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vpx/vp9/encoder/vp9_ransac.c
Sarah Parker a7aab42915 Optical flow for computing global motion params 
Addressing comments, fixing style issues

Change-Id: I91b72ab5cdf80d68476858f442616ab3af41e709
2016-01-22 11:29:33 -08:00

1022 lines
26 KiB
C
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/*
* Copyright (c) 2015 The WebM project authors. All Rights Reserved.
*
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be
* found in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
#include <memory.h>
#include <math.h>
#include <time.h>
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include "vp9_ransac.h"
#define MAX_PARAMDIM 9
#define MAX_MINPTS 4
#define MAX_DEGENERATE_ITER 10
#define MINPTS_MULTIPLIER 5
// svdcmp
// Adopted from Numerical Recipes in C
static const double TINY_NEAR_ZERO = 1.0E-12;
static inline double SIGN(double a, double b) {
return ((b) >= 0 ? fabs(a) : -fabs(a));
}
static inline double PYTHAG(double a, double b) {
double absa, absb, ct;
absa = fabs(a);
absb = fabs(b);
if(absa > absb) {
ct = absb / absa;
return absa * sqrt(1.0 + ct * ct);
} else {
ct = absa / absb;
return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);
}
}
int IMIN(int a, int b) {
return (((a) < (b)) ? (a) : (b));
}
int IMAX(int a, int b) {
return (((a) < (b)) ? (b) : (a));
}
void MultiplyMat(double *m1, double *m2, double *res,
const int M1, const int N1, const int N2) {
int timesInner = N1;
int timesRows = M1;
int timesCols = N2;
double sum;
int row, col, inner;
for( row = 0; row < timesRows; ++row ) {
for( col = 0; col < timesCols; ++col ) {
sum = 0;
for (inner = 0; inner < timesInner; ++inner )
sum += m1[row * N1 + inner] * m2[inner * N2 + col];
*(res++) = sum;
}
}
}
static int svdcmp_(double **u, int m, int n, double w[], double **v) {
const int max_its = 30;
int flag, i, its, j, jj, k, l, nm;
double anorm, c, f, g, h, s, scale, x, y, z;
double *rv1 = (double *)malloc(sizeof(double) * (n + 1));
g = scale = anorm = 0.0;
for (i = 0; i < n; i++) {
l = i + 1;
rv1[i] = scale * g;
g = s = scale = 0.0;
if (i < m) {
for (k = i; k < m; k++) scale += fabs(u[k][i]);
if (scale) {
for (k = i; k < m; k++) {
u[k][i] /= scale;
s += u[k][i] * u[k][i];
}
f = u[i][i];
g = -SIGN(sqrt(s), f);
h = f * g - s;
u[i][i] = f - g;
for (j = l; j < n; j++) {
for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];
f = s / h;
for (k = i; k < m; k++) u[k][j] += f * u[k][i];
}
for (k = i; k < m; k++) u[k][i] *= scale;
}
}
w[i] = scale * g;
g = s = scale = 0.0;
if (i < m && i != n - 1) {
for (k = l; k < n; k++)
scale += fabs(u[i][k]);
if (scale) {
for (k = l; k < n; k++) {
u[i][k] /= scale;
s += u[i][k] * u[i][k];
}
f = u[i][l];
g = -SIGN(sqrt(s),f);
h = f * g - s;
u[i][l] = f - g;
for (k = l; k < n; k++) rv1[k] = u[i][k] / h;
for (j = l; j < m; j++) {
for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];
for (k = l; k < n; k++) u[j][k] += s * rv1[k];
}
for (k = l; k < n; k++) u[i][k] *= scale;
}
}
anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));
}
for (i = n - 1; i >= 0; i--) {
if (i < n - 1) {
if (g) {
for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;
for (j = l; j < n; j++) {
