader(read_file("smoothness.frag"), GL_FRAGMENT_SHADER);
 553         smoothness_program = link_program(smoothness_vs_obj, smoothness_fs_obj);
 554
 555         // Set up the VAO containing all the required position/texcoord data.
 556         glCreateVertexArrays(1, &smoothness_vao);
 557         glBindVertexArray(smoothness_vao);
 558         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 559
 560         GLint position_attrib = glGetAttribLocation(smoothness_program, "position");
 561         glEnableVertexArrayAttrib(smoothness_vao, position_attrib);
 562         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 563
 564         uniform_flow_tex = glGetUniformLocation(smoothness_program, "flow_tex");
 565         uniform_diff_flow_tex = glGetUniformLocation(smoothness_program, "diff_flow_tex");
 566 }
 567
 568 void ComputeSmoothness::exec(GLuint flow_tex, GLuint diff_flow_tex, GLuint smoothness_x_tex, GLuint smoothness_y_tex, int level_width, int level_height)
 569 {
 570         glUseProgram(smoothness_program);
 571
 572         bind_sampler(smoothness_program, uniform_flow_tex, 0, flow_tex, nearest_sampler);
 573         bind_sampler(smoothness_program, uniform_diff_flow_tex, 1, diff_flow_tex, nearest_sampler);
 574
 575         GLuint smoothness_fbo;  // TODO: cleanup
 576         glCreateFramebuffers(1, &smoothness_fbo);
 577         GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
 578         glNamedFramebufferDrawBuffers(smoothness_fbo, 2, bufs);
 579         glNamedFramebufferTexture(smoothness_fbo, GL_COLOR_ATTACHMENT0, smoothness_x_tex, 0);
 580         glNamedFramebufferTexture(smoothness_fbo, GL_COLOR_ATTACHMENT1, smoothness_y_tex, 0);
 581
 582         glViewport(0, 0, level_width, level_height);
 583
 584         // Make sure the smoothness on the right and upper borders is zero.
 585         // We could have done this by making a (W-1)x(H-1) texture instead
 586         // (we're sampling smoothness with all-zero border color), but we'd
 587         // have to adjust the sampling coordinates, which is annoying.
 588         glScissor(0, 0, level_width - 1, level_height - 1);
 589         glEnable(GL_SCISSOR_TEST);
 590
 591         glDisable(GL_BLEND);
 592         glBindVertexArray(smoothness_vao);
 593         glBindFramebuffer(GL_FRAMEBUFFER, smoothness_fbo);
 594         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 595
 596         glDisable(GL_SCISSOR_TEST);
 597 }
 598
 599 // Set up the equations set (two equations in two unknowns, per pixel).
 600 // We store five floats; the three non-redundant elements of the 2x2 matrix (A)
 601 // as 32-bit floats, and the two elements on the right-hand side (b) as 16-bit
 602 // floats. (Actually, we store the inverse of the diagonal elements, because
 603 // we only ever need to divide by them.) This fits into four u32 values;
 604 // R, G, B for the matrix (the last element is symmetric) and A for the two b values.
 605 // All the values of the energy term (E_I, E_G, E_S), except the smoothness
 606 // terms that depend on other pixels, are calculated in one pass.
 607 //
 608 // See variational_refinement.txt for more information.
 609 class SetupEquations {
 610 public:
 611         SetupEquations();
 612         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);
 613
 614 private:
 615         GLuint equations_vs_obj;
 616         GLuint equations_fs_obj;
 617         GLuint equations_program;
 618         GLuint equations_vao;
 619
 620         GLuint uniform_I_x_y_tex, uniform_I_t_tex;
 621         GLuint uniform_diff_flow_tex, uniform_flow_tex;
 622         GLuint uniform_beta_0_tex;
 623         GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
 624
 625 };
 626
 627 SetupEquations::SetupEquations()
 628 {
 629         equations_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 630         equations_fs_obj = compile_shader(read_file("equations.frag"), GL_FRAGMENT_SHADER);
 631         equations_program = link_program(equations_vs_obj, equations_fs_obj);
 632
 633         // Set up the VAO containing all the required position/texcoord data.
