aom_dsp/flow_estimation/ransac.c - aom - Git at Google

 /*
  * Copyright (c) 2016, Alliance for Open Media. All rights reserved
  *
  * This source code is subject to the terms of the BSD 2 Clause License and
  * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
  * was not distributed with this source code in the LICENSE file, you can
  * obtain it at www.aomedia.org/license/software. If the Alliance for Open
  * Media Patent License 1.0 was not distributed with this source code in the
  * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
  */

 #include <memory.h>
 #include <math.h>
 #include <time.h>
 #include <stdio.h>
 #include <stdbool.h>
 #include <assert.h>

 #include "aom_dsp/flow_estimation/ransac.h"
 #include "aom_dsp/mathutils.h"
 #include "aom_mem/aom_mem.h"

 // TODO(rachelbarker): Remove dependence on code in av1/encoder/
 #include "av1/encoder/random.h"

 #define MAX_MINPTS 4
 #define MAX_DEGENERATE_ITER 10
 #define MINPTS_MULTIPLIER 5

 #define INLIER_THRESHOLD 1.25
 #define MIN_TRIALS 20

 // Flag to enable functions for finding TRANSLATION type models.
 //
 // These modes are not considered currently due to a spec bug (see comments
 // in gm_get_motion_vector() in av1/common/mv.h). Thus we don't need to compile
 // the corresponding search functions, but it is nice to keep the source around
 // but disabled, for completeness.
 #define ALLOW_TRANSLATION_MODELS 0

 ////////////////////////////////////////////////////////////////////////////////
 // ransac
 typedef bool (*IsDegenerateFunc)(double *p);
 typedef bool (*FindTransformationFunc)(int points, const double *points1,
                                        const double *points2, double *params);
 typedef void (*ProjectPointsFunc)(const double *mat, const double *points,
                                   double *proj, int n, int stride_points,
                                   int stride_proj);

 // vtable-like structure which stores all of the information needed by RANSAC
 // for a particular model type
 typedef struct {
   IsDegenerateFunc is_degenerate;
   FindTransformationFunc find_transformation;
   ProjectPointsFunc project_points;
   int minpts;
 } RansacModelInfo;

 #if ALLOW_TRANSLATION_MODELS
 static void project_points_translation(const double *mat, const double *points,
                                        double *proj, int n, int stride_points,
                                        int stride_proj) {
   int i;
   for (i = 0; i < n; ++i) {
     const double x = *(points++), y = *(points++);
     *(proj++) = x + mat[0];
     *(proj++) = y + mat[1];
     points += stride_points - 2;
     proj += stride_proj - 2;
   }
 }
 #endif  // ALLOW_TRANSLATION_MODELS

 static void project_points_affine(const double *mat, const double *points,
                                   double *proj, int n, int stride_points,
                                   int stride_proj) {
   int i;
   for (i = 0; i < n; ++i) {
     const double x = *(points++), y = *(points++);
     *(proj++) = mat[2] * x + mat[3] * y + mat[0];
     *(proj++) = mat[4] * x + mat[5] * y + mat[1];
     points += stride_points - 2;
     proj += stride_proj - 2;
   }
 }

 #if ALLOW_TRANSLATION_MODELS
 static bool find_translation(int np, const double *pts1, const double *pts2,
                              double *params) {
   double sumx = 0;
   double sumy = 0;

   for (int i = 0; i < np; ++i) {
     double dx = *(pts2++);
     double dy = *(pts2++);
     double sx = *(pts1++);
     double sy = *(pts1++);

     sumx += dx - sx;
     sumy += dy - sy;
   }

   params[0] = sumx / np;
   params[1] = sumy / np;
   params[2] = 1;
   params[3] = 0;
   params[4] = 0;
   params[5] = 1;
   return true;
 }
 #endif  // ALLOW_TRANSLATION_MODELS

 static bool find_rotzoom(int np, const double *pts1, const double *pts2,
                          double *params) {
   const int n = 4;    // Size of least-squares problem
   double mat[4 * 4];  // Accumulator for A'A
   double y[4];        // Accumulator for A'b
   double x[4];        // Output vector
   double a[4];        // Single row of A
   double b;           // Single element of b

