/* * Copyright (c) 2015 The WebM project authors. All Rights Reserved. * * Use of this source code is governed by a BSD-style license * that can be found in the LICENSE file in the root of the source * tree. An additional intellectual property rights grant can be * found in the file PATENTS. All contributing project authors may * be found in the AUTHORS file in the root of the source tree. */ #include #include #include #include #include #include #include "vp9_ransac.h" #define MAX_PARAMDIM 9 #define MAX_MINPTS 4 #define MAX_DEGENERATE_ITER 10 #define MINPTS_MULTIPLIER 5 // svdcmp // Adopted from Numerical Recipes in C static const double TINY_NEAR_ZERO = 1.0E-12; static inline double SIGN(double a, double b) { return ((b) >= 0 ? fabs(a) : -fabs(a)); } static inline double PYTHAG(double a, double b) { double absa, absb, ct; absa = fabs(a); absb = fabs(b); if(absa > absb) { ct = absb / absa; return absa * sqrt(1.0 + ct * ct); } else { ct = absa / absb; return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct); } } int IMIN(int a, int b) { return (((a) < (b)) ? (a) : (b)); } int IMAX(int a, int b) { return (((a) < (b)) ? (b) : (a)); } void MultiplyMat(double *m1, double *m2, double *res, const int M1, const int N1, const int N2) { int timesInner = N1; int timesRows = M1; int timesCols = N2; double sum; int row, col, inner; for( row = 0; row < timesRows; ++row ) { for( col = 0; col < timesCols; ++col ) { sum = 0; for (inner = 0; inner < timesInner; ++inner ) sum += m1[row * N1 + inner] * m2[inner * N2 + col]; *(res++) = sum; } } } static int svdcmp_(double **u, int m, int n, double w[], double **v) { const int max_its = 30; int flag, i, its, j, jj, k, l, nm; double anorm, c, f, g, h, s, scale, x, y, z; double *rv1 = (double *)malloc(sizeof(double) * (n + 1)); g = scale = anorm = 0.0; for (i = 0; i < n; i++) { l = i + 1; rv1[i] = scale * g; g = s = scale = 0.0; if (i < m) { for (k = i; k < m; k++) scale += fabs(u[k][i]); if (scale) { for (k = i; k < m; k++) { u[k][i] /= scale; s += u[k][i] * u[k][i]; } f = u[i][i]; g = -SIGN(sqrt(s), f); h = f * g - s; u[i][i] = f - g; for (j = l; j < n; j++) { for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j]; f = s / h; for (k = i; k < m; k++) u[k][j] += f * u[k][i]; } for (k = i; k < m; k++) u[k][i] *= scale; } } w[i] = scale * g; g = s = scale = 0.0; if (i < m && i != n - 1) { for (k = l; k < n; k++) scale += fabs(u[i][k]); if (scale) { for (k = l; k < n; k++) { u[i][k] /= scale; s += u[i][k] * u[i][k]; } f = u[i][l]; g = -SIGN(sqrt(s),f); h = f * g - s; u[i][l] = f - g; for (k = l; k < n; k++) rv1[k] = u[i][k] / h; for (j = l; j < m; j++) { for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k]; for (k = l; k < n; k++) u[j][k] += s * rv1[k]; } for (k = l; k < n; k++) u[i][k] *= scale; } } anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i]))); } for (i = n - 1; i >= 0; i--) { if (i < n - 1) { if (g) { for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g; for (j = l; j < n; j++) { for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j]; for (k = l; k < n; k++) v[k][j] += s * v[k][i]; } } for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0; } v[i][i] = 1.0; g = rv1[i]; l = i; } for (i = IMIN(m, n) - 1; i >= 0; i--) { l = i + 1; g = w[i]; for (j = l; j < n; j++) u[i][j] = 0.0; if (g) { g = 1.0 / g; for (j = l; j < n; j++) { for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j]; f = (s / u[i][i]) * g; for (k = i; k < m; k++) u[k][j] += f * u[k][i]; } for (j = i; j < m; j++) u[j][i] *= g; } else { for (j = i; j < m; j++) u[j][i] = 0.0; } ++u[i][i]; } for (k = n - 1; k >= 0; k--) { for (its = 0; its < max_its; its++) { flag = 1; for (l = k; l >= 0; l--) { nm = l - 1; if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) { flag = 0; break; } if ((double)(fabs(w[nm]) + anorm) == anorm) break; } if (flag) { c = 0.0; s = 1.0; for (i = l; i <= k; i++) { f = s * rv1[i]; rv1[i] = c * rv1[i]; if ((double)(fabs(f) + anorm) == anorm) break; g = w[i]; h = PYTHAG(f, g); w[i] = h; h = 1.0 / h; c = g * h; s = -f * h; for (j = 0; j < m; j++) { y = u[j][nm]; z = u[j][i]; u[j][nm] = y * c + z * s; u[j][i] = z * c - y * s; } } } z = w[k]; if (l == k) { if (z < 0.0) { w[k] = -z; for (j = 0; j < n; j++) v[j][k] = -v[j][k]; } break; } if (its == max_its - 1) { return 1; } assert(k > 0); x = w[l]; nm = k - 1; y = w[nm]; g = rv1[nm]; h = rv1[k]; f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y); g = PYTHAG(f, 1.0); f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x; c = s = 1.0; for (j = l; j <= nm; j++) { i = j + 1; g = rv1[i]; y = w[i]; h = s * g; g = c * g; z = PYTHAG(f, h); rv1[j] = z; c = f / z; s = h / z; f = x * c + g * s; g = g * c - x * s; h = y * s; y *= c; for (jj = 0; jj < n; jj++) { x = v[jj][j]; z = v[jj][i]; v[jj][j] = x * c + z * s; v[jj][i] = z * c - x * s; } z = PYTHAG(f, h); w[j] = z; if (z) { z = 1.0 / z; c = f * z; s = h * z; } f = c * g + s * y; x = c * y - s * g; for (jj = 0; jj < m; jj++) { y = u[jj][j]; z = u[jj][i]; u[jj][j] = y * c + z * s; u[jj][i] = z * c - y * s; } } rv1[l] = 0.0; rv1[k] = f; w[k] = x; } } free(rv1); return 0; } static int SVD(double *U, double *W, double *V, double *matx, int M, int N) { // Assumes allocation for U is MxN double **nrU, **nrV; int problem, i; nrU = (double **)malloc((M)*sizeof(double*)); nrV = (double **)malloc((N)*sizeof(double*)); problem = !(nrU && nrV); if (!problem) { problem = 0; for (i = 0; i < M; i++) { nrU[i] = &U[i * N]; } for (i = 0; i < N; i++) { nrV[i] = &V[i * N]; } } if (problem) { return 1; } /* copy from given matx into nrU */ for (i = 0; i < M; i++) { memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx)); } /* HERE IT IS: do SVD */ if (svdcmp_(nrU, M, N, W, nrV)) { return 1; } /* free Numerical Recipes arrays */ free(nrU); free(nrV); return 0; } int PseudoInverse(double *inv, double *matx, const int M, const int N) { double *U, *W, *V, ans; int i, j, k; U = (double *)malloc(M * N * sizeof(*matx)); W = (double *)malloc(N * sizeof(*matx)); V = (double *)malloc(N * N * sizeof(*matx)); if (!(U && W && V)) { return 1; } if (SVD(U, W, V, matx, M, N)) { return 1; } for (i = 0; i < N; i++) { if (fabs(W[i]) < TINY_NEAR_ZERO) { return 1; } } for (i = 0; i < N; i++) { for (j = 0; j < M; j++) { ans = 0; for (k = 0; k < N; k++) { ans += V[k + N * i] * U[k + N * j] / W[k]; } inv[j + M * i] = ans; } } free(U); free(W); free(V); return 0; } static double compute_error(projectPointsType projectPoints, double *points1, int stride1, double *points2, int stride2, int npoints, double *H, int *mask) { int i, n = 0; double pt[2]; double *mp1 = points1; double *mp2 = points2; double sqerr = 0.0; if (projectPoints == NULL) return -1.0; if (mask) { for (i = 0; i < npoints; ++i, mp1 += stride1, mp2 += stride2) { if (mask[i]) { projectPoints(H, mp1, pt, 1, stride1, stride2); sqerr += (pt[0] - mp2[0]) * (pt[0] - mp2[0]) + (pt[1] - mp2[1]) * (pt[1] - mp2[1]); n++; } } } else { for (i = 0; i < npoints; ++i, mp1 += stride1, mp2 += stride2) { projectPoints(H, mp1, pt, 1, stride1, stride2); sqerr += (pt[0] - mp2[0]) * (pt[0] - mp2[0]) + (pt[1] - mp2[1]) * (pt[1] - mp2[1]); n++; } } return sqrt(sqerr / n); } //////////////////////////////////////////////////////////////////////////////// // ransac typedef int (*isDegenerateType)(double *p); typedef void (*normalizeType)(double *p, int np, double *T); typedef void (*denormalizeType)(double *H, double *T1, double *T2); typedef int (*findTransformationType)(int points, double *points1, double *points2, double *H); static int get_rand_indices(int npoints, int minpts, int *indices) { int i, j; int ptr = rand() % npoints; if (minpts > npoints) return 0; indices[0] = ptr; ptr = (ptr == npoints - 1 ? 0 : ptr + 1); i = 1; while (i < minpts) { int index = rand() % 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; } int ransac_(double *matched_points, int npoints, int *number_of_inliers, int *best_inlier_mask, double *bestH, const int minpts, const int paramdim, isDegenerateType isDegenerate, normalizeType normalize, denormalizeType denormalize, findTransformationType findTransformation, projectPointsType projectPoints) { static const double INLIER_THRESHOLD_NORMALIZED = 0.1; static const double INLIER_THRESHOLD_UNNORMALIZED = 1.0; static const double PROBABILITY_REQUIRED = 0.9; static const double EPS = 1e-12; static const int MIN_TRIALS = 20; const double inlier_threshold = (normalize && denormalize ? INLIER_THRESHOLD_NORMALIZED : INLIER_THRESHOLD_UNNORMALIZED); int N = 10000, trial_count = 0; int i; int ret_val = 0; int max_inliers = 0; double best_variance = 0.0; double H[MAX_PARAMDIM]; double points1[2 * MAX_MINPTS]; double points2[2 * MAX_MINPTS]; int indices[MAX_MINPTS]; double *best_inlier_set1; double *best_inlier_set2; double *inlier_set1; double *inlier_set2; double *corners1; double *corners2; double *image1_coord; double *image2_coord; int *inlier_mask; double *cnp1, *cnp2; double T1[9], T2[9]; // srand((unsigned)time(NULL)) ; // better to make this deterministic for a given sequence for ease of testing srand(npoints); *number_of_inliers = 0; if (npoints < minpts * MINPTS_MULTIPLIER) { printf("Cannot find motion with %d matches\n", npoints); return 1; } best_inlier_set1 = (double *)malloc(sizeof(double) * npoints * 2); best_inlier_set2 = (double *)malloc(sizeof(double) * npoints * 2); inlier_set1 = (double *)malloc(sizeof(double) * npoints * 2); inlier_set2 = (double *)malloc(sizeof(double) * npoints * 2); corners1 = (double *)malloc(sizeof(double) * npoints * 2); corners2 = (double *)malloc(sizeof(double) * npoints * 2); image1_coord = (double *)malloc(sizeof(double) * npoints * 2); image2_coord = (double *)malloc(sizeof(double) * npoints * 2); inlier_mask = (int*)malloc(sizeof(int) * npoints); for(cnp1 = corners1, cnp2 = corners2, i = 0; i < npoints; ++i) { *(cnp1++) = *(matched_points++); *(cnp1++) = *(matched_points++); *(cnp2++) = *(matched_points++); *(cnp2++) = *(matched_points++); } matched_points -= 4 * npoints; if (normalize && denormalize) { normalize(corners1, npoints, T1); normalize(corners2, npoints, T2); } while (N > trial_count) { int