Implement global motion parameter computation
This computes global motion parameters between 2 frames by
matching corresponding points using FAST feature and then
fitting a model using RANSAC.
Change-Id: Ib6664df44090e8cfa4db9f2f9e0556931ccfe5c8
diff --git a/vp10/encoder/ransac.c b/vp10/encoder/ransac.c
new file mode 100644
index 0000000..e925068
--- /dev/null
+++ b/vp10/encoder/ransac.c
@@ -0,0 +1,940 @@
+/*
+ * (c) 2010 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 <memory.h>
+#include <math.h>
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+#include "vp10/encoder/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(*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) {
+ 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(*nrU));
+ nrV = (double **)malloc((N) * sizeof(*nrV));
+ 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;
+}
+
+////////////////////////////////////////////////////////////////////////////////
+// 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;
+ unsigned int seed = (unsigned int)npoints;
+ 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;
+}
+
+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, TransformationType type) {
+ 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];
+ WarpedMotionParams wm;
+ 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;
+ int *corners1_int;
+ double *corners2;
+ int *image1_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;
+ }
+
+ memset(&wm, 0, sizeof(wm));
+ best_inlier_set1 = (double *)malloc(sizeof(*best_inlier_set1) * npoints * 2);
+ best_inlier_set2 = (double *)malloc(sizeof(*best_inlier_set2) * npoints * 2);
+ inlier_set1 = (double *)malloc(sizeof(*inlier_set1) * npoints * 2);
+ inlier_set2 = (double *)malloc(sizeof(*inlier_set2) * npoints * 2);
+ corners1 = (double *)malloc(sizeof(*corners1) * npoints * 2);
+ corners1_int = (int *)malloc(sizeof(*corners1_int) * npoints * 2);
+ corners2 = (double *)malloc(sizeof(*corners2) * npoints * 2);
+ image1_coord = (int *)malloc(sizeof(*image1_coord) * npoints * 2);
+ inlier_mask = (int *)malloc(sizeof(*inlier_mask) * 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;
+ }
+
+ for (i = 0; i < npoints; ++i) {
+ corners1_int[2 * i] = (int)corners1[i * 2];
+ corners1_int[2 * i + 1] = (int)corners1[i * 2 + 1];
+ }
+
+ vp10_integerize_model(H, type, &wm);
+ projectpoints(wm.wmmat, corners1_int, image1_coord, npoints, 2, 2, 0, 0);
+
+ for (i = 0; i < npoints; ++i) {
+ double dx =
+ (image1_coord[i * 2] >> WARPEDPIXEL_PREC_BITS) - corners2[i * 2];
+ double dy = (image1_coord[i * 2 + 1] >> WARPEDPIXEL_PREC_BITS) -
+ 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(*bestH));
+ 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));
+ memcpy(best_inlier_mask, inlier_mask,
+ npoints * sizeof(*best_inlier_mask));
+
+ 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++;
+ }
+ findTransformation(max_inliers, best_inlier_set1, best_inlier_set2, bestH);
+ if (normalize && denormalize) {
+ denormalize(bestH, T1, T2);
+ }
+ *number_of_inliers = max_inliers;
+finish_ransac:
+ free(best_inlier_set1);
+ free(best_inlier_set2);
+ free(inlier_set1);
+ free(inlier_set2);
+ free(corners1);
+ free(corners2);
+ free(image1_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[2];
+ H[1] = Ha[5];
+ H[2] = Ha[0];
+ H[3] = Ha[1];
+ H[4] = Ha[3];
+ H[5] = Ha[4];
+}
+
+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[2];
+ H[1] = Ha[5];
+ H[2] = Ha[0];
+ H[3] = Ha[1];
+}
+
+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(*a) * 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(*a) * 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(*a) * 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(*a) * 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, TRANSLATION);
+}
+
+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, ROTZOOM);
+}
+
+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, AFFINE);
+}
+
+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, HOMOGRAPHY);
+ 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;
+}