   least_squares_init(mat, y, n);
   for (int i = 0; i < np; ++i) {
     double dx = *(pts2++);
     double dy = *(pts2++);
     double sx = *(pts1++);
     double sy = *(pts1++);

     a[0] = sx;
     a[1] = sy;
     a[2] = 1;
     a[3] = 0;
     b = dx;
     least_squares_accumulate(mat, y, a, b, n);

     a[0] = sy;
     a[1] = -sx;
     a[2] = 0;
     a[3] = 1;
     b = dy;
     least_squares_accumulate(mat, y, a, b, n);
   }

   if (!least_squares_solve(mat, y, x, n)) {
     return false;
   }

   // Rearrange least squares result to form output model
   params[0] = x[2];
   params[1] = x[3];
   params[2] = x[0];
   params[3] = x[1];
   params[4] = -params[3];
   params[5] = params[2];

   return true;
 }

 // TODO(rachelbarker): As the x and y equations are decoupled in find_affine(),
 // the least-squares problem can be split this into two 3-dimensional problems,
 // which should be faster to solve.
 static bool find_affine(int np, const double *pts1, const double *pts2,
                         double *params) {
   const int n = 6;    // Size of least-squares problem
   double mat[6 * 6];  // Accumulator for A'A
   double y[6];        // Accumulator for A'b
   double x[6];        // Output vector
   double a[6];        // Single row of A
   double b;           // Single element of b

   least_squares_init(mat, y, n);
   for (int i = 0; i < np; ++i) {
     double dx = *(pts2++);
     double dy = *(pts2++);
     double sx = *(pts1++);
     double sy = *(pts1++);

     a[0] = sx;
     a[1] = sy;
     a[2] = 0;
     a[3] = 0;
     a[4] = 1;
     a[5] = 0;
     b = dx;
     least_squares_accumulate(mat, y, a, b, n);

     a[0] = 0;
     a[1] = 0;
     a[2] = sx;
     a[3] = sy;
     a[4] = 0;
     a[5] = 1;
     b = dy;
     least_squares_accumulate(mat, y, a, b, n);
   }

   if (!least_squares_solve(mat, y, x, n)) {
     return false;
   }

   // Rearrange least squares result to form output model
   params[0] = mat[4];
   params[1] = mat[5];
   params[2] = mat[0];
   params[3] = mat[1];
   params[4] = mat[2];
   params[5] = mat[3];

   return true;
 }

 // Returns true on success, false if not enough points provided
 static bool get_rand_indices(int npoints, int minpts, int *indices,
                              unsigned int *seed) {
   int i, j;
   int ptr = lcg_rand16(seed) % npoints;
   if (minpts > npoints) return false;
   indices[0] = ptr;
   ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
   i = 1;
   while (i < minpts) {
     int index = lcg_rand16(seed) % npoints;
     while (index) {
       ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
       for (j = 0; j < i; ++j) {
         if (indices[j] == ptr) break;
       }
       if (j == i) index--;
     }
     indices[i++] = ptr;
   }
   return true;
 }

 typedef struct {
   int num_inliers;
   double variance;
   int *inlier_indices;
 } RANSAC_MOTION;

 // Return -1 if 'a' is a better motion, 1 if 'b' is better, 0 otherwise.
 static int compare_motions(const void *arg_a, const void *arg_b) {
   const RANSAC_MOTION *motion_a = (RANSAC_MOTION *)arg_a;
   const RANSAC_MOTION *motion_b = (RANSAC_MOTION *)arg_b;

   if (motion_a->num_inliers > motion_b->num_inliers) return -1;
   if (motion_a->num_inliers < motion_b->num_inliers) return 1;
   if (motion_a->variance < motion_b->variance) return -1;
   if (motion_a->variance > motion_b->variance) return 1;
   return 0;
 }

 static bool is_better_motion(const RANSAC_MOTION *motion_a,
                              const RANSAC_MOTION *motion_b) {
   return compare_motions(motion_a, motion_b) < 0;
 }

 static void copy_points_at_indices(double *dest, const double *src,
                                    const int *indices, int num_points) {
   for (int i = 0; i < num_points; ++i) {
     const int index = indices[i];
     dest[i * 2] = src[index * 2];
     dest[i * 2 + 1] = src[index * 2 + 1];
   }
 }

 static const double kInfiniteVariance = 1e12;

 static void clear_motion(RANSAC_MOTION *motion, int num_points) {
   motion->num_inliers = 0;
   motion->variance = kInfiniteVariance;
   memset(motion->inlier_indices, 0,
          sizeof(*motion->inlier_indices) * num_points);
 }

