blob: ab0d53022e09460b95ad3771e2b25b89d965c797 [file] [log] [blame]
/*
* 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);
}