av1/encoder/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 <stdlib.h>
 #include <assert.h>

 #include "av1/encoder/ransac.h"
 #include "av1/encoder/mathutils.h"
 #include "av1/encoder/random.h"

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

 #define INLIER_THRESHOLD 1.0
 #define MIN_TRIALS 20

 ////////////////////////////////////////////////////////////////////////////////
 // ransac
 typedef int (*IsDegenerateFunc)(double *p);
 typedef void (*NormalizeFunc)(double *p, int np, double *T);
 typedef void (*DenormalizeFunc)(double *params, double *T1, double *T2);
 typedef int (*FindTransformationFunc)(int points, double *points1,
                                       double *points2, double *params);
 typedef void (*ProjectPointsDoubleFunc)(double *mat, double *points,
                                         double *proj, const int n,
                                         const int stride_points,
                                         const int stride_proj);

 static void project_points_double_translation(double *mat, double *points,
                                               double *proj, const int n,
                                               const int stride_points,
                                               const 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;
   }
 }

 static void project_points_double_rotzoom(double *mat, double *points,
                                           double *proj, const int n,
                                           const int stride_points,
                                           const 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[3] * x + mat[2] * y + mat[1];
     points += stride_points - 2;
     proj += stride_proj - 2;
   }
 }

 static void project_points_double_affine(double *mat, double *points,
                                          double *proj, const int n,
                                          const int stride_points,
                                          const 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;
   }
 }

 static void normalize_homography(double *pts, int n, double *T) {
   double *p = pts;
   double mean[2] = { 0, 0 };
   double msqe = 0;
   double scale;
   int i;

   assert(n > 0);
   for (i = 0; i < n; ++i, p += 2) {
     mean[0] += p[0];
     mean[1] += p[1];
   }
   mean[0] /= n;
   mean[1] /= n;
   for (p = pts, i = 0; i < n; ++i, p += 2) {
     p[0] -= mean[0];
     p[1] -= mean[1];
     msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
   }
   msqe /= n;
   scale = (msqe == 0 ? 1.0 : sqrt(2) / msqe);
   T[0] = scale;
   T[1] = 0;
   T[2] = -scale * mean[0];
   T[3] = 0;
   T[4] = scale;
   T[5] = -scale * mean[1];
   T[6] = 0;
   T[7] = 0;
   T[8] = 1;
   for (p = pts, i = 0; i < n; ++i, p += 2) {
     p[0] *= scale;
     p[1] *= scale;
   }
 }

 static void invnormalize_mat(double *T, double *iT) {
   double is = 1.0 / T[0];
   double m0 = -T[2] * is;
   double m1 = -T[5] * is;
   iT[0] = is;
   iT[1] = 0;
   iT[2] = m0;
   iT[3] = 0;
   iT[4] = is;
   iT[5] = m1;
   iT[6] = 0;
   iT[7] = 0;
   iT[8] = 1;
 }

 static void denormalize_homography(double *params, double *T1, double *T2) {
   double iT2[9];
   double params2[9];
   invnormalize_mat(T2, iT2);
   multiply_mat(params, T1, params2, 3, 3, 3);
   multiply_mat(iT2, params2, params, 3, 3, 3);
 }

 static void denormalize_affine_reorder(double *params, double *T1, double *T2) {
   double params_denorm[MAX_PARAMDIM];
   params_denorm[0] = params[0];
   params_denorm[1] = params[1];
   params_denorm[2] = params[4];
   params_denorm[3] = params[2];
   params_denorm[4] = params[3];
   params_denorm[5] = params[5];
   params_denorm[6] = params_denorm[7] = 0;
   params_denorm[8] = 1;
   denormalize_homography(params_denorm, T1, T2);
   params[0] = params_denorm[2];
   params[1] = params_denorm[5];
   params[2] = params_denorm[0];
   params[3] = params_denorm[1];
   params[4] = params_denorm[3];
   params[5] = params_denorm[4];
   params[6] = params[7] = 0;
 }