 634         glCreateVertexArrays(1, &equations_vao);
 635         glBindVertexArray(equations_vao);
 636         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 637
 638         GLint position_attrib = glGetAttribLocation(equations_program, "position");
 639         glEnableVertexArrayAttrib(equations_vao, position_attrib);
 640         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 641
 642         uniform_I_x_y_tex = glGetUniformLocation(equations_program, "I_x_y_tex");
 643         uniform_I_t_tex = glGetUniformLocation(equations_program, "I_t_tex");
 644         uniform_diff_flow_tex = glGetUniformLocation(equations_program, "diff_flow_tex");
 645         uniform_flow_tex = glGetUniformLocation(equations_program, "flow_tex");
 646         uniform_beta_0_tex = glGetUniformLocation(equations_program, "beta_0_tex");
 647         uniform_smoothness_x_tex = glGetUniformLocation(equations_program, "smoothness_x_tex");
 648         uniform_smoothness_y_tex = glGetUniformLocation(equations_program, "smoothness_y_tex");
 649 }
 650
 651 void SetupEquations::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)
 652 {
 653         glUseProgram(equations_program);
 654
 655         bind_sampler(equations_program, uniform_I_x_y_tex, 0, I_x_y_tex, nearest_sampler);
 656         bind_sampler(equations_program, uniform_I_t_tex, 1, I_t_tex, nearest_sampler);
 657         bind_sampler(equations_program, uniform_diff_flow_tex, 2, diff_flow_tex, nearest_sampler);
 658         bind_sampler(equations_program, uniform_flow_tex, 3, flow_tex, nearest_sampler);
 659         bind_sampler(equations_program, uniform_beta_0_tex, 4, beta_0_tex, nearest_sampler);
 660         bind_sampler(equations_program, uniform_smoothness_x_tex, 5, smoothness_x_tex, smoothness_sampler);
 661         bind_sampler(equations_program, uniform_smoothness_y_tex, 6, smoothness_y_tex, smoothness_sampler);
 662
 663         GLuint equations_fbo;  // TODO: cleanup
 664         glCreateFramebuffers(1, &equations_fbo);
 665         glNamedFramebufferTexture(equations_fbo, GL_COLOR_ATTACHMENT0, equation_tex, 0);
 666
 667         glViewport(0, 0, level_width, level_height);
 668         glDisable(GL_BLEND);
 669         glBindVertexArray(equations_vao);
 670         glBindFramebuffer(GL_FRAMEBUFFER, equations_fbo);
 671         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 672 }
 673
 674 // Calculate the smoothness constraints between neighboring pixels;
 675 // s_x(x,y) stores smoothness between pixel (x,y) and (x+1,y),
 676 // and s_y(x,y) stores between (x,y) and (x,y+1). We'll sample with
 677 // border color (0,0) later, so that there's zero diffusion out of
 678 // the border.
 679 //
 680 // See variational_refinement.txt for more information.
 681 class SOR {
 682 public:
 683         SOR();
 684         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);
 685
 686 private:
 687         GLuint sor_vs_obj;
 688         GLuint sor_fs_obj;
 689         GLuint sor_program;
 690         GLuint sor_vao;
 691
 692         GLuint uniform_diff_flow_tex;
 693         GLuint uniform_equation_tex;
 694         GLuint uniform_smoothness_x_tex, uniform_smoothness_y_tex;
 695 };
 696
 697 SOR::SOR()
 698 {
 699         sor_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 700         sor_fs_obj = compile_shader(read_file("sor.frag"), GL_FRAGMENT_SHADER);
 701         sor_program = link_program(sor_vs_obj, sor_fs_obj);
 702
 703         // Set up the VAO containing all the required position/texcoord data.
 704         glCreateVertexArrays(1, &sor_vao);
 705         glBindVertexArray(sor_vao);
 706         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 707
 708         GLint position_attrib = glGetAttribLocation(sor_program, "position");
 709         glEnableVertexArrayAttrib(sor_vao, position_attrib);
 710         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 711
 712         uniform_diff_flow_tex = glGetUniformLocation(sor_program, "diff_flow_tex");
 713         uniform_equation_tex = glGetUniformLocation(sor_program, "equation_tex");
 714         uniform_smoothness_x_tex = glGetUniformLocation(sor_program, "smoothness_x_tex");
 715         uniform_smoothness_y_tex = glGetUniformLocation(sor_program, "smoothness_y_tex");
 716 }
 717
 718 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)
 719 {
 720         glUseProgram(sor_program);
 721
 722         bind_sampler(sor_program, uniform_diff_flow_tex, 0, diff_flow_tex, nearest_sampler);
 723         bind_sampler(sor_program, uniform_smoothness_x_tex, 1, smoothness_x_tex, smoothness_sampler);
 724         bind_sampler(sor_program, uniform_smoothness_y_tex, 2, smoothness_y_tex, smoothness_sampler);
 725         bind_sampler(sor_program, uniform_equation_tex, 3, equation_tex, nearest_sampler);
 726
 727         GLuint sor_fbo;  // TODO: cleanup
 728         glCreateFramebuffers(1, &sor_fbo);
 729         glNamedFramebufferTexture(sor_fbo, GL_COLOR_ATTACHMENT0, diff_flow_tex, 0);  // NOTE: Bind to same as we render from!
