| /* |
| * 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. |
| */ |
| #define _POSIX_C_SOURCE 200112L // rand_r() |
| #include <memory.h> |
| #include <math.h> |
| #include <time.h> |
| #include <stdio.h> |
| #include <stdlib.h> |
| #include <assert.h> |
| |
| #include "av1/encoder/ransac.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 project_points_double_hortrapezoid(double *mat, double *points, |
| double *proj, const int n, |
| const int stride_points, |
| const int stride_proj) { |
| int i; |
| double x, y, Z, Z_inv; |
| for (i = 0; i < n; ++i) { |
| x = *(points++), y = *(points++); |
| Z_inv = mat[7] * y + 1; |
| assert(fabs(Z_inv) > 0.000001); |
| Z = 1. / Z_inv; |
| *(proj++) = (mat[2] * x + mat[3] * y + mat[0]) * Z; |
| *(proj++) = (mat[5] * y + mat[1]) * Z; |
| points += stride_points - 2; |
| proj += stride_proj - 2; |
| } |
| } |
| |
| static void project_points_double_vertrapezoid(double *mat, double *points, |
| double *proj, const int n, |
| const int stride_points, |
| const int stride_proj) { |
| int i; |
| double x, y, Z, Z_inv; |
| for (i = 0; i < n; ++i) { |
| x = *(points++), y = *(points++); |
| Z_inv = mat[6] * x + 1; |
| assert(fabs(Z_inv) > 0.000001); |
| Z = 1. / Z_inv; |
| *(proj++) = (mat[2] * x + mat[0]) * Z; |
| *(proj++) = (mat[4] * x + mat[5] * y + mat[1]) * Z; |
| points += stride_points - 2; |
| proj += stride_proj - 2; |
| } |
| } |
| |
| static void project_points_double_homography(double *mat, double *points, |
| double *proj, const int n, |
| const int stride_points, |
| const int stride_proj) { |
| int i; |
| double x, y, Z, Z_inv; |
| for (i = 0; i < n; ++i) { |
| x = *(points++), y = *(points++); |
| Z_inv = mat[6] * x + mat[7] * y + 1; |
| assert(fabs(Z_inv) > 0.000001); |
| Z = 1. / Z_inv; |
| *(proj++) = (mat[2] * x + mat[3] * y + mat[0]) * Z; |
| *(proj++) = (mat[4] * x + mat[5] * y + mat[1]) * Z; |
| points += stride_points - 2; |
| proj += stride_proj - 2; |
| } |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // 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 ct; |
| const double absa = fabs(a); |
| const double 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); |
| } |
| } |
| |
| static void multiply_mat(const double *m1, const double *m2, double *res, |
| const int m1_rows, const int inner_dim, |
| const int m2_cols) { |
| double sum; |
| |
| int row, col, inner; |
| for (row = 0; row < m1_rows; ++row) { |
| for (col = 0; col < m2_cols; ++col) { |
| sum = 0; |
| for (inner = 0; inner < inner_dim; ++inner) |
| sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + 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 *)aom_malloc(sizeof(*rv1) * (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 != 0.) { |
| 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 != 0.) { |
| 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 != 0.) { |
| 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 = AOMMIN(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 != 0.) { |
| 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) { |
| aom_free(rv1); |
| 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 != 0.) { |
| 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; |
| } |
| } |
| aom_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 = (double **)aom_malloc((M) * sizeof(*nrU)); |
| double **nrV = (double **)aom_malloc((N) * sizeof(*nrV)); |
| int problem, i; |
| |
| problem = !(nrU && nrV); |
| if (!problem) { |
| for (i = 0; i < M; i++) { |
| nrU[i] = &U[i * N]; |
| } |
| for (i = 0; i < N; i++) { |
| nrV[i] = &V[i * N]; |
| } |
| } else { |
| if (nrU) aom_free(nrU); |
| if (nrV) aom_free(nrV); |
| 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)) { |
| aom_free(nrU); |
| aom_free(nrV); |
| return 1; |
| } |
| |
| /* aom_free Numerical Recipes arrays */ |
| aom_free(nrU); |