 static void denormalize_rotzoom_reorder(double *params, double *T1,
                                         double *T2) {
   double params_denorm[MAX_PARAMDIM];
   params_denorm[0] = params[0];
   params_denorm[1] = params[1];
   params_denorm[2] = params[2];
   params_denorm[3] = -params[1];
   params_denorm[4] = params[0];
   params_denorm[5] = params[3];
   params_denorm[6] = params_denorm[7] = 0;
   params_denorm[8] = 1;
   denormalize_homography(params_denorm, T1, T2);
   params[0] = params_denorm[2];
   params[1] = params_denorm[5];
   params[2] = params_denorm[0];
   params[3] = params_denorm[1];
   params[4] = -params[3];
   params[5] = params[2];
   params[6] = params[7] = 0;
 }

 static void denormalize_translation_reorder(double *params, double *T1,
                                             double *T2) {
   double params_denorm[MAX_PARAMDIM];
   params_denorm[0] = 1;
   params_denorm[1] = 0;
   params_denorm[2] = params[0];
   params_denorm[3] = 0;
   params_denorm[4] = 1;
   params_denorm[5] = params[1];
   params_denorm[6] = params_denorm[7] = 0;
   params_denorm[8] = 1;
   denormalize_homography(params_denorm, T1, T2);
   params[0] = params_denorm[2];
   params[1] = params_denorm[5];
   params[2] = params[5] = 1;
   params[3] = params[4] = 0;
   params[6] = params[7] = 0;
 }

 static int find_translation(int np, double *pts1, double *pts2, double *mat) {
   int i;
   double sx, sy, dx, dy;
   double sumx, sumy;

   double T1[9], T2[9];
   normalize_homography(pts1, np, T1);
   normalize_homography(pts2, np, T2);

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

     sumx += dx - sx;
     sumy += dy - sy;
   }
   mat[0] = sumx / np;
   mat[1] = sumy / np;
   denormalize_translation_reorder(mat, T1, T2);
   return 0;
 }

 static int find_rotzoom(int np, double *pts1, double *pts2, double *mat) {
   const int np2 = np * 2;
   double *a = (double *)aom_malloc(sizeof(*a) * (np2 * 5 + 20));
   double *b = a + np2 * 4;
   double *temp = b + np2;
   int i;
   double sx, sy, dx, dy;

   double T1[9], T2[9];
   normalize_homography(pts1, np, T1);
   normalize_homography(pts2, np, T2);

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

     a[i * 2 * 4 + 0] = sx;
     a[i * 2 * 4 + 1] = sy;
     a[i * 2 * 4 + 2] = 1;
     a[i * 2 * 4 + 3] = 0;
     a[(i * 2 + 1) * 4 + 0] = sy;
     a[(i * 2 + 1) * 4 + 1] = -sx;
     a[(i * 2 + 1) * 4 + 2] = 0;
     a[(i * 2 + 1) * 4 + 3] = 1;

     b[2 * i] = dx;
     b[2 * i + 1] = dy;
   }
   if (!least_squares(4, a, np2, 4, b, temp, mat)) {
     aom_free(a);
     return 1;
   }
   denormalize_rotzoom_reorder(mat, T1, T2);
   aom_free(a);
   return 0;
 }

 static int find_affine(int np, double *pts1, double *pts2, double *mat) {
   const int np2 = np * 2;
   double *a = (double *)aom_malloc(sizeof(*a) * (np2 * 7 + 42));
   double *b = a + np2 * 6;
   double *temp = b + np2;
   int i;
   double sx, sy, dx, dy;

   double T1[9], T2[9];
   normalize_homography(pts1, np, T1);
   normalize_homography(pts2, np, T2);

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

     a[i * 2 * 6 + 0] = sx;
     a[i * 2 * 6 + 1] = sy;
     a[i * 2 * 6 + 2] = 0;
     a[i * 2 * 6 + 3] = 0;
     a[i * 2 * 6 + 4] = 1;
     a[i * 2 * 6 + 5] = 0;
     a[(i * 2 + 1) * 6 + 0] = 0;
     a[(i * 2 + 1) * 6 + 1] = 0;
     a[(i * 2 + 1) * 6 + 2] = sx;
     a[(i * 2 + 1) * 6 + 3] = sy;
     a[(i * 2 + 1) * 6 + 4] = 0;
     a[(i * 2 + 1) * 6 + 5] = 1;

     b[2 * i] = dx;
     b[2 * i + 1] = dy;
   }
   if (!least_squares(6, a, np2, 6, b, temp, mat)) {
     aom_free(a);
     return 1;
   }
   denormalize_affine_reorder(mat, T1, T2);
   aom_free(a);
   return 0;
 }

 static int 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 0;
   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 1;
 }