 730
 731         glViewport(0, 0, level_width, level_height);
 732         glDisable(GL_BLEND);
 733         glBindVertexArray(sor_vao);
 734         glBindFramebuffer(GL_FRAMEBUFFER, sor_fbo);
 735
 736         for (int i = 0; i < num_iterations; ++i) {
 737                 glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 738                 if (i != num_iterations - 1) {
 739                         glTextureBarrier();
 740                 }
 741         }
 742 }
 743
 744 // Simply add the differential flow found by the variational refinement to the base flow.
 745 // The output is in diff_flow_tex; we don't need to make a new texture.
 746 class AddBaseFlow {
 747 public:
 748         AddBaseFlow();
 749         void exec(GLuint base_flow_tex, GLuint diff_flow_tex, int level_width, int level_height);
 750
 751 private:
 752         GLuint add_flow_vs_obj;
 753         GLuint add_flow_fs_obj;
 754         GLuint add_flow_program;
 755         GLuint add_flow_vao;
 756
 757         GLuint uniform_base_flow_tex;
 758 };
 759
 760 AddBaseFlow::AddBaseFlow()
 761 {
 762         add_flow_vs_obj = compile_shader(read_file("vs.vert"), GL_VERTEX_SHADER);
 763         add_flow_fs_obj = compile_shader(read_file("add_base_flow.frag"), GL_FRAGMENT_SHADER);
 764         add_flow_program = link_program(add_flow_vs_obj, add_flow_fs_obj);
 765
 766         // Set up the VAO containing all the required position/texcoord data.
 767         glCreateVertexArrays(1, &add_flow_vao);
 768         glBindVertexArray(add_flow_vao);
 769         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 770
 771         GLint position_attrib = glGetAttribLocation(add_flow_program, "position");
 772         glEnableVertexArrayAttrib(add_flow_vao, position_attrib);
 773         glVertexAttribPointer(position_attrib, 2, GL_FLOAT, GL_FALSE, 0, BUFFER_OFFSET(0));
 774
 775         uniform_base_flow_tex = glGetUniformLocation(add_flow_program, "base_flow_tex");
 776 }
 777
 778 void AddBaseFlow::exec(GLuint base_flow_tex, GLuint diff_flow_tex, int level_width, int level_height)
 779 {
 780         glUseProgram(add_flow_program);
 781
 782         bind_sampler(add_flow_program, uniform_base_flow_tex, 0, base_flow_tex, nearest_sampler);
 783
 784         GLuint add_flow_fbo;  // TODO: cleanup
 785         glCreateFramebuffers(1, &add_flow_fbo);
 786         glNamedFramebufferTexture(add_flow_fbo, GL_COLOR_ATTACHMENT0, diff_flow_tex, 0);
 787
 788         glViewport(0, 0, level_width, level_height);
 789         glEnable(GL_BLEND);
 790         glBlendFunc(GL_ONE, GL_ONE);
 791         glBindVertexArray(add_flow_vao);
 792         glBindFramebuffer(GL_FRAMEBUFFER, add_flow_fbo);
 793
 794         glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 795 }
 796
 797 int main(void)
 798 {
 799         if (SDL_Init(SDL_INIT_EVERYTHING) == -1) {
 800                 fprintf(stderr, "SDL_Init failed: %s\n", SDL_GetError());
 801                 exit(1);
 802         }
 803         SDL_GL_SetAttribute(SDL_GL_ALPHA_SIZE, 8);
 804         SDL_GL_SetAttribute(SDL_GL_DEPTH_SIZE, 0);
 805         SDL_GL_SetAttribute(SDL_GL_STENCIL_SIZE, 0);
 806         SDL_GL_SetAttribute(SDL_GL_DOUBLEBUFFER, 1);
 807
 808         SDL_GL_SetAttribute(SDL_GL_CONTEXT_PROFILE_MASK, SDL_GL_CONTEXT_PROFILE_CORE);
 809         SDL_GL_SetAttribute(SDL_GL_CONTEXT_MAJOR_VERSION, 4);
 810         SDL_GL_SetAttribute(SDL_GL_CONTEXT_MINOR_VERSION, 5);
 811         // SDL_GL_SetAttribute(SDL_GL_CONTEXT_FLAGS, SDL_GL_CONTEXT_DEBUG_FLAG);
 812         SDL_Window *window = SDL_CreateWindow("OpenGL window",
 813                         SDL_WINDOWPOS_UNDEFINED,
 814                         SDL_WINDOWPOS_UNDEFINED,
 815                         64, 64,
 816                         SDL_WINDOW_OPENGL);
 817         SDL_GLContext context = SDL_GL_CreateContext(window);
 818         assert(context != nullptr);
 819
 820         // Load pictures.