 // Returns true on success, false on error
 static bool ransac_internal(const Correspondence *matched_points, int npoints,
                             MotionModel *motion_models, int num_desired_motions,
                             const RansacModelInfo *model_info) {
   int trial_count = 0;
   int i = 0;
   int minpts = model_info->minpts;
   bool ret_val = true;

   unsigned int seed = (unsigned int)npoints;

   int indices[MAX_MINPTS] = { 0 };

   double *points1, *points2;
   double *corners1, *corners2;
   double *image1_coord;

   // Store information for the num_desired_motions best transformations found
   // and the worst motion among them, as well as the motion currently under
   // consideration.
   RANSAC_MOTION *motions, *worst_kept_motion = NULL;
   RANSAC_MOTION current_motion;

   // Store the parameters and the indices of the inlier points for the motion
   // currently under consideration.
   double params_this_motion[MAX_PARAMDIM];

   for (i = 0; i < num_desired_motions; ++i) {
     motion_models[i].num_inliers = 0;
   }
   if (npoints < minpts * MINPTS_MULTIPLIER || npoints == 0) {
     return false;
   }

   points1 = (double *)aom_malloc(sizeof(*points1) * npoints * 2);
   points2 = (double *)aom_malloc(sizeof(*points2) * npoints * 2);
   corners1 = (double *)aom_malloc(sizeof(*corners1) * npoints * 2);
   corners2 = (double *)aom_malloc(sizeof(*corners2) * npoints * 2);
   image1_coord = (double *)aom_malloc(sizeof(*image1_coord) * npoints * 2);

   motions =
       (RANSAC_MOTION *)aom_malloc(sizeof(RANSAC_MOTION) * num_desired_motions);
   for (i = 0; i < num_desired_motions; ++i) {
     motions[i].inlier_indices =
         (int *)aom_malloc(sizeof(*motions->inlier_indices) * npoints);
     clear_motion(motions + i, npoints);
   }
   current_motion.inlier_indices =
       (int *)aom_malloc(sizeof(*current_motion.inlier_indices) * npoints);
   clear_motion(&current_motion, npoints);

   worst_kept_motion = motions;

   if (!(points1 && points2 && corners1 && corners2 && image1_coord && motions &&
         current_motion.inlier_indices)) {
     ret_val = false;
     goto finish_ransac;
   }

   for (i = 0; i < npoints; ++i) {
     corners1[2 * i + 0] = matched_points[i].x;
     corners1[2 * i + 1] = matched_points[i].y;
     corners2[2 * i + 0] = matched_points[i].rx;
     corners2[2 * i + 1] = matched_points[i].ry;
   }

   while (MIN_TRIALS > trial_count) {
     double sum_distance = 0.0;
     double sum_distance_squared = 0.0;

     clear_motion(&current_motion, npoints);

     int degenerate = 1;
     int num_degenerate_iter = 0;

     while (degenerate) {
       num_degenerate_iter++;
       if (!get_rand_indices(npoints, minpts, indices, &seed)) {
         ret_val = false;
         goto finish_ransac;
       }

       copy_points_at_indices(points1, corners1, indices, minpts);
       copy_points_at_indices(points2, corners2, indices, minpts);

       degenerate = model_info->is_degenerate(points1);
       if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
         ret_val = false;
         goto finish_ransac;
       }
     }

     if (!model_info->find_transformation(minpts, points1, points2,
                                          params_this_motion)) {
       trial_count++;
       continue;
     }

     model_info->project_points(params_this_motion, corners1, image1_coord,
                                npoints, 2, 2);

     for (i = 0; i < npoints; ++i) {
       double dx = image1_coord[i * 2] - corners2[i * 2];
       double dy = image1_coord[i * 2 + 1] - corners2[i * 2 + 1];
       double distance = sqrt(dx * dx + dy * dy);

       if (distance < INLIER_THRESHOLD) {
         current_motion.inlier_indices[current_motion.num_inliers++] = i;
         sum_distance += distance;
         sum_distance_squared += distance * distance;
       }
     }