| aom_free(nrV); |
| |
| return 0; |
| } |
| |
| int pseudo_inverse(double *inv, double *matx, const int M, const int N) { |
| double ans; |
| int i, j, k; |
| double *const U = (double *)aom_malloc(M * N * sizeof(*matx)); |
| double *const W = (double *)aom_malloc(N * sizeof(*matx)); |
| double *const V = (double *)aom_malloc(N * N * sizeof(*matx)); |
| |
| if (!(U && W && V)) { |
| return 1; |
| } |
| if (SVD(U, W, V, matx, M, N)) { |
| aom_free(U); |
| aom_free(W); |
| aom_free(V); |
| return 1; |
| } |
| for (i = 0; i < N; i++) { |
| if (fabs(W[i]) < TINY_NEAR_ZERO) { |
| aom_free(U); |
| aom_free(W); |
| aom_free(V); |
| 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; |
| } |
| } |
| aom_free(U); |
| aom_free(W); |
| aom_free(V); |
| return 0; |
| } |
| |
| 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; |
| 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 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_homography_reorder(double *params, double *T1, |
| double *T2) { |
| double params_denorm[MAX_PARAMDIM]; |
| memcpy(params_denorm, params, sizeof(*params) * 8); |
| params_denorm[8] = 1.0; |
| 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_denorm[6]; |
| params[7] = params_denorm[7]; |
| } |
| |
| 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(const 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(const int np, double *pts1, double *pts2, double *mat) { |
| const int np2 = np * 2; |
| double *a = (double *)aom_malloc(sizeof(*a) * np2 * 9); |
| 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 (pseudo_inverse(temp, a, np2, 4)) { |
| aom_free(a); |
| return 1; |
| } |
| multiply_mat(temp, b, mat, 4, np2, 1); |
| denormalize_rotzoom_reorder(mat, T1, T2); |
| aom_free(a); |
| return 0; |
| } |
| |
| static int find_affine(const int np, double *pts1, double *pts2, double *mat) { |
| const int np2 = np * 2; |
| double *a = (double *)aom_malloc(sizeof(*a) * np2 * 13); |
| 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 (pseudo_inverse(temp, a, np2, 6)) { |
| aom_free(a); |
| return 1; |
| } |
| multiply_mat(temp, b, mat, 6, np2, 1); |
| denormalize_affine_reorder(mat, T1, T2); |
| aom_free(a); |
| return 0; |
| } |
| |
| static int find_vertrapezoid(const int np, double *pts1, double *pts2, |
| double *mat) { |
| const int np3 = np * 3; |
| double *a = (double *)aom_malloc(sizeof(*a) * np3 * 14); |
| double *U = a + np3 * 7; |
| double S[7], V[7 * 7], H[9]; |
| int i, mini; |
| 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 * 3 * 7 + 0] = a[i * 3 * 7 + 1] = 0; |
| a[i * 3 * 7 + 2] = -sx; |
| a[i * 3 * 7 + 3] = -sy; |
| a[i * 3 * 7 + 4] = -1; |
| a[i * 3 * 7 + 5] = dy * sx; |
| a[i * 3 * 7 + 6] = dy; |
| |
| a[(i * 3 + 1) * 7 + 0] = sx; |
| a[(i * 3 + 1) * 7 + 1] = 1; |
| a[(i * 3 + 1) * 7 + 2] = a[(i * 3 + 1) * 7 + 3] = a[(i * 3 + 1) * 7 + 4] = |
| 0; |
| a[(i * 3 + 1) * 7 + 5] = -dx * sx; |
| a[(i * 3 + 1) * 7 + 6] = -dx; |
| |
| a[(i * 3 + 2) * 7 + 0] = -dy * sx; |
| a[(i * 3 + 2) * 7 + 1] = -dy; |
| a[(i * 3 + 2) * 7 + 2] = dx * sx; |
| a[(i * 3 + 2) * 7 + 3] = dx * sy; |
| a[(i * 3 + 2) * 7 + 4] = dx; |
| a[(i * 3 + 2) * 7 + 5] = a[(i * 3 + 2) * 7 + 6] = 0; |
| } |
| if (SVD(U, S, V, a, np3, 7)) { |
| aom_free(a); |
| return 1; |
| } else { |
| double minS = 1e12; |
| mini = -1; |
| for (i = 0; i < 7; ++i) { |
| if (S[i] < minS) { |
| minS = S[i]; |
| mini = i; |
| } |
| } |
| } |
| H[1] = H[7] = 0; |
| for (i = 0; i < 1; i++) H[i] = V[i * 7 + mini]; |
| for (; i < 6; i++) H[i + 1] = V[i * 7 + mini]; |
| for (; i < 7; i++) H[i + 2] = V[i * 7 + mini]; |
| |
| denormalize_homography_reorder(H, T1, T2); |
| aom_free(a); |
| if (H[8] == 0.0) { |
| return 1; |
| } else { |
| // normalize |
| double f = 1.0 / H[8]; |
| for (i = 0; i < 8; i++) mat[i] = f * H[i]; |
| } |
| return 0; |
| } |
| |