 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 int 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));
 }

 static int ransac(const int *matched_points, int npoints,
                   int *num_inliers_by_motion, double *params_by_motion,
                   int num_desired_motions, const int minpts,
                   IsDegenerateFunc is_degenerate,
                   FindTransformationFunc find_transformation,
                   ProjectPointsDoubleFunc projectpoints) {
   static const double PROBABILITY_REQUIRED = 0.9;
   static const double EPS = 1e-12;

   int N = 10000, trial_count = 0;
   int i = 0;
   int ret_val = 0;

   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];

   double *cnp1, *cnp2;

   for (i = 0; i < num_desired_motions; ++i) {
     num_inliers_by_motion[i] = 0;
   }
   if (npoints < minpts * MINPTS_MULTIPLIER || npoints == 0) {
     return 1;
   }

   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 = 1;
     goto finish_ransac;
   }

   cnp1 = corners1;
   cnp2 = corners2;
   for (i = 0; i < npoints; ++i) {
     *(cnp1++) = *(matched_points++);
     *(cnp1++) = *(matched_points++);
     *(cnp2++) = *(matched_points++);
     *(cnp2++) = *(matched_points++);
   }

   while (N > 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 = 1;
         goto finish_ransac;
       }

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

       degenerate = is_degenerate(points1);
       if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
         ret_val = 1;
         goto finish_ransac;
       }
     }

     if (find_transformation(minpts, points1, points2, params_this_motion)) {
       trial_count++;
       continue;
     }

     projectpoints(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) {
       int temp;
       double fracinliers, pNoOutliers, mean_distance, dtemp;
       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);
         fracinliers = (double)current_motion.num_inliers / (double)npoints;
         pNoOutliers = 1 - pow(fracinliers, minpts);
         pNoOutliers = fmax(EPS, pNoOutliers);
         pNoOutliers = fmin(1 - EPS, pNoOutliers);
         dtemp = log(1.0 - PROBABILITY_REQUIRED) / log(pNoOutliers);
         temp = (dtemp > (double)INT32_MAX)
                    ? INT32_MAX
                    : dtemp < (double)INT32_MIN ? INT32_MIN : (int)dtemp;

         if (temp > 0 && temp < N) {
           N = AOMMAX(temp, MIN_TRIALS);
         }

         // 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) {
       copy_points_at_indices(points1, corners1, motions[i].inlier_indices,
                              motions[i].num_inliers);
       copy_points_at_indices(points2, corners2, motions[i].inlier_indices,
                              motions[i].num_inliers);

       find_transformation(motions[i].num_inliers, points1, points2,
                           params_by_motion + (MAX_PARAMDIM - 1) * i);
     }
     num_inliers_by_motion[i] = 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);
   for (i = 0; i < num_desired_motions; ++i) {
     aom_free(motions[i].inlier_indices);
   }
   aom_free(motions);

   return ret_val;
 }

 static int 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;
 }

 static int is_degenerate_translation(double *p) {
   return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
 }

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

 int ransac_translation(int *matched_points, int npoints,
                        int *num_inliers_by_motion, double *params_by_motion,
                        int num_desired_motions) {
   return ransac(matched_points, npoints, num_inliers_by_motion,
                 params_by_motion, num_desired_motions, 3,
                 is_degenerate_translation, find_translation,
                 project_points_double_translation);
 }

 int ransac_rotzoom(int *matched_points, int npoints, int *num_inliers_by_motion,
                    double *params_by_motion, int num_desired_motions) {
   return ransac(matched_points, npoints, num_inliers_by_motion,
                 params_by_motion, num_desired_motions, 3, is_degenerate_affine,
                 find_rotzoom, project_points_double_rotzoom);
 }

 int ransac_affine(int *matched_points, int npoints, int *num_inliers_by_motion,
                   double *params_by_motion, int num_desired_motions) {
   return ransac(matched_points, npoints, num_inliers_by_motion,
                 params_by_motion, num_desired_motions, 3, is_degenerate_affine,
                 find_affine, project_points_double_affine);
 }
	/*
	* 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 <stdlib.h>
	#include <assert.h>