for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];
for (k = l; k < n; k++) v[k][j] += s * v[k][i];
}
}
for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
}
v[i][i] = 1.0;
g = rv1[i];
l = i;
}
for (i = IMIN(m, n) - 1; i >= 0; i--) {
l = i + 1;
g = w[i];
for (j = l; j < n; j++) u[i][j] = 0.0;
if (g) {
g = 1.0 / g;
for (j = l; j < n; j++) {
for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];
f = (s / u[i][i]) * g;
for (k = i; k < m; k++) u[k][j] += f * u[k][i];
}
for (j = i; j < m; j++) u[j][i] *= g;
} else {
for (j = i; j < m; j++) u[j][i] = 0.0;
}
++u[i][i];
}
for (k = n - 1; k >= 0; k--) {
for (its = 0; its < max_its; its++) {
flag = 1;
for (l = k; l >= 0; l--) {
nm = l - 1;
if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {
flag = 0;
break;
}
if ((double)(fabs(w[nm]) + anorm) == anorm) break;
}
if (flag) {
c = 0.0;
s = 1.0;
for (i = l; i <= k; i++) {
f = s * rv1[i];
rv1[i] = c * rv1[i];
if ((double)(fabs(f) + anorm) == anorm) break;
g = w[i];
h = PYTHAG(f, g);
w[i] = h;
h = 1.0 / h;
c = g * h;
s = -f * h;
for (j = 0; j < m; j++) {
y = u[j][nm];
z = u[j][i];
u[j][nm] = y * c + z * s;
u[j][i] = z * c - y * s;
}
}
}
z = w[k];
if (l == k) {
if (z < 0.0) {
w[k] = -z;
for (j = 0; j < n; j++) v[j][k] = -v[j][k];
}
break;
}
if (its == max_its - 1) {
return 1;
}
assert(k > 0);
x = w[l];
nm = k - 1;
y = w[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = PYTHAG(f, 1.0);
f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x;
c = s = 1.0;
for (j = l; j <= nm; j++) {
i = j + 1;
g = rv1[i];
y = w[i];
h = s * g;
g = c * g;
z = PYTHAG(f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y *= c;
for (jj = 0; jj < n; jj++) {
x = v[jj][j];
z = v[jj][i];
v[jj][j] = x * c + z * s;
v[jj][i] = z * c - x * s;
}
z = PYTHAG(f, h);
w[j] = z;
if (z) {
z = 1.0 / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
for (jj = 0; jj < m; jj++) {
y = u[jj][j];
z = u[jj][i];
u[jj][j] = y * c + z * s;
u[jj][i] = z * c - y * s;
}
}
rv1[l] = 0.0;
rv1[k] = f;
w[k] = x;
}
}
free(rv1);
return 0;
}
static int SVD(double *U, double *W, double *V, double *matx, int M, int N) {
// Assumes allocation for U is MxN
double **nrU, **nrV;
int problem, i;
nrU = (double **)malloc((M)*sizeof(double*));
nrV = (double **)malloc((N)*sizeof(double*));
problem = !(nrU && nrV);
if (!problem) {
problem = 0;
for (i = 0; i < M; i++) {
nrU[i] = &U[i * N];
}
for (i = 0; i < N; i++) {
nrV[i] = &V[i * N];
}
}
if (problem) {
return 1;
}
/* copy from given matx into nrU */
for (i = 0; i < M; i++) {
memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));
}
/* HERE IT IS: do SVD */
if (svdcmp_(nrU, M, N, W, nrV)) {
return 1;
}
/* free Numerical Recipes arrays */
free(nrU);
free(nrV);
return 0;
}
int PseudoInverse(double *inv, double *matx, const int M, const int N) {
double *U, *W, *V, ans;
int i, j, k;
U = (double *)malloc(M * N * sizeof(*matx));
W = (double *)malloc(N * sizeof(*matx));
V = (double *)malloc(N * N * sizeof(*matx));
if (!(U && W && V)) {
return 1;
}
if (SVD(U, W, V, matx, M, N)) {
return 1;
}
for (i = 0; i < N; i++) {
if (fabs(W[i]) < TINY_NEAR_ZERO) {
return 1;
}
}
for (i = 0; i < N; i++) {
for (j = 0; j < M; j++) {
ans = 0;
for (k = 0; k < N; k++) {