num_inliers = 0; double sum_distance = 0.0; double sum_distance_squared = 0.0; int degenerate = 1; int num_degenerate_iter = 0; while (degenerate) { num_degenerate_iter++; if (!get_rand_indices(npoints, minpts, indices)) { ret_val = 1; goto finish_ransac; } i = 0; while (i < minpts) { int index = indices[i]; // add to list points1[i*2] = corners1[index*2]; points1[i*2+1] = corners1[index*2+1]; points2[i*2] = corners2[index*2]; points2[i*2+1] = corners2[index*2+1]; i++; } degenerate = isDegenerate(points1); if (num_degenerate_iter > MAX_DEGENERATE_ITER) { ret_val = 1; goto finish_ransac; } } if (findTransformation(minpts, points1, points2, H)) { trial_count++; continue; } projectPoints(H, 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); inlier_mask[i] = distance < inlier_threshold; if (inlier_mask[i]) { inlier_set1[num_inliers*2] = corners1[i*2]; inlier_set1[num_inliers*2 + 1] = corners1[i*2 + 1]; inlier_set2[num_inliers*2] = corners2[i*2]; inlier_set2[num_inliers*2 + 1] = corners2[i*2 + 1]; num_inliers++; sum_distance += distance; sum_distance_squared += distance*distance; } } if (num_inliers >= max_inliers) { double mean_distance = sum_distance / ((double)num_inliers); double variance = sum_distance_squared / ((double)num_inliers - 1.0) - mean_distance * mean_distance * ((double)num_inliers) / ((double)num_inliers - 1.0); if ((num_inliers > max_inliers) || (num_inliers==max_inliers && variance < best_variance)) { best_variance = variance; max_inliers = num_inliers; memcpy(bestH, H, paramdim * sizeof(double)); memcpy(best_inlier_set1, inlier_set1, num_inliers*2 * sizeof(double)); memcpy(best_inlier_set2, inlier_set2, num_inliers*2 * sizeof(double)); memcpy(best_inlier_mask, inlier_mask, npoints * sizeof(int)); if (num_inliers > 0) { double fracinliers = (double)num_inliers/(double)npoints; double pNoOutliers = 1 - pow(fracinliers, minpts); int temp; pNoOutliers = fmax(EPS, pNoOutliers); pNoOutliers = fmin(1 - EPS, pNoOutliers); temp = (int)(log(1.0 - PROBABILITY_REQUIRED)/log(pNoOutliers)); if (temp > 0 && temp < N) { N = IMAX(temp, MIN_TRIALS); } } } } trial_count++; } // printf("Number of trials = %d\n", trial_count); findTransformation(max_inliers, best_inlier_set1, best_inlier_set2, bestH); if (normalize && denormalize) { denormalize(bestH, T1, T2); } *number_of_inliers = max_inliers; /* printf("Error score (all) = %g\n", compute_error(projectPoints, matched_points, 4, matched_points + 2, 4, npoints, bestH, NULL)); printf("Error score (inliers) = %g\n", compute_error(projectPoints, matched_points, 4, matched_points + 2, 4, npoints, bestH, best_inlier_mask)); */ finish_ransac: free(best_inlier_set1); free(best_inlier_set2); free(inlier_set1); free(inlier_set2); free(corners1); free(corners2); free(image1_coord); free(image2_coord); free(inlier_mask); return ret_val; } /////////////////////////////////////////////////////////////////////////////////////////////////////////// static void normalizeHomography(double *pts, int n, double *T) { // Assume the points are 2d coordinates with scale = 1 double *p = pts; double mean[2] = {0, 0}; double msqe = 0; double scale; int i; 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 = 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 denormalizeHomography(double *H, double *T1, double *T2) { double iT2[9]; double H2[9]; invnormalize_mat(T2, iT2); MultiplyMat(H, T1, H2, 