	#include "av1/encoder/ransac.h"
	#include "av1/encoder/mathutils.h"
	#include "av1/encoder/random.h"

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

	#define INLIER_THRESHOLD 1.0
	#define MIN_TRIALS 20

	////////////////////////////////////////////////////////////////////////////////
	// ransac
	typedef int (IsDegenerateFunc)(double p);
	typedef void (NormalizeFunc)(double p, int np, double *T);
	typedef void (DenormalizeFunc)(double params, double T1, double T2);
	typedef int (FindTransformationFunc)(int points, double points1,
	double points2, double params);
	typedef void (ProjectPointsDoubleFunc)(double mat, double *points,
	double *proj, const int n,
	const int stride_points,
	const int stride_proj);

	static void project_points_double_translation(double mat, double points,
	double *proj, const int n,
	const int stride_points,
	const 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;
	}
	}

	static void project_points_double_rotzoom(double mat, double points,
	double *proj, const int n,
	const int stride_points,
	const 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[3] x + mat[2] * y + mat[1];
	points += stride_points - 2;
	proj += stride_proj - 2;
	}
	}

	static void project_points_double_affine(double mat, double points,
	double *proj, const int n,
	const int stride_points,
	const 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;
	}
	}

	static void normalize_homography(double pts, int n, double T) {
	double *p = pts;
	double mean[2] = { 0, 0 };
	double msqe = 0;
	double scale;
	int i;

	assert(n > 0);
	for (i = 0; i < n; ++i, p += 2) {
	mean[0] += p[0];
	mean[1] += p[1];
	}
	mean[0] /= n;
	mean[1] /= n;
	for (p = pts, i = 0; i < n; ++i, p += 2) {
	p[0] -= mean[0];
	p[1] -= mean[1];
	msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
	}
	msqe /= n;
	scale = (msqe == 0 ? 1.0 : sqrt(2) / msqe);
	T[0] = scale;
	T[1] = 0;
	T[2] = -scale * mean[0];
	T[3] = 0;
	T[4] = scale;
	T[5] = -scale * mean[1];
	T[6] = 0;
	T[7] = 0;
	T[8] = 1;
	for (p = pts, i = 0; i < n; ++i, p += 2) {
	p[0] *= scale;
	p[1] *= scale;
	}
	}

	static void invnormalize_mat(double T, double iT) {
	double is = 1.0 / T[0];
	double m0 = -T[2] * is;
	double m1 = -T[5] * is;
	iT[0] = is;
	iT[1] = 0;
	iT[2] = m0;
	iT[3] = 0;
	iT[4] = is;
	iT[5] = m1;
	iT[6] = 0;
	iT[7] = 0;
	iT[8] = 1;
	}

	static void denormalize_homography(double params, double T1, double *T2) {
	double iT2[9];
	double params2[9];
	invnormalize_mat(T2, iT2);
	multiply_mat(params, T1, params2, 3, 3, 3);
	multiply_mat(iT2, params2, params, 3, 3, 3);
	}

	static void denormalize_affine_reorder(double params, double T1, double *T2) {
	double params_denorm[MAX_PARAMDIM];
	params_denorm[0] = params[0];
	params_denorm[1] = params[1];
	params_denorm[2] = params[4];
	params_denorm[3] = params[2];
	params_denorm[4] = params[3];
	params_denorm[5] = params[5];
	params_denorm[6] = params_denorm[7] = 0;
	params_denorm[8] = 1;
	denormalize_homography(params_denorm, T1, T2);
	params[0] = params_denorm[2];
	params[1] = params_denorm[5];
	params[2] = params_denorm[0];
	params[3] = params_denorm[1];
	params[4] = params_denorm[3];
	params[5] = params_denorm[4];
	params[6] = params[7] = 0;
	}