     if (current_motion.num_inliers >= worst_kept_motion->num_inliers &&
         current_motion.num_inliers > 1) {
       double mean_distance;
       mean_distance = sum_distance / ((double)current_motion.num_inliers);
       current_motion.variance =
           sum_distance_squared / ((double)current_motion.num_inliers - 1.0) -
           mean_distance * mean_distance * ((double)current_motion.num_inliers) /
               ((double)current_motion.num_inliers - 1.0);
       if (is_better_motion(&current_motion, worst_kept_motion)) {
         // This motion is better than the worst currently kept motion. Remember
         // the inlier points and variance. The parameters for each kept motion
         // will be recomputed later using only the inliers.
         worst_kept_motion->num_inliers = current_motion.num_inliers;
         worst_kept_motion->variance = current_motion.variance;
         memcpy(worst_kept_motion->inlier_indices, current_motion.inlier_indices,
                sizeof(*current_motion.inlier_indices) * npoints);
         assert(npoints > 0);
         // Determine the new worst kept motion and its num_inliers and variance.
         for (i = 0; i < num_desired_motions; ++i) {
           if (is_better_motion(worst_kept_motion, &motions[i])) {
             worst_kept_motion = &motions[i];
           }
         }
       }
     }
     trial_count++;
   }

   // Sort the motions, best first.
   qsort(motions, num_desired_motions, sizeof(RANSAC_MOTION), compare_motions);

   // Recompute the motions using only the inliers.
   for (i = 0; i < num_desired_motions; ++i) {
     if (motions[i].num_inliers >= minpts) {
       int num_inliers = motions[i].num_inliers;
       copy_points_at_indices(points1, corners1, motions[i].inlier_indices,
                              num_inliers);
       copy_points_at_indices(points2, corners2, motions[i].inlier_indices,
                              num_inliers);

       model_info->find_transformation(num_inliers, points1, points2,
                                       motion_models[i].params);

       // Populate inliers array
       for (int j = 0; j < num_inliers; j++) {
         int index = motions[i].inlier_indices[j];
         const Correspondence *corr = &matched_points[index];
         motion_models[i].inliers[2 * j + 0] = (int)rint(corr->x);
         motion_models[i].inliers[2 * j + 1] = (int)rint(corr->y);
       }
     }
     motion_models[i].num_inliers = motions[i].num_inliers;
   }

 finish_ransac:
   aom_free(points1);
   aom_free(points2);
   aom_free(corners1);
   aom_free(corners2);
   aom_free(image1_coord);
   aom_free(current_motion.inlier_indices);
   if (motions) {
     for (i = 0; i < num_desired_motions; ++i) {
       aom_free(motions[i].inlier_indices);
     }
     aom_free(motions);
   }

   return ret_val;
 }

 static bool is_collinear3(double *p1, double *p2, double *p3) {
   static const double collinear_eps = 1e-3;
   const double v =
       (p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0]);
   return fabs(v) < collinear_eps;
 }

 #if ALLOW_TRANSLATION_MODELS
 static bool is_degenerate_translation(double *p) {
   return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
 }
 #endif  // ALLOW_TRANSLATION_MODELS

 static bool is_degenerate_affine(double *p) {
   return is_collinear3(p, p + 2, p + 4);
 }

 static const RansacModelInfo ransac_model_info[TRANS_TYPES] = {
   // IDENTITY
   { NULL, NULL, NULL, 0 },
 // TRANSLATION
 #if ALLOW_TRANSLATION_MODELS
   { is_degenerate_translation, find_translation, project_points_translation,
     3 },
 #else
   { NULL, NULL, NULL, 0 },
 #endif
   // ROTZOOM
   { is_degenerate_affine, find_rotzoom, project_points_affine, 3 },
   // AFFINE
   { is_degenerate_affine, find_affine, project_points_affine, 3 },
 };