3, 3, 3); MultiplyMat(iT2, H2, H, 3, 3, 3); } static void denormalizeAffine(double *H, double *T1, double *T2) { double Ha[MAX_PARAMDIM]; Ha[0] = H[0]; Ha[1] = H[1]; Ha[2] = H[4]; Ha[3] = H[2]; Ha[4] = H[3]; Ha[5] = H[5]; Ha[6] = Ha[7] = 0; Ha[8] = 1; denormalizeHomography(Ha, T1, T2); H[0] = Ha[0]; H[1] = Ha[1]; H[2] = Ha[3]; H[3] = Ha[4]; H[4] = Ha[2]; H[5] = Ha[5]; } static void denormalizeRotZoom(double *H, double *T1, double *T2) { double Ha[MAX_PARAMDIM]; Ha[0] = H[0]; Ha[1] = H[1]; Ha[2] = H[2]; Ha[3] = -H[1]; Ha[4] = H[0]; Ha[5] = H[3]; Ha[6] = Ha[7] = 0; Ha[8] = 1; denormalizeHomography(Ha, T1, T2); H[0] = Ha[0]; H[1] = Ha[1]; H[2] = Ha[2]; H[3] = Ha[5]; } static void denormalizeTranslation(double *H, double *T1, double *T2) { double Ha[MAX_PARAMDIM]; Ha[0] = 1; Ha[1] = 0; Ha[2] = H[0]; Ha[3] = 0; Ha[4] = 1; Ha[5] = H[1]; Ha[6] = Ha[7] = 0; Ha[8] = 1; denormalizeHomography(Ha, T1, T2); H[0] = Ha[2]; H[1] = Ha[5]; } 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 isDegenerateTranslation(double *p) { return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2; } static int isDegenerateAffine(double *p) { return is_collinear3(p, p + 2, p + 4); } static int isDegenerateHomography(double *p) { return is_collinear3(p, p + 2, p + 4) || is_collinear3(p, p + 2, p + 6) || is_collinear3(p, p + 4, p + 6) || is_collinear3(p + 2, p + 4, p + 6); } int findTranslation(const int np, double *pts1, double *pts2, double *mat) { int i; double sx, sy, dx, dy; double sumx, sumy; double T1[9], T2[9]; normalizeHomography(pts1, np, T1); normalizeHomography(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; denormalizeTranslation(mat, T1, T2); return 0; } int findRotZoom(const int np, double *pts1, double *pts2, double *mat) { const int np2 = np * 2; double *a = (double *)malloc(sizeof(double) * np2 * 9); double *b = a + np2 * 4; double *temp = b + np2; int i; double sx, sy, dx, dy; double T1[9], T2[9]; normalizeHomography(pts1, np, T1); normalizeHomography(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 (PseudoInverse(temp, a, np2, 4)){ free(a); return 1; } MultiplyMat(temp, b, mat, 4, np2, 1); denormalizeRotZoom(mat, T1, T2); free(a); return 0; } int findAffine(const int np, double *pts1, double *pts2, double *mat) { const int np2 = np * 2; double *a = (double *)malloc(sizeof(double) * np2 * 13); double *b = a + np2 * 6; double *temp = b + np2; int i; double sx, sy, dx, dy; double T1[9], T2[9]; normalizeHomography(pts1, np, T1); normalizeHomography(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 (PseudoInverse(temp, a, np2, 6)){ free(a); return 1; } MultiplyMat(temp, b, mat, 6, np2, 1); denormalizeAffine(mat, T1, T2); free(a); return 0; } int findHomography(const int np, double *pts1, double *pts2, double *mat) { // Implemented from Peter Kovesi's normalized implementation const int np3 = np * 3; double *a = (double *)malloc(sizeof(double) * np3 * 18); double *U = a + np3 * 9; double S[9], V[9 * 9]; int i, mini; double sx, sy, dx, dy; double T1[9], T2[9]; normalizeHomography(pts1, np, T1); normalizeHomography(pts2, np, T2); for (i = 0; i < np; ++i) { dx = *(pts2++); dy = *(pts2++); sx = *(pts1++); sy = *(pts1++); a[i * 3 * 9 + 0] = a[i * 3 * 9 + 1] = a[i * 3 * 9 + 2] = 0; a[i * 3 * 9 + 3] = -sx; a[i * 3 * 9 + 4] = -sy; a[i * 3 * 9 + 5] = -1; a[i * 3 * 9 + 6] = dy * sx; a[i * 3 * 9 + 