| static int find_hortrapezoid(const int np, double *pts1, double *pts2, |
| double *mat) { |
| const int np3 = np * 3; |
| double *a = (double *)aom_malloc(sizeof(*a) * np3 * 14); |
| double *U = a + np3 * 7; |
| double S[7], V[7 * 7], H[9]; |
| int i, mini; |
| 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 * 3 * 7 + 0] = a[i * 3 * 7 + 1] = a[i * 3 * 7 + 2] = 0; |
| a[i * 3 * 7 + 3] = -sy; |
| a[i * 3 * 7 + 4] = -1; |
| a[i * 3 * 7 + 5] = dy * sy; |
| a[i * 3 * 7 + 6] = dy; |
| |
| a[(i * 3 + 1) * 7 + 0] = sx; |
| a[(i * 3 + 1) * 7 + 1] = sy; |
| a[(i * 3 + 1) * 7 + 2] = 1; |
| a[(i * 3 + 1) * 7 + 3] = a[(i * 3 + 1) * 7 + 4] = 0; |
| a[(i * 3 + 1) * 7 + 5] = -dx * sy; |
| a[(i * 3 + 1) * 7 + 6] = -dx; |
| |
| a[(i * 3 + 2) * 7 + 0] = -dy * sx; |
| a[(i * 3 + 2) * 7 + 1] = -dy * sy; |
| a[(i * 3 + 2) * 7 + 2] = -dy; |
| a[(i * 3 + 2) * 7 + 3] = dx * sy; |
| a[(i * 3 + 2) * 7 + 4] = dx; |
| a[(i * 3 + 2) * 7 + 5] = a[(i * 3 + 2) * 7 + 6] = 0; |
| } |
| |
| if (SVD(U, S, V, a, np3, 7)) { |
| aom_free(a); |
| return 1; |
| } else { |
| double minS = 1e12; |
| mini = -1; |
| for (i = 0; i < 7; ++i) { |
| if (S[i] < minS) { |
| minS = S[i]; |
| mini = i; |
| } |
| } |
| } |
| H[3] = H[6] = 0; |
| for (i = 0; i < 3; i++) H[i] = V[i * 7 + mini]; |
| for (; i < 5; i++) H[i + 1] = V[i * 7 + mini]; |
| for (; i < 7; i++) H[i + 2] = V[i * 7 + mini]; |
| |
| denormalize_homography_reorder(H, T1, T2); |
| aom_free(a); |
| if (H[8] == 0.0) { |
| return 1; |
| } else { |
| // normalize |
| double f = 1.0 / H[8]; |
| for (i = 0; i < 8; i++) mat[i] = f * H[i]; |
| } |
| return 0; |
| } |
| |
| static int find_homography(const int np, double *pts1, double *pts2, |
| double *mat) { |
| // Implemented from Peter Kovesi's normalized implementation |
| const int np3 = np * 3; |
| double *a = (double *)aom_malloc(sizeof(*a) * np3 * 18); |
| double *U = a + np3 * 9; |
| double S[9], V[9 * 9], H[9]; |
| int i, mini; |
| 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 * 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)) { |
| aom_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++) H[i] = V[i * 9 + mini]; |
| denormalize_homography_reorder(H, T1, T2); |
| aom_free(a); |
| if (H[8] == 0.0) { |
| return 1; |
| } else { |
| // normalize |
| double f = 1.0 / H[8]; |
| for (i = 0; i < 8; i++) mat[i] = f * H[i]; |
| } |
| return 0; |
| } |
| |
| static int get_rand_indices(int npoints, int minpts, int *indices, |
| unsigned int *seed) { |
| int i, j; |
| int ptr = rand_r(seed) % npoints; |
| if (minpts > npoints) return 0; |
| indices[0] = ptr; |
| ptr = (ptr == npoints - 1 ? 0 : ptr + 1); |
| i = 1; |
| while (i < minpts) { |
| int index = rand_r(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; |
| } |
| |
| static int ransac(int *matched_points, int npoints, int *number_of_inliers, |
| double *best_params, 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; |
| int ret_val = 0; |
| unsigned int seed = (unsigned int)npoints; |
| |
| int max_inliers = 0; |
| double best_variance = 0.0; |
| double params[MAX_PARAMDIM]; |
| WarpedMotionParams wm; |
| double points1[2 * MAX_MINPTS]; |
| double points2[2 * MAX_MINPTS]; |
| int indices[MAX_MINPTS] = { 0 }; |
| |
| double *best_inlier_set1; |
| double *best_inlier_set2; |
| double *inlier_set1; |
| double *inlier_set2; |
| double *corners1; |
| double *corners2; |
| double *image1_coord; |
| |
| double *cnp1, *cnp2; |
| |
| *number_of_inliers = 0; |
| if (npoints < minpts * MINPTS_MULTIPLIER || npoints == 0) { |
| return 1; |
| } |
| |
| memset(&wm, 0, sizeof(wm)); |
| best_inlier_set1 = |
| (double *)aom_malloc(sizeof(*best_inlier_set1) * npoints * 2); |
| best_inlier_set2 = |
| (double *)aom_malloc(sizeof(*best_inlier_set2) * npoints * 2); |
| inlier_set1 = (double *)aom_malloc(sizeof(*inlier_set1) * npoints * 2); |