 // Returns true on success, false on error
 bool ransac(const Correspondence *matched_points, int npoints,
             TransformationType type, MotionModel *motion_models,
             int num_desired_motions) {
 #if ALLOW_TRANSLATION_MODELS
   assert(type > IDENTITY && type < TRANS_TYPES);
 #else
   assert(type > TRANSLATION && type < TRANS_TYPES);
 #endif  // ALLOW_TRANSLATION_MODELS

   return ransac_internal(matched_points, npoints, motion_models,
                          num_desired_motions, &ransac_model_info[type]);
 }
	/*
	* Copyright (c) 2016, Alliance for Open Media. All rights reserved
	*
	* This source code is subject to the terms of the BSD 2 Clause License and
	* the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
	* was not distributed with this source code in the LICENSE file, you can
	* obtain it at www.aomedia.org/license/software. If the Alliance for Open
	* Media Patent License 1.0 was not distributed with this source code in the
	* PATENTS file, you can obtain it at www.aomedia.org/license/patent.
	*/

	#include <memory.h>
	#include <math.h>
	#include <time.h>
	#include <stdio.h>
	#include <stdbool.h>
	#include <assert.h>

	#include "aom_dsp/flow_estimation/ransac.h"
	#include "aom_dsp/mathutils.h"
	#include "aom_mem/aom_mem.h"

	// TODO(rachelbarker): Remove dependence on code in av1/encoder/
	#include "av1/encoder/random.h"

	#define MAX_MINPTS 4
	#define MAX_DEGENERATE_ITER 10
	#define MINPTS_MULTIPLIER 5

	#define INLIER_THRESHOLD 1.25
	#define MIN_TRIALS 20

	// Flag to enable functions for finding TRANSLATION type models.
	//
	// These modes are not considered currently due to a spec bug (see comments
	// in gm_get_motion_vector() in av1/common/mv.h). Thus we don't need to compile
	// the corresponding search functions, but it is nice to keep the source around
	// but disabled, for completeness.
	#define ALLOW_TRANSLATION_MODELS 0

	////////////////////////////////////////////////////////////////////////////////
	// ransac
	typedef bool (IsDegenerateFunc)(double p);
	typedef bool (FindTransformationFunc)(int points, const double points1,
	const double points2, double params);
	typedef void (ProjectPointsFunc)(const double mat, const double *points,
	double *proj, int n, int stride_points,
	int stride_proj);

	// vtable-like structure which stores all of the information needed by RANSAC
	// for a particular model type
	typedef struct {
	IsDegenerateFunc is_degenerate;
	FindTransformationFunc find_transformation;
	ProjectPointsFunc project_points;
	int minpts;
	} RansacModelInfo;

	#if ALLOW_TRANSLATION_MODELS
	static void project_points_translation(const double mat, const double points,
	double *proj, int n, int stride_points,
	int stride_proj) {
	int i;
	for (i = 0; i < n; ++i) {
	const double x = (points++), y = (points++);
	*(proj++) = x + mat[0];
	*(proj++) = y + mat[1];
	points += stride_points - 2;
	proj += stride_proj - 2;
	}
	}
	#endif // ALLOW_TRANSLATION_MODELS

	static void project_points_affine(const double mat, const double points,
	double *proj, int n, int stride_points,
	int stride_proj) {
	int i;
	for (i = 0; i < n; ++i) {
	const double x = (points++), y = (points++);
	(proj++) = mat[2] x + mat[3] * y + mat[0];
	(proj++) = mat[4] x + mat[5] * y + mat[1];
	points += stride_points - 2;
	proj += stride_proj - 2;
	}
	}

	#if ALLOW_TRANSLATION_MODELS
	static bool find_translation(int np, const double pts1, const double pts2,
	double *params) {
	double sumx = 0;
	double sumy = 0;

	for (int i = 0; i < np; ++i) {
	double dx = *(pts2++);
	double dy = *(pts2++);
	double sx = *(pts1++);
	double sy = *(pts1++);

	sumx += dx - sx;
	sumy += dy - sy;
	}

	params[0] = sumx / np;
	params[1] = sumy / np;
	params[2] = 1;
	params[3] = 0;
	params[4] = 0;
	params[5] = 1;
	return true;
	}
	#endif // ALLOW_TRANSLATION_MODELS

	static bool find_rotzoom(int np, const double pts1, const double pts2,
	double *params) {
	const int n = 4; // Size of least-squares problem
	double mat[4 * 4]; // Accumulator for A'A
	double y[4]; // Accumulator for A'b
	double x[4]; // Output vector
	double a[4]; // Single row of A
	double b; // Single element of b