7] = dy * sy; a[i * 3 * 9 + 8] = dy; a[(i * 3 + 1) * 9 + 0] = sx; a[(i * 3 + 1) * 9 + 1] = sy; a[(i * 3 + 1) * 9 + 2] = 1; a[(i * 3 + 1) * 9 + 3] = a[(i * 3 + 1) * 9 + 4] = a[(i * 3 + 1) * 9 + 5] = 0; a[(i * 3 + 1) * 9 + 6] = -dx * sx; a[(i * 3 + 1) * 9 + 7] = -dx * sy; a[(i * 3 + 1) * 9 + 8] = -dx; a[(i * 3 + 2) * 9 + 0] = -dy * sx; a[(i * 3 + 2) * 9 + 1] = -dy * sy; a[(i * 3 + 2) * 9 + 2] = -dy; a[(i * 3 + 2) * 9 + 3] = dx * sx; a[(i * 3 + 2) * 9 + 4] = dx * sy; a[(i * 3 + 2) * 9 + 5] = dx; a[(i * 3 + 2) * 9 + 6] = a[(i * 3 + 2) * 9 + 7] = a[(i * 3 + 2) * 9 + 8] = 0; } if (SVD(U, S, V, a, np3, 9)) { free(a); return 1; } else { double minS = 1e12; mini = -1; for (i = 0; i < 9; ++i) { if (S[i] < minS) { minS = S[i]; mini = i; } } } for (i = 0; i < 9; i++) mat[i] = V[i * 9 + mini]; denormalizeHomography(mat, T1, T2); free(a); if (mat[8] == 0.0) { return 1; } return 0; } int findHomographyScale1(const int np, double *pts1, double *pts2, double *mat) { // This implementation assumes h33 = 1, but does not seem to give good results const int np2 = np * 2; double *a = (double *)malloc(sizeof(double) * np2 * 17); double *b = a + np2 * 8; double *temp = b + np2; int i, j; double sx, sy, dx, dy; double T1[9], T2[9]; normalizeHomography(pts1, np, T1); normalizeHomography(pts2, np, T2); for (i = 0, j = np; i < np; ++i, ++j) { dx = *(pts2++); dy = *(pts2++); sx = *(pts1++); sy = *(pts1++); a[i * 8 + 0] = a[j * 8 + 3] = sx; a[i * 8 + 1] = a[j * 8 + 4] = sy; a[i * 8 + 2] = a[j * 8 + 5] = 1; a[i * 8 + 3] = a[i * 8 + 4] = a[i * 8 + 5] = a[j * 8 + 0] = a[j * 8 + 1] = a[j * 8 + 2] = 0; a[i * 8 + 6] = -dx * sx; a[i * 8 + 7] = -dx * sy; a[j * 8 + 6] = -dy * sx; a[j * 8 + 7] = -dy * sy; b[i] = dx; b[j] = dy; } if (PseudoInverse(temp, a, np2, 8)) { free(a); return 1; } MultiplyMat(temp, b, &*mat, 8, np2, 1); mat[8] = 1; denormalizeHomography(mat, T1, T2); free(a); return 0; } int ransacTranslation(double *matched_points, int npoints, int *number_of_inliers, int *best_inlier_mask, double *bestH) { return ransac_(matched_points, npoints, number_of_inliers, best_inlier_mask, bestH, 3, 2, isDegenerateTranslation, NULL, // normalizeHomography, NULL, // denormalizeRotZoom, findTranslation, projectPointsTranslation); } int ransacRotZoom(double *matched_points, int npoints, int *number_of_inliers, int *best_inlier_mask, double *bestH) { return ransac_(matched_points, npoints, number_of_inliers, best_inlier_mask, bestH, 3, 4, isDegenerateAffine, NULL, // normalizeHomography, NULL, // denormalizeRotZoom, findRotZoom, projectPointsRotZoom); } int ransacAffine(double *matched_points, int npoints, int *number_of_inliers, int *best_inlier_mask, double *bestH) { return ransac_(matched_points, npoints, number_of_inliers, best_inlier_mask, bestH, 3, 6, isDegenerateAffine, NULL, // normalizeHomography, NULL, // denormalizeAffine, findAffine, projectPointsAffine); } int ransacHomography(double *matched_points, int npoints, int *number_of_inliers, int *best_inlier_mask, double *bestH) { int result = ransac_(matched_points, npoints, number_of_inliers, best_inlier_mask, bestH, 4, 8, isDegenerateHomography, NULL, // normalizeHomography, NULL, // denormalizeHomography, findHomography, projectPointsHomography); if (!result) { // normalize so that H33 = 1 int i; double m = 1.0 / bestH[8]; for (i = 0; i < 8; ++i) bestH[i] *= m; bestH[8] = 1.0; } return result; }