ans += V[k + N * i] * U[k + N * j] / W[k];
}
inv[j + M * i] = ans;
}
}
free(U);
free(W);
free(V);
return 0;
}
static double compute_error(projectPointsType projectPoints,
double *points1, int stride1,
double *points2, int stride2,
int npoints, double *H, int *mask) {
int i, n = 0;
double pt[2];
double *mp1 = points1;
double *mp2 = points2;
double sqerr = 0.0;
if (projectPoints == NULL) return -1.0;
if (mask) {
for (i = 0; i < npoints; ++i, mp1 += stride1, mp2 += stride2) {
if (mask[i]) {
projectPoints(H, mp1, pt, 1, stride1, stride2);
sqerr += (pt[0] - mp2[0]) * (pt[0] - mp2[0]) +
(pt[1] - mp2[1]) * (pt[1] - mp2[1]);
n++;
}
}
} else {
for (i = 0; i < npoints; ++i, mp1 += stride1, mp2 += stride2) {
projectPoints(H, mp1, pt, 1, stride1, stride2);
sqerr += (pt[0] - mp2[0]) * (pt[0] - mp2[0]) +
(pt[1] - mp2[1]) * (pt[1] - mp2[1]);
n++;
}
}
return sqrt(sqerr / n);
}
////////////////////////////////////////////////////////////////////////////////
// ransac
typedef int (*isDegenerateType)(double *p);
typedef void (*normalizeType)(double *p, int np, double *T);
typedef void (*denormalizeType)(double *H, double *T1, double *T2);
typedef int (*findTransformationType)(int points,
double *points1,
double *points2,
double *H);
static int get_rand_indices(int npoints, int minpts, int *indices) {
int i, j;
int ptr = rand() % npoints;
if (minpts > npoints)
return 0;
indices[0] = ptr;
ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
i = 1;
while (i < minpts) {
int index = rand() % npoints;
while (index) {
ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
for (j = 0; j < i; ++j) {
if (indices[j] == ptr)
break;
}
if (j == i)
index--;
}
indices[i++] = ptr;
}
return 1;
}
int ransac_(double *matched_points,
int npoints,
int *number_of_inliers,
int *best_inlier_mask,
double *bestH,
const int minpts,
const int paramdim,
isDegenerateType isDegenerate,
normalizeType normalize,
denormalizeType denormalize,
findTransformationType findTransformation,
projectPointsType projectPoints) {
static const double INLIER_THRESHOLD_NORMALIZED = 0.1;
static const double INLIER_THRESHOLD_UNNORMALIZED = 1.0;
static const double PROBABILITY_REQUIRED = 0.9;
static const double EPS = 1e-12;
static const int MIN_TRIALS = 20;
const double inlier_threshold = (normalize && denormalize ?
INLIER_THRESHOLD_NORMALIZED :
INLIER_THRESHOLD_UNNORMALIZED);
int N = 10000, trial_count = 0;
int i;
int ret_val = 0;
int max_inliers = 0;
double best_variance = 0.0;
double H[MAX_PARAMDIM];
double points1[2 * MAX_MINPTS];
double points2[2 * MAX_MINPTS];
int indices[MAX_MINPTS];
double *best_inlier_set1;
double *best_inlier_set2;
double *inlier_set1;
double *inlier_set2;
double *corners1;
double *corners2;
double *image1_coord;
double *image2_coord;
int *inlier_mask;
double *cnp1, *cnp2;
double T1[9], T2[9];
// srand((unsigned)time(NULL)) ;
// better to make this deterministic for a given sequence for ease of testing
srand(npoints);
*number_of_inliers = 0;
if (npoints < minpts * MINPTS_MULTIPLIER) {
printf("Cannot find motion with %d matches\n", npoints);
return 1;
}
best_inlier_set1 = (double *)malloc(sizeof(double) * npoints * 2);
best_inlier_set2 = (double *)malloc(sizeof(double) * npoints * 2);