	least_squares_init(mat, y, n);
	for (int i = 0; i < np; ++i) {
	double dx = *(pts2++);
	double dy = *(pts2++);
	double sx = *(pts1++);
	double sy = *(pts1++);

	a[0] = sx;
	a[1] = sy;
	a[2] = 1;
	a[3] = 0;
	b = dx;
	least_squares_accumulate(mat, y, a, b, n);

	a[0] = sy;
	a[1] = -sx;
	a[2] = 0;
	a[3] = 1;
	b = dy;
	least_squares_accumulate(mat, y, a, b, n);
	}

	if (!least_squares_solve(mat, y, x, n)) {
	return false;
	}

	// Rearrange least squares result to form output model
	params[0] = x[2];
	params[1] = x[3];
	params[2] = x[0];
	params[3] = x[1];
	params[4] = -params[3];
	params[5] = params[2];

	return true;
	}

	// TODO(rachelbarker): As the x and y equations are decoupled in find_affine(),
	// the least-squares problem can be split this into two 3-dimensional problems,
	// which should be faster to solve.
	static bool find_affine(int np, const double pts1, const double pts2,
	double *params) {
	const int n = 6; // Size of least-squares problem
	double mat[6 * 6]; // Accumulator for A'A
	double y[6]; // Accumulator for A'b
	double x[6]; // Output vector
	double a[6]; // Single row of A
	double b; // Single element of b

	least_squares_init(mat, y, n);
	for (int i = 0; i < np; ++i) {
	double dx = *(pts2++);
	double dy = *(pts2++);
	double sx = *(pts1++);
	double sy = *(pts1++);

	a[0] = sx;
	a[1] = sy;
	a[2] = 0;
	a[3] = 0;
	a[4] = 1;
	a[5] = 0;
	b = dx;
	least_squares_accumulate(mat, y, a, b, n);

	a[0] = 0;
	a[1] = 0;
	a[2] = sx;
	a[3] = sy;
	a[4] = 0;
	a[5] = 1;
	b = dy;
	least_squares_accumulate(mat, y, a, b, n);
	}

	if (!least_squares_solve(mat, y, x, n)) {
	return false;
	}

	// Rearrange least squares result to form output model
	params[0] = mat[4];
	params[1] = mat[5];
	params[2] = mat[0];
	params[3] = mat[1];
	params[4] = mat[2];
	params[5] = mat[3];

	return true;
	}

	// Returns true on success, false if not enough points provided
	static bool get_rand_indices(int npoints, int minpts, int *indices,
	unsigned int *seed) {
	int i, j;
	int ptr = lcg_rand16(seed) % npoints;
	if (minpts > npoints) return false;
	indices[0] = ptr;
	ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
	i = 1;
	while (i < minpts) {
	int index = lcg_rand16(seed) % npoints;
	while (index) {
	ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
	for (j = 0; j < i; ++j) {
	if (indices[j] == ptr) break;
	}
	if (j == i) index--;
	}
	indices[i++] = ptr;
	}
	return true;
	}

	typedef struct {
	int num_inliers;
	double variance;
	int *inlier_indices;
	} RANSAC_MOTION;

	// Return -1 if 'a' is a better motion, 1 if 'b' is better, 0 otherwise.
	static int compare_motions(const void arg_a, const void arg_b) {
	const RANSAC_MOTION motion_a = (RANSAC_MOTION )arg_a;
	const RANSAC_MOTION motion_b = (RANSAC_MOTION )arg_b;

	if (motion_a->num_inliers > motion_b->num_inliers) return -1;
	if (motion_a->num_inliers < motion_b->num_inliers) return 1;
	if (motion_a->variance < motion_b->variance) return -1;
	if (motion_a->variance > motion_b->variance) return 1;
	return 0;
	}

	static bool is_better_motion(const RANSAC_MOTION *motion_a,
	const RANSAC_MOTION *motion_b) {
	return compare_motions(motion_a, motion_b) < 0;
	}

	static void copy_points_at_indices(double dest, const double src,
	const int *indices, int num_points) {
	for (int i = 0; i < num_points; ++i) {
	const int index = indices[i];
	dest[i * 2] = src[index * 2];
	dest[i * 2 + 1] = src[index * 2 + 1];
	}
	}

	static const double kInfiniteVariance = 1e12;

	static void clear_motion(RANSAC_MOTION *motion, int num_points) {
	motion->num_inliers = 0;
	motion->variance = kInfiniteVariance;
	memset(motion->inlier_indices, 0,
	sizeof(motion->inlier_indices) num_points);
	}