	static void denormalize_rotzoom_reorder(double params, double T1,
	double *T2) {
	double params_denorm[MAX_PARAMDIM];
	params_denorm[0] = params[0];
	params_denorm[1] = params[1];
	params_denorm[2] = params[2];
	params_denorm[3] = -params[1];
	params_denorm[4] = params[0];
	params_denorm[5] = params[3];
	params_denorm[6] = params_denorm[7] = 0;
	params_denorm[8] = 1;
	denormalize_homography(params_denorm, T1, T2);
	params[0] = params_denorm[2];
	params[1] = params_denorm[5];
	params[2] = params_denorm[0];
	params[3] = params_denorm[1];
	params[4] = -params[3];
	params[5] = params[2];
	params[6] = params[7] = 0;
	}

	static void denormalize_translation_reorder(double params, double T1,
	double *T2) {
	double params_denorm[MAX_PARAMDIM];
	params_denorm[0] = 1;
	params_denorm[1] = 0;
	params_denorm[2] = params[0];
	params_denorm[3] = 0;
	params_denorm[4] = 1;
	params_denorm[5] = params[1];
	params_denorm[6] = params_denorm[7] = 0;
	params_denorm[8] = 1;
	denormalize_homography(params_denorm, T1, T2);
	params[0] = params_denorm[2];
	params[1] = params_denorm[5];
	params[2] = params[5] = 1;
	params[3] = params[4] = 0;
	params[6] = params[7] = 0;
	}

	static int find_translation(int np, double pts1, double pts2, double *mat) {
	int i;
	double sx, sy, dx, dy;
	double sumx, sumy;

	double T1[9], T2[9];
	normalize_homography(pts1, np, T1);
	normalize_homography(pts2, np, T2);

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

	sumx += dx - sx;
	sumy += dy - sy;
	}
	mat[0] = sumx / np;
	mat[1] = sumy / np;
	denormalize_translation_reorder(mat, T1, T2);
	return 0;
	}

	static int find_rotzoom(int np, double pts1, double pts2, double *mat) {
	const int np2 = np * 2;
	double a = (double )aom_malloc(sizeof(a) (np2 * 5 + 20));
	double b = a + np2 4;
	double *temp = b + np2;
	int i;
	double sx, sy, dx, dy;

	double T1[9], T2[9];
	normalize_homography(pts1, np, T1);
	normalize_homography(pts2, np, T2);

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

	a[i * 2 * 4 + 0] = sx;
	a[i * 2 * 4 + 1] = sy;
	a[i * 2 * 4 + 2] = 1;
	a[i * 2 * 4 + 3] = 0;
	a[(i * 2 + 1) * 4 + 0] = sy;
	a[(i * 2 + 1) * 4 + 1] = -sx;
	a[(i * 2 + 1) * 4 + 2] = 0;
	a[(i * 2 + 1) * 4 + 3] = 1;

	b[2 * i] = dx;
	b[2 * i + 1] = dy;
	}
	if (!least_squares(4, a, np2, 4, b, temp, mat)) {
	aom_free(a);
	return 1;
	}
	denormalize_rotzoom_reorder(mat, T1, T2);
	aom_free(a);
	return 0;
	}

	static int find_affine(int np, double pts1, double pts2, double *mat) {
	const int np2 = np * 2;
	double a = (double )aom_malloc(sizeof(a) (np2 * 7 + 42));
	double b = a + np2 6;
	double *temp = b + np2;
	int i;
	double sx, sy, dx, dy;

	double T1[9], T2[9];
	normalize_homography(pts1, np, T1);
	normalize_homography(pts2, np, T2);

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

	a[i * 2 * 6 + 0] = sx;
	a[i * 2 * 6 + 1] = sy;
	a[i * 2 * 6 + 2] = 0;
	a[i * 2 * 6 + 3] = 0;
	a[i * 2 * 6 + 4] = 1;
	a[i * 2 * 6 + 5] = 0;
	a[(i * 2 + 1) * 6 + 0] = 0;
	a[(i * 2 + 1) * 6 + 1] = 0;
	a[(i * 2 + 1) * 6 + 2] = sx;
	a[(i * 2 + 1) * 6 + 3] = sy;
	a[(i * 2 + 1) * 6 + 4] = 0;
	a[(i * 2 + 1) * 6 + 5] = 1;

	b[2 * i] = dx;
	b[2 * i + 1] = dy;
	}
	if (!least_squares(6, a, np2, 6, b, temp, mat)) {
	aom_free(a);
	return 1;
	}
	denormalize_affine_reorder(mat, T1, T2);
	aom_free(a);
	return 0;
	}

	static int 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 0;
	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 1;
	}