inlier_set1 = (double *)malloc(sizeof(double) * npoints * 2);
inlier_set2 = (double *)malloc(sizeof(double) * npoints * 2);
corners1 = (double *)malloc(sizeof(double) * npoints * 2);
corners2 = (double *)malloc(sizeof(double) * npoints * 2);
image1_coord = (double *)malloc(sizeof(double) * npoints * 2);
image2_coord = (double *)malloc(sizeof(double) * npoints * 2);
inlier_mask = (int*)malloc(sizeof(int) * npoints);
for(cnp1 = corners1, cnp2 = corners2, i = 0; i < npoints; ++i) {
*(cnp1++) = *(matched_points++);
*(cnp1++) = *(matched_points++);
*(cnp2++) = *(matched_points++);
*(cnp2++) = *(matched_points++);
}
matched_points -= 4 * npoints;
if (normalize && denormalize) {
normalize(corners1, npoints, T1);
normalize(corners2, npoints, T2);
}
while (N > trial_count) {
int num_inliers = 0;
double sum_distance = 0.0;
double sum_distance_squared = 0.0;
int degenerate = 1;
int num_degenerate_iter = 0;
while (degenerate) {
num_degenerate_iter++;
if (!get_rand_indices(npoints, minpts, indices)) {
ret_val = 1;
goto finish_ransac;
}
i = 0;
while (i < minpts) {
int index = indices[i];
// add to list
points1[i*2] = corners1[index*2];
points1[i*2+1] = corners1[index*2+1];
points2[i*2] = corners2[index*2];
points2[i*2+1] = corners2[index*2+1];
i++;
}
degenerate = isDegenerate(points1);
if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
ret_val = 1;
goto finish_ransac;
}
}
if (findTransformation(minpts, points1, points2, H)) {
trial_count++;
continue;
}
projectPoints(H, corners1, image1_coord, npoints, 2, 2);
for( i = 0; i < npoints; ++i ) {
double dx = image1_coord[i*2] - corners2[i*2];
double dy = image1_coord[i*2 + 1] - corners2[i*2 + 1];
double distance = sqrt(dx*dx + dy*dy);
inlier_mask[i] = distance < inlier_threshold;
if (inlier_mask[i]) {
inlier_set1[num_inliers*2] = corners1[i*2];
inlier_set1[num_inliers*2 + 1] = corners1[i*2 + 1];
inlier_set2[num_inliers*2] = corners2[i*2];
inlier_set2[num_inliers*2 + 1] = corners2[i*2 + 1];
num_inliers++;
sum_distance += distance;
sum_distance_squared += distance*distance;
}
}
if (num_inliers >= max_inliers) {
double mean_distance = sum_distance / ((double)num_inliers);
double variance = sum_distance_squared / ((double)num_inliers - 1.0) -
mean_distance * mean_distance *
((double)num_inliers) / ((double)num_inliers - 1.0);
if ((num_inliers > max_inliers) ||
(num_inliers==max_inliers && variance < best_variance)) {
best_variance = variance;
max_inliers = num_inliers;
memcpy(bestH, H, paramdim * sizeof(double));
memcpy(best_inlier_set1, inlier_set1, num_inliers*2 * sizeof(double));
memcpy(best_inlier_set2, inlier_set2, num_inliers*2 * sizeof(double));
memcpy(best_inlier_mask, inlier_mask, npoints * sizeof(int));
if (num_inliers > 0) {
double fracinliers = (double)num_inliers/(double)npoints;
double pNoOutliers = 1 - pow(fracinliers, minpts);
int temp;
pNoOutliers = fmax(EPS, pNoOutliers);
pNoOutliers = fmin(1 - EPS, pNoOutliers);
temp = (int)(log(1.0 - PROBABILITY_REQUIRED)/log(pNoOutliers));
if (temp > 0 && temp < N) {
N = IMAX(temp, MIN_TRIALS);
}
}
}
}
trial_count++;
}
// printf("Number of trials = %d\n", trial_count);
findTransformation(max_inliers, best_inlier_set1, best_inlier_set2, bestH);
if (normalize && denormalize) {