	// Returns true on success, false on error
	static bool ransac_internal(const Correspondence *matched_points, int npoints,
	MotionModel *motion_models, int num_desired_motions,
	const RansacModelInfo *model_info) {
	int trial_count = 0;
	int i = 0;
	int minpts = model_info->minpts;
	bool ret_val = true;

	unsigned int seed = (unsigned int)npoints;

	int indices[MAX_MINPTS] = { 0 };

	double points1, points2;
	double corners1, corners2;
	double *image1_coord;

	// Store information for the num_desired_motions best transformations found
	// and the worst motion among them, as well as the motion currently under
	// consideration.
	RANSAC_MOTION motions, worst_kept_motion = NULL;
	RANSAC_MOTION current_motion;

	// Store the parameters and the indices of the inlier points for the motion
	// currently under consideration.
	double params_this_motion[MAX_PARAMDIM];

	for (i = 0; i < num_desired_motions; ++i) {
	motion_models[i].num_inliers = 0;
	}
	if (npoints < minpts * MINPTS_MULTIPLIER \|\| npoints == 0) {
	return false;
	}

	points1 = (double )aom_malloc(sizeof(points1) * npoints * 2);
	points2 = (double )aom_malloc(sizeof(points2) * npoints * 2);
	corners1 = (double )aom_malloc(sizeof(corners1) * npoints * 2);
	corners2 = (double )aom_malloc(sizeof(corners2) * npoints * 2);
	image1_coord = (double )aom_malloc(sizeof(image1_coord) * npoints * 2);

	motions =
	(RANSAC_MOTION )aom_malloc(sizeof(RANSAC_MOTION) num_desired_motions);
	for (i = 0; i < num_desired_motions; ++i) {
	motions[i].inlier_indices =
	(int )aom_malloc(sizeof(motions->inlier_indices) * npoints);
	clear_motion(motions + i, npoints);
	}
	current_motion.inlier_indices =
	(int )aom_malloc(sizeof(current_motion.inlier_indices) * npoints);
	clear_motion(&current_motion, npoints);

	worst_kept_motion = motions;

	if (!(points1 && points2 && corners1 && corners2 && image1_coord && motions &&
	current_motion.inlier_indices)) {
	ret_val = false;
	goto finish_ransac;
	}

	for (i = 0; i < npoints; ++i) {
	corners1[2 * i + 0] = matched_points[i].x;
	corners1[2 * i + 1] = matched_points[i].y;
	corners2[2 * i + 0] = matched_points[i].rx;
	corners2[2 * i + 1] = matched_points[i].ry;
	}

	while (MIN_TRIALS > trial_count) {
	double sum_distance = 0.0;
	double sum_distance_squared = 0.0;

	clear_motion(&current_motion, npoints);

	int degenerate = 1;
	int num_degenerate_iter = 0;

	while (degenerate) {
	num_degenerate_iter++;
	if (!get_rand_indices(npoints, minpts, indices, &seed)) {
	ret_val = false;
	goto finish_ransac;
	}

	copy_points_at_indices(points1, corners1, indices, minpts);
	copy_points_at_indices(points2, corners2, indices, minpts);

	degenerate = model_info->is_degenerate(points1);
	if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
	ret_val = false;
	goto finish_ransac;
	}
	}

	if (!model_info->find_transformation(minpts, points1, points2,
	params_this_motion)) {
	trial_count++;
	continue;
	}

	model_info->project_points(params_this_motion, corners1, image1_coord,
	npoints, 2, 2);

	for (i = 0; i < npoints; ++i) {
	double dx = image1_coord[i * 2] - corners2[i * 2];
	double dy = image1_coord[i * 2 + 1] - corners2[i * 2 + 1];
	double distance = sqrt(dx * dx + dy * dy);

	if (distance < INLIER_THRESHOLD) {
	current_motion.inlier_indices[current_motion.num_inliers++] = i;
	sum_distance += distance;
	sum_distance_squared += distance * distance;
	}
	}

