Move warping model estimation functions to COMMON folder
These functions will be called by both enc and dec in WARPED_MOTION
experiment.
Change-Id: I4b4a20af111b30822760aee8c9451e9ccbb2dd05
diff --git a/av1/common/warped_motion.c b/av1/common/warped_motion.c
index 167cb66..fc632c3 100644
--- a/av1/common/warped_motion.c
+++ b/av1/common/warped_motion.c
@@ -632,3 +632,587 @@
default: assert(0 && "Invalid TransformationType");
}
}
+
+///////////////////////////////////////////////////////////////////////////////
+// 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) {
+ 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 = 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) {
+ 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;
+ }
+ }
+ 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)) {
+ 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;
+ }
+ }
+ aom_free(U);
+ aom_free(W);
+ aom_free(V);
+ return 0;
+}
+
+static void normalize_homography(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 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(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[5];
+ params[1] = params_denorm[2];
+ params[2] = params_denorm[1];
+ params[3] = params_denorm[0];
+ params[4] = params_denorm[3];
+ params[5] = params_denorm[4];
+}
+
+static void denormalize_rotzoom(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[5];
+ params[1] = params_denorm[2];
+ params[2] = params_denorm[1];
+ params[3] = params_denorm[0];
+}
+
+static void denormalize_translation(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[5];
+ params[1] = params_denorm[2];
+}
+
+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(mat, T1, T2);
+ return 0;
+}
+
+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(mat, T1, T2);
+ aom_free(a);
+ return 0;
+}
+
+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(mat, T1, T2);
+ aom_free(a);
+ return 0;
+}
+
+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];
+ 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++) mat[i] = V[i * 9 + mini];
+ denormalize_homography(mat, T1, T2);
+ aom_free(a);
+ if (mat[8] == 0.0) {
+ return 1;
+ }
+ return 0;
+}
diff --git a/av1/common/warped_motion.h b/av1/common/warped_motion.h
index 53f06dd..da92599 100644
--- a/av1/common/warped_motion.h
+++ b/av1/common/warped_motion.h
@@ -22,6 +22,8 @@
#include "aom_dsp/aom_dsp_common.h"
#include "av1/common/mv.h"
+#define MAX_PARAMDIM 9
+
typedef void (*ProjectPointsFunc)(int16_t *mat, int *points, int *proj,
const int n, const int stride_points,
const int stride_proj,
@@ -67,4 +69,9 @@
// Integerize model into the WarpedMotionParams structure
void av1_integerize_model(const double *model, TransformationType wmtype,
WarpedMotionParams *wm);
+
+int find_translation(const int np, double *pts1, double *pts2, double *mat);
+int find_rotzoom(const int np, double *pts1, double *pts2, double *mat);
+int find_affine(const int np, double *pts1, double *pts2, double *mat);
+int find_homography(const int np, double *pts1, double *pts2, double *mat);
#endif // AV1_COMMON_WARPED_MOTION_H_
diff --git a/av1/encoder/ransac.c b/av1/encoder/ransac.c
index 0a26396..0c8ad67 100644
--- a/av1/encoder/ransac.c
+++ b/av1/encoder/ransac.c
@@ -17,307 +17,11 @@
#include "av1/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 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) {
- 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 = 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) {
- 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;
- }
- }
- 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)) {
- 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;
- }
- }
- aom_free(U);
- aom_free(W);
- aom_free(V);
- return 0;
-}
-
////////////////////////////////////////////////////////////////////////////////
// ransac
typedef int (*IsDegenerateFunc)(double *p);
@@ -351,7 +55,7 @@
int i;
for (i = 0; i < n; ++i) {
const double x = *(points++), y = *(points++);
- *(proj++) = mat[3] * x + mat[2] * y + mat[1];
+ *(proj++) = mat[3] * x + mat[2] * y + mat[1];
*(proj++) = -mat[2] * x + mat[3] * y + mat[0];
points += stride_points - 2;
proj += stride_proj - 2;
@@ -594,117 +298,6 @@
return ret_val;
}
-///////////////////////////////////////////////////////////////////////////////
-
-static void normalize_homography(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 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(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[5];
- params[1] = params_denorm[2];
- params[2] = params_denorm[1];
- params[3] = params_denorm[0];
- params[4] = params_denorm[3];
- params[5] = params_denorm[4];
-}
-
-static void denormalize_rotzoom(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[5];
- params[1] = params_denorm[2];
- params[2] = params_denorm[1];
- params[3] = params_denorm[0];
-}
-
-static void denormalize_translation(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[5];
- params[1] = params_denorm[2];
-}
-
static int is_collinear3(double *p1, double *p2, double *p3) {
static const double collinear_eps = 1e-3;
const double v =
@@ -725,185 +318,6 @@
is_collinear3(p, p + 4, p + 6) || is_collinear3(p + 2, p + 4, p + 6);
}
-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(mat, T1, T2);
- return 0;
-}
-
-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(mat, T1, T2);
- aom_free(a);
- return 0;
-}
-
-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(mat, T1, T2);
- aom_free(a);
- return 0;
-}
-
-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];
- 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++) mat[i] = V[i * 9 + mini];
- denormalize_homography(mat, T1, T2);
- aom_free(a);
- if (mat[8] == 0.0) {
- return 1;
- }
- return 0;
-}
-
int ransac_translation(double *matched_points, int npoints,
int *number_of_inliers, int *best_inlier_mask,
double *best_params) {