denormalize(bestH, T1, T2);
}
*number_of_inliers = max_inliers;
/*
printf("Error score (all) = %g\n",
compute_error(projectPoints, matched_points, 4,
matched_points + 2, 4,
npoints, bestH, NULL));
printf("Error score (inliers) = %g\n",
compute_error(projectPoints, matched_points, 4,
matched_points + 2, 4,
npoints, bestH,
best_inlier_mask));
*/
finish_ransac:
free(best_inlier_set1);
free(best_inlier_set2);
free(inlier_set1);
free(inlier_set2);
free(corners1);
free(corners2);
free(image1_coord);
free(image2_coord);
free(inlier_mask);
return ret_val;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////
static void normalizeHomography(double *pts, int n, double *T) {
// Assume the points are 2d coordinates with scale = 1
double *p = pts;
double mean[2] = {0, 0};
double msqe = 0;
double scale;
int i;
for (i = 0; i < n; ++i, p+=2) {
mean[0] += p[0];
mean[1] += p[1];
}
mean[0] /= n;
mean[1] /= n;
for (p = pts, i = 0; i < n; ++i, p+=2) {
p[0] -= mean[0];
p[1] -= mean[1];
msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
}
msqe /= n;
scale = sqrt(2)/msqe;
T[0] = scale;
T[1] = 0;
T[2] = -scale * mean[0];
T[3] = 0;
T[4] = scale;
T[5] = -scale * mean[1];
T[6] = 0;
T[7] = 0;
T[8] = 1;
for (p = pts, i = 0; i < n; ++i, p+=2) {
p[0] *= scale;
p[1] *= scale;
}
}
static void invnormalize_mat(double *T, double *iT) {
double is = 1.0/T[0];
double m0 = -T[2]*is;
double m1 = -T[5]*is;
iT[0] = is;
iT[1] = 0;
iT[2] = m0;
iT[3] = 0;
iT[4] = is;
iT[5] = m1;
iT[6] = 0;
iT[7] = 0;
iT[8] = 1;
}
static void denormalizeHomography(double *H, double *T1, double *T2) {
double iT2[9];
double H2[9];
invnormalize_mat(T2, iT2);
MultiplyMat(H, T1, H2, 3, 3, 3);
MultiplyMat(iT2, H2, H, 3, 3, 3);
}
static void denormalizeAffine(double *H, double *T1, double *T2) {
double Ha[MAX_PARAMDIM];
Ha[0] = H[0];
Ha[1] = H[1];
Ha[2] = H[4];
Ha[3] = H[2];
Ha[4] = H[3];
Ha[5] = H[5];
Ha[6] = Ha[7] = 0;
Ha[8] = 1;
denormalizeHomography(Ha, T1, T2);
H[0] = Ha[0];
H[1] = Ha[1];
H[2] = Ha[3];
H[3] = Ha[4];
H[4] = Ha[2];
H[5] = Ha[5];
}
static void denormalizeRotZoom(double *H, double *T1, double *T2) {
double Ha[MAX_PARAMDIM];
Ha[0] = H[0];
Ha[1] = H[1];
Ha[2] = H[2];
Ha[3] = -H[1];
Ha[4] = H[0];
Ha[5] = H[3];
Ha[6] = Ha[7] = 0;
Ha[8] = 1;
denormalizeHomography(Ha, T1, T2);
H[0] = Ha[0];
H[1] = Ha[1];
H[2] = Ha[2];
H[3] = Ha[5];
}
static void denormalizeTranslation(double *H, double *T1, double *T2) {
double Ha[MAX_PARAMDIM];
Ha[0] = 1;
Ha[1] = 0;
Ha[2] = H[0];
Ha[3] = 0;
Ha[4] = 1;
Ha[5] = H[1];
Ha[6] = Ha[7] = 0;
Ha[8] = 1;
denormalizeHomography(Ha, T1, T2);
H[0] = Ha[2];
H[1] = Ha[5];
}
static int is_collinear3(double *p1, double *p2, double *p3) {
static const double collinear_eps = 1e-3;
const double v = (p2[0] - p1[0]) * (p3[1] - p1[1]) -
(p2[1] - p1[1]) * (p3[0] - p1[0]);
return fabs(v) < collinear_eps;
}
static int isDegenerateTranslation(double *p) {
return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
}
static int isDegenerateAffine(double *p) {
return is_collinear3(p, p + 2, p + 4);
}
static int isDegenerateHomography(double *p) {
return is_collinear3(p, p + 2, p + 4) ||
is_collinear3(p, p + 2, p + 6) ||
is_collinear3(p, p + 4, p + 6) ||
is_collinear3(p + 2, p + 4, p + 6);