| inlier_set2 = (double *)aom_malloc(sizeof(*inlier_set2) * 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); |
| |
| if (!(best_inlier_set1 && best_inlier_set2 && inlier_set1 && inlier_set2 && |
| corners1 && corners2 && image1_coord)) { |
| ret_val = 1; |
| goto finish_ransac; |
| } |
| |
| 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; |
| |
| 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, &seed)) { |
| 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 = is_degenerate(points1); |
| if (num_degenerate_iter > MAX_DEGENERATE_ITER) { |
| ret_val = 1; |
| goto finish_ransac; |
| } |
| } |
| |
| if (find_transformation(minpts, points1, points2, params)) { |
| trial_count++; |
| continue; |
| } |
| |
| projectpoints(params, 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) { |
| 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 && num_inliers > 1) { |
| int temp; |
| double fracinliers, pNoOutliers, mean_distance, variance; |
| |
| mean_distance = sum_distance / ((double)num_inliers); |
| 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; |
| // Save parameters, excluding the implicit '1' in the bottom-right |
| // entry of the parameter matrix |
| memcpy(best_params, params, (MAX_PARAMDIM - 1) * sizeof(*best_params)); |
| memcpy(best_inlier_set1, inlier_set1, |
| num_inliers * 2 * sizeof(*best_inlier_set1)); |
| memcpy(best_inlier_set2, inlier_set2, |
| num_inliers * 2 * sizeof(*best_inlier_set2)); |
| |
| assert(npoints > 0); |
| fracinliers = (double)num_inliers / (double)npoints; |
| pNoOutliers = 1 - pow(fracinliers, minpts); |
| pNoOutliers = fmax(EPS, pNoOutliers); |
| pNoOutliers = fmin(1 - EPS, pNoOutliers); |
| temp = (int)(log(1.0 - PROBABILITY_REQUIRED) / log(pNoOutliers)); |
| if (temp > 0 && temp < N) { |
| N = AOMMAX(temp, MIN_TRIALS); |
| } |
| } |
| } |
| trial_count++; |
| } |
| find_transformation(max_inliers, best_inlier_set1, best_inlier_set2, |
| best_params); |
| *number_of_inliers = max_inliers; |
| finish_ransac: |
| aom_free(best_inlier_set1); |
| aom_free(best_inlier_set2); |
| aom_free(inlier_set1); |
| aom_free(inlier_set2); |
| aom_free(corners1); |
| aom_free(corners2); |
| aom_free(image1_coord); |
| 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); |
| } |
| |
| static int is_degenerate_homography(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 ransac_translation(int *matched_points, int npoints, int *number_of_inliers, |
| double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 3, |
| is_degenerate_translation, find_translation, |
| project_points_double_translation); |
| } |
| |
| int ransac_rotzoom(int *matched_points, int npoints, int *number_of_inliers, |
| double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 3, |
| is_degenerate_affine, find_rotzoom, |
| project_points_double_rotzoom); |
| } |
| |
| int ransac_affine(int *matched_points, int npoints, int *number_of_inliers, |
| double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 3, |
| is_degenerate_affine, find_affine, |
| project_points_double_affine); |
| } |
| |
| int ransac_homography(int *matched_points, int npoints, int *number_of_inliers, |
| double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 4, |
| is_degenerate_homography, find_homography, |
| project_points_double_homography); |
| } |
| |
| int ransac_hortrapezoid(int *matched_points, int npoints, |
| int *number_of_inliers, double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 4, |
| is_degenerate_homography, find_hortrapezoid, |
| project_points_double_hortrapezoid); |
| } |
| |
| int ransac_vertrapezoid(int *matched_points, int npoints, |
| int *number_of_inliers, double *best_params) { |
| return ransac(matched_points, npoints, number_of_inliers, best_params, 4, |
| is_degenerate_homography, find_vertrapezoid, |
| project_points_double_vertrapezoid); |
| } |