	if (current_motion.num_inliers >= worst_kept_motion->num_inliers &&
	current_motion.num_inliers > 1) {
	double mean_distance;
	mean_distance = sum_distance / ((double)current_motion.num_inliers);
	current_motion.variance =
	sum_distance_squared / ((double)current_motion.num_inliers - 1.0) -
	mean_distance * mean_distance * ((double)current_motion.num_inliers) /
	((double)current_motion.num_inliers - 1.0);
	if (is_better_motion(&current_motion, worst_kept_motion)) {
	// This motion is better than the worst currently kept motion. Remember
	// the inlier points and variance. The parameters for each kept motion
	// will be recomputed later using only the inliers.
	worst_kept_motion->num_inliers = current_motion.num_inliers;
	worst_kept_motion->variance = current_motion.variance;
	memcpy(worst_kept_motion->inlier_indices, current_motion.inlier_indices,
	sizeof(current_motion.inlier_indices) npoints);
	assert(npoints > 0);
	// Determine the new worst kept motion and its num_inliers and variance.
	for (i = 0; i < num_desired_motions; ++i) {
	if (is_better_motion(worst_kept_motion, &motions[i])) {
	worst_kept_motion = &motions[i];
	}
	}
	}
	}
	trial_count++;
	}

	// Sort the motions, best first.
	qsort(motions, num_desired_motions, sizeof(RANSAC_MOTION), compare_motions);

	// Recompute the motions using only the inliers.
	for (i = 0; i < num_desired_motions; ++i) {
	if (motions[i].num_inliers >= minpts) {
	int num_inliers = motions[i].num_inliers;
	copy_points_at_indices(points1, corners1, motions[i].inlier_indices,
	num_inliers);
	copy_points_at_indices(points2, corners2, motions[i].inlier_indices,
	num_inliers);

	model_info->find_transformation(num_inliers, points1, points2,
	motion_models[i].params);

	// Populate inliers array
	for (int j = 0; j < num_inliers; j++) {
	int index = motions[i].inlier_indices[j];
	const Correspondence *corr = &matched_points[index];
	motion_models[i].inliers[2 * j + 0] = (int)rint(corr->x);
	motion_models[i].inliers[2 * j + 1] = (int)rint(corr->y);
	}
	}
	motion_models[i].num_inliers = motions[i].num_inliers;
	}

	finish_ransac:
	aom_free(points1);
	aom_free(points2);
	aom_free(corners1);
	aom_free(corners2);
	aom_free(image1_coord);
	aom_free(current_motion.inlier_indices);
	if (motions) {
	for (i = 0; i < num_desired_motions; ++i) {
	aom_free(motions[i].inlier_indices);
	}
	aom_free(motions);
	}

	return ret_val;
	}

	static bool is_collinear3(double p1, double p2, double *p3) {
	static const double collinear_eps = 1e-3;
	const double v =
	(p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0]);
	return fabs(v) < collinear_eps;
	}

	#if ALLOW_TRANSLATION_MODELS
	static bool is_degenerate_translation(double *p) {
	return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
	}
	#endif // ALLOW_TRANSLATION_MODELS

	static bool is_degenerate_affine(double *p) {
	return is_collinear3(p, p + 2, p + 4);
	}

	static const RansacModelInfo ransac_model_info[TRANS_TYPES] = {
	// IDENTITY
	{ NULL, NULL, NULL, 0 },
	// TRANSLATION
	#if ALLOW_TRANSLATION_MODELS
	{ is_degenerate_translation, find_translation, project_points_translation,
	3 },
	#else
	{ NULL, NULL, NULL, 0 },
	#endif
	// ROTZOOM
	{ is_degenerate_affine, find_rotzoom, project_points_affine, 3 },
	// AFFINE
	{ is_degenerate_affine, find_affine, project_points_affine, 3 },
	};

	// Returns true on success, false on error
	bool ransac(const Correspondence *matched_points, int npoints,
	TransformationType type, MotionModel *motion_models,
	int num_desired_motions) {
	#if ALLOW_TRANSLATION_MODELS
	assert(type > IDENTITY && type < TRANS_TYPES);
	#else
	assert(type > TRANSLATION && type < TRANS_TYPES);
	#endif // ALLOW_TRANSLATION_MODELS

	return ransac_internal(matched_points, npoints, motion_models,
	num_desired_motions, &ransac_model_info[type]);
	}