 821         GLuint tex0 = load_texture("test1499.pgm", WIDTH, HEIGHT);
 822         GLuint tex1 = load_texture("test1500.pgm", WIDTH, HEIGHT);
 823
 824         // Make some samplers.
 825         glCreateSamplers(1, &nearest_sampler);
 826         glSamplerParameteri(nearest_sampler, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
 827         glSamplerParameteri(nearest_sampler, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
 828         glSamplerParameteri(nearest_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
 829         glSamplerParameteri(nearest_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
 830
 831         glCreateSamplers(1, &linear_sampler);
 832         glSamplerParameteri(linear_sampler, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
 833         glSamplerParameteri(linear_sampler, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
 834         glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
 835         glSamplerParameteri(linear_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
 836
 837         // The smoothness is sampled so that once we get to a smoothness involving
 838         // a value outside the border, the diffusivity between the two becomes zero.
 839         glCreateSamplers(1, &smoothness_sampler);
 840         glSamplerParameteri(smoothness_sampler, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
 841         glSamplerParameteri(smoothness_sampler, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
 842         glSamplerParameteri(smoothness_sampler, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);
 843         glSamplerParameteri(smoothness_sampler, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);
 844         float zero[] = { 0.0f, 0.0f, 0.0f, 0.0f };
 845         glSamplerParameterfv(smoothness_sampler, GL_TEXTURE_BORDER_COLOR, zero);
 846
 847         float vertices[] = {
 848                 0.0f, 1.0f,
 849                 0.0f, 0.0f,
 850                 1.0f, 1.0f,
 851                 1.0f, 0.0f,
 852         };
 853         glCreateBuffers(1, &vertex_vbo);
 854         glNamedBufferData(vertex_vbo, sizeof(vertices), vertices, GL_STATIC_DRAW);
 855         glBindBuffer(GL_ARRAY_BUFFER, vertex_vbo);
 856
 857         // Initial flow is zero, 1x1.
 858         GLuint initial_flow_tex;
 859         glCreateTextures(GL_TEXTURE_2D, 1, &initial_flow_tex);
 860         glTextureStorage2D(initial_flow_tex, 1, GL_RG16F, 1, 1);
 861
 862         GLuint prev_level_flow_tex = initial_flow_tex;
 863
 864         Sobel sobel;
 865         MotionSearch motion_search;
 866         Densify densify;
 867         Prewarp prewarp;
 868         Derivatives derivatives;
 869         ComputeSmoothness compute_smoothness;
 870         SetupEquations setup_equations;
 871         SOR sor;
 872         AddBaseFlow add_base_flow;
 873
 874         GLuint query;
 875         glGenQueries(1, &query);
 876         glBeginQuery(GL_TIME_ELAPSED, query);
 877
 878         for (int level = coarsest_level; level >= int(finest_level); --level) {
 879                 int level_width = WIDTH >> level;
 880                 int level_height = HEIGHT >> level;
 881                 float patch_spacing_pixels = patch_size_pixels * (1.0f - patch_overlap_ratio);
 882                 int width_patches = 1 + lrintf((level_width - patch_size_pixels) / patch_spacing_pixels);
 883                 int height_patches = 1 + lrintf((level_height - patch_size_pixels) / patch_spacing_pixels);
 884
 885                 // Make sure we always read from the correct level; the chosen
 886                 // mipmapping could otherwise be rather unpredictable, especially
 887                 // during motion search.