	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 int 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));
	}

	static int ransac(const int *matched_points, int npoints,
	int num_inliers_by_motion, double params_by_motion,
	int num_desired_motions, const int minpts,
	IsDegenerateFunc is_degenerate,
	FindTransformationFunc find_transformation,
	ProjectPointsDoubleFunc projectpoints) {
	static const double PROBABILITY_REQUIRED = 0.9;
	static const double EPS = 1e-12;

	int N = 10000, trial_count = 0;
	int i = 0;
	int ret_val = 0;

	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];

	double cnp1, cnp2;

	for (i = 0; i < num_desired_motions; ++i) {
	num_inliers_by_motion[i] = 0;
	}
	if (npoints < minpts * MINPTS_MULTIPLIER \|\| npoints == 0) {
	return 1;
	}

	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 = 1;
	goto finish_ransac;
	}

	cnp1 = corners1;
	cnp2 = corners2;
	for (i = 0; i < npoints; ++i) {
	(cnp1++) = (matched_points++);
	(cnp1++) = (matched_points++);
	(cnp2++) = (matched_points++);
	(cnp2++) = (matched_points++);
	}

	while (N > 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 = 1;
	goto finish_ransac;
	}

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

	degenerate = is_degenerate(points1);
	if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
	ret_val = 1;
	goto finish_ransac;
	}
	}

	if (find_transformation(minpts, points1, points2, params_this_motion)) {
	trial_count++;
	continue;
	}

	projectpoints(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) {
	int temp;
	double fracinliers, pNoOutliers, mean_distance, dtemp;
	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);
	fracinliers = (double)current_motion.num_inliers / (double)npoints;
	pNoOutliers = 1 - pow(fracinliers, minpts);
	pNoOutliers = fmax(EPS, pNoOutliers);
	pNoOutliers = fmin(1 - EPS, pNoOutliers);
	dtemp = log(1.0 - PROBABILITY_REQUIRED) / log(pNoOutliers);
	temp = (dtemp > (double)INT32_MAX)
	? INT32_MAX
	: dtemp < (double)INT32_MIN ? INT32_MIN : (int)dtemp;

	if (temp > 0 && temp < N) {
	N = AOMMAX(temp, MIN_TRIALS);
	}

	// 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) {
	copy_points_at_indices(points1, corners1, motions[i].inlier_indices,
	motions[i].num_inliers);
	copy_points_at_indices(points2, corners2, motions[i].inlier_indices,
	motions[i].num_inliers);

	find_transformation(motions[i].num_inliers, points1, points2,
	params_by_motion + (MAX_PARAMDIM - 1) * i);
	}
	num_inliers_by_motion[i] = 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);
	for (i = 0; i < num_desired_motions; ++i) {
	aom_free(motions[i].inlier_indices);
	}
	aom_free(motions);

	return ret_val;
	}

	static int 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;
	}

	static int is_degenerate_translation(double *p) {
	return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
	}

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

	int ransac_translation(int *matched_points, int npoints,
	int num_inliers_by_motion, double params_by_motion,
	int num_desired_motions) {
	return ransac(matched_points, npoints, num_inliers_by_motion,
	params_by_motion, num_desired_motions, 3,
	is_degenerate_translation, find_translation,
	project_points_double_translation);
	}

	int ransac_rotzoom(int matched_points, int npoints, int num_inliers_by_motion,
	double *params_by_motion, int num_desired_motions) {
	return ransac(matched_points, npoints, num_inliers_by_motion,
	params_by_motion, num_desired_motions, 3, is_degenerate_affine,
	find_rotzoom, project_points_double_rotzoom);
	}

	int ransac_affine(int matched_points, int npoints, int num_inliers_by_motion,
	double *params_by_motion, int num_desired_motions) {
	return ransac(matched_points, npoints, num_inliers_by_motion,
	params_by_motion, num_desired_motions, 3, is_degenerate_affine,
	find_affine, project_points_double_affine);
	}