 888                 // TODO: create these beforehand, and stop leaking them.
 889                 GLuint tex0_view, tex1_view;
 890                 glGenTextures(1, &tex0_view);
 891                 glTextureView(tex0_view, GL_TEXTURE_2D, tex0, GL_R8, level, 1, 0, 1);
 892                 glGenTextures(1, &tex1_view);
 893                 glTextureView(tex1_view, GL_TEXTURE_2D, tex1, GL_R8, level, 1, 0, 1);
 894
 895                 // Create a new texture; we could be fancy and render use a multi-level
 896                 // texture, but meh.
 897                 GLuint grad0_tex;
 898                 glCreateTextures(GL_TEXTURE_2D, 1, &grad0_tex);
 899                 glTextureStorage2D(grad0_tex, 1, GL_RG16F, level_width, level_height);
 900
 901                 // Find the derivative.
 902                 sobel.exec(tex0_view, grad0_tex, level_width, level_height);
 903
 904                 // Motion search to find the initial flow. We use the flow from the previous
 905                 // level (sampled bilinearly; no fancy tricks) as a guide, then search from there.
 906
 907                 // Create an output flow texture.
 908                 GLuint flow_out_tex;
 909                 glCreateTextures(GL_TEXTURE_2D, 1, &flow_out_tex);
 910                 glTextureStorage2D(flow_out_tex, 1, GL_RGB16F, width_patches, height_patches);
 911
 912                 // And draw.
 913                 motion_search.exec(tex0_view, tex1_view, grad0_tex, prev_level_flow_tex, flow_out_tex, level_width, level_height, width_patches, height_patches);
 914
 915                 // Densification.
 916
 917                 // Set up an output texture (initially zero).
 918                 GLuint dense_flow_tex;
 919                 glCreateTextures(GL_TEXTURE_2D, 1, &dense_flow_tex);
 920                 glTextureStorage2D(dense_flow_tex, 1, GL_RGB16F, level_width, level_height);
 921
 922                 // And draw.
 923                 densify.exec(tex0_view, tex1_view, flow_out_tex, dense_flow_tex, level_width, level_height, width_patches, height_patches);
 924
 925                 // Everything below here in the loop belongs to variational refinement.
 926                 // It is not done yet.
 927
 928                 // Prewarping; create I and I_t.
 929                 GLuint I_tex, I_t_tex;
 930                 glCreateTextures(GL_TEXTURE_2D, 1, &I_tex);
 931                 glCreateTextures(GL_TEXTURE_2D, 1, &I_t_tex);
 932                 glTextureStorage2D(I_tex, 1, GL_R16F, level_width, level_height);
 933                 glTextureStorage2D(I_t_tex, 1, GL_R16F, level_width, level_height);
 934                 prewarp.exec(tex0_view, tex1_view, dense_flow_tex, I_tex, I_t_tex, level_width, level_height);
 935
 936                 // Calculate I_x and I_y. We're only calculating first derivatives;
 937                 // the others will be taken on-the-fly in order to sample from fewer
 938                 // textures overall, since sampling from the L1 cache is cheap.
 939                 // (TODO: Verify that this is indeed faster than making separate
 940                 // double-derivative textures.)
 941                 GLuint I_x_y_tex, beta_0_tex;
 942                 glCreateTextures(GL_TEXTURE_2D, 1, &I_x_y_tex);
 943                 glCreateTextures(GL_TEXTURE_2D, 1, &beta_0_tex);
 944                 glTextureStorage2D(I_x_y_tex, 1, GL_RG16F, level_width, level_height);
 945                 glTextureStorage2D(beta_0_tex, 1, GL_R16F, level_width, level_height);
 946                 derivatives.exec(I_tex, I_x_y_tex, beta_0_tex, level_width, level_height);
 947
 948                 // We need somewhere to store du and dv (the flow increment, relative
 949                 // to the non-refined base flow u0 and v0). It starts at zero.
 950                 GLuint du_dv_tex;
 951                 glCreateTextures(GL_TEXTURE_2D, 1, &du_dv_tex);
 952                 glTextureStorage2D(du_dv_tex, 1, GL_RG16F, level_width, level_height);
 953
 954                 // And for smoothness.
 955                 GLuint smoothness_x_tex, smoothness_y_tex;
 956                 glCreateTextures(GL_TEXTURE_2D, 1, &smoothness_x_tex);
 957                 glCreateTextures(GL_TEXTURE_2D, 1, &smoothness_y_tex);
 958                 glTextureStorage2D(smoothness_x_tex, 1, GL_R16F, level_width, level_height);
 959                 glTextureStorage2D(smoothness_y_tex, 1, GL_R16F, level_width, level_height);
 960
 961                 // And finally for the equation set. See SetupEquations for
 962                 // the storage format.
 963                 GLuint equation_tex;
 964                 glCreateTextures(GL_TEXTURE_2D, 1, &equation_tex);
 965                 glTextureStorage2D(equation_tex, 1, GL_RGBA32UI, level_width, level_height);
 966
 967                 for (int outer_idx = 0; outer_idx < level + 1; ++outer_idx) {
 968                         // Calculate the smoothness terms between the neighboring pixels,
 969                         // both in x and y direction.
 970                         compute_smoothness.exec(dense_flow_tex, du_dv_tex, smoothness_x_tex, smoothness_y_tex, level_width, level_height);
 971
 972                         // Set up the 2x2 equation system for each pixel.
 973                         setup_equations.exec(I_x_y_tex, I_t_tex, du_dv_tex, dense_flow_tex, beta_0_tex, smoothness_x_tex, smoothness_y_tex, equation_tex, level_width, level_height);
 974
 975                         // Run a few SOR (or quasi-SOR, since we're not really Jacobi) iterations.
 976                         // Note that these are to/from the same texture.
 977                         sor.exec(du_dv_tex, equation_tex, smoothness_x_tex, smoothness_y_tex, level_width, level_height, 5);
 978                 }
 979
 980                 // Add the differential flow found by the variational refinement to the base flow,
 981                 // giving the final flow estimate for this level.
 982                 // The output is in diff_flow_tex; we don't need to make a new texture.
 983                 add_base_flow.exec(dense_flow_tex, du_dv_tex, level_width, level_height);
 984
 985                 prev_level_flow_tex = du_dv_tex;
 986         }
 987         glEndQuery(GL_TIME_ELAPSED);
 988
 989         GLint available;
 990         do {
 991                 glGetQueryObjectiv(query, GL_QUERY_RESULT_AVAILABLE, &available);
 992                 usleep(1000);
 993         } while (!available);
 994         GLuint64 time_elapsed;
 995         glGetQueryObjectui64v(query, GL_QUERY_RESULT, &time_elapsed);
 996         fprintf(stderr, "GPU time used = %.1f ms\n", time_elapsed / 1e6);
 997
 998         int level_width = WIDTH >> finest_level;
 999         int level_height = HEIGHT >> finest_level;
1000         unique_ptr<float[]> dense_flow(new float[level_width * level_height * 2]);
1001         glGetTextureImage(prev_level_flow_tex, 0, GL_RG, GL_FLOAT, level_width * level_height * 2 * sizeof(float), dense_flow.get());
1002
1003         FILE *fp = fopen("flow.ppm", "wb");
1004         FILE *flowfp = fopen("flow.flo", "wb");
1005         fprintf(fp, "P6\n%d %d\n255\n", level_width, level_height);
1006         fprintf(flowfp, "FEIH");
1007         fwrite(&level_width, 4, 1, flowfp);
1008         fwrite(&level_height, 4, 1, flowfp);
1009         for (unsigned y = 0; y < unsigned(level_height); ++y) {
1010                 int yy = level_height - y - 1;
1011                 for (unsigned x = 0; x < unsigned(level_width); ++x) {
1012                         float du = dense_flow[(yy * level_width + x) * 2 + 0];
1013                         float dv = dense_flow[(yy * level_width + x) * 2 + 1];
1014
1015                         du = du * level_width;
1016                         dv = -dv * level_height;
1017
1018                         fwrite(&du, 4, 1, flowfp);
1019                         fwrite(&dv, 4, 1, flowfp);
1020
1021                         uint8_t r, g, b;
1022                         flow2rgb(du, dv, &r, &g, &b);
1023                         putc(r, fp);
1024                         putc(g, fp);
1025                         putc(b, fp);
1026                 }
1027         }
1028         fclose(fp);
1029         fclose(flowfp);
1030
1031         fprintf(stderr, "err = %d\n", glGetError());
1032 }