}
int findTranslation(const int np, double *pts1, double *pts2, double *mat) {
int i;
double sx, sy, dx, dy;
double sumx, sumy;
double T1[9], T2[9];
normalizeHomography(pts1, np, T1);
normalizeHomography(pts2, np, T2);
sumx = 0;
sumy = 0;
for (i = 0; i < np; ++i) {
dx = *(pts2++);
dy = *(pts2++);
sx = *(pts1++);
sy = *(pts1++);
sumx += dx - sx;
sumy += dy - sy;
}
mat[0] = sumx / np;
mat[1] = sumy / np;
denormalizeTranslation(mat, T1, T2);
return 0;
}
int findRotZoom(const int np, double *pts1, double *pts2, double *mat) {
const int np2 = np * 2;
double *a = (double *)malloc(sizeof(double) * np2 * 9);
double *b = a + np2 * 4;
double *temp = b + np2;
int i;
double sx, sy, dx, dy;
double T1[9], T2[9];
normalizeHomography(pts1, np, T1);
normalizeHomography(pts2, np, T2);
for (i = 0; i < np; ++i) {
dx = *(pts2++);
dy = *(pts2++);
sx = *(pts1++);
sy = *(pts1++);
a[i * 2 * 4 + 0] = sx;
a[i * 2 * 4 + 1] = sy;
a[i * 2 * 4 + 2] = 1;
a[i * 2 * 4 + 3] = 0;
a[(i * 2 + 1) * 4 + 0] = sy;
a[(i * 2 + 1) * 4 + 1] = -sx;
a[(i * 2 + 1) * 4 + 2] = 0;
a[(i * 2 + 1) * 4 + 3] = 1;
b[2 * i] = dx;
b[2 * i + 1] = dy;
}
if (PseudoInverse(temp, a, np2, 4)){
free(a);
return 1;
}
MultiplyMat(temp, b, mat, 4, np2, 1);
denormalizeRotZoom(mat, T1, T2);
free(a);
return 0;
}
int findAffine(const int np, double *pts1, double *pts2, double *mat) {
const int np2 = np * 2;
double *a = (double *)malloc(sizeof(double) * np2 * 13);
double *b = a + np2 * 6;
double *temp = b + np2;
int i;
double sx, sy, dx, dy;
double T1[9], T2[9];
normalizeHomography(pts1, np, T1);
normalizeHomography(pts2, np, T2);
for (i = 0; i < np; ++i) {
dx = *(pts2++);
dy = *(pts2++);
sx = *(pts1++);
sy = *(pts1++);
a[i * 2 * 6 + 0] = sx;
a[i * 2 * 6 + 1] = sy;
a[i * 2 * 6 + 2] = 0;
a[i * 2 * 6 + 3] = 0;
a[i * 2 * 6 + 4] = 1;
a[i * 2 * 6 + 5] = 0;
a[(i * 2 + 1) * 6 + 0] = 0;
a[(i * 2 + 1) * 6 + 1] = 0;
a[(i * 2 + 1) * 6 + 2] = sx;
a[(i * 2 + 1) * 6 + 3] = sy;
a[(i * 2 + 1) * 6 + 4] = 0;
a[(i * 2 + 1) * 6 + 5] = 1;
b[2 * i] = dx;
b[2 * i + 1] = dy;
}
if (PseudoInverse(temp, a, np2, 6)){
free(a);
return 1;
}
MultiplyMat(temp, b, mat, 6, np2, 1);
denormalizeAffine(mat, T1, T2);
free(a);
return 0;
}
int findHomography(const int np, double *pts1, double *pts2, double *mat) {
// Implemented from Peter Kovesi's normalized implementation
const int np3 = np * 3;
double *a = (double *)malloc(sizeof(double) * np3 * 18);
double *U = a + np3 * 9;
double S[9], V[9 * 9];
int i, mini;
double sx, sy, dx, dy;
double T1[9], T2[9];
normalizeHomography(pts1, np, T1);
normalizeHomography(pts2, np, T2);
for (i = 0; i < np; ++i) {
dx = *(pts2++);
dy = *(pts2++);
sx = *(pts1++);
sy = *(pts1++);
a[i * 3 * 9 + 0] = a[i * 3 * 9 + 1] = a[i * 3 * 9 + 2] = 0;
a[i * 3 * 9 + 3] = -sx;
a[i * 3 * 9 + 4] = -sy;
a[i * 3 * 9 + 5] = -1;
a[i * 3 * 9 + 6] = dy * sx;
a[i * 3 * 9 + 7] = dy * sy;
a[i * 3 * 9 + 8] = dy;
a[(i * 3 + 1) * 9 + 0] = sx;
a[(i * 3 + 1) * 9 + 1] = sy;
a[(i * 3 + 1) * 9 + 2] = 1;
a[(i * 3 + 1) * 9 + 3] = a[(i * 3 + 1) * 9 + 4] =
a[(i * 3 + 1) * 9 + 5] = 0;
a[(i * 3 + 1) * 9 + 6] = -dx * sx;
a[(i * 3 + 1) * 9 + 7] = -dx * sy;
a[(i * 3 + 1) * 9 + 8] = -dx;
a[(i * 3 + 2) * 9 + 0] = -dy * sx;
a[(i * 3 + 2) * 9 + 1] = -dy * sy;
a[(i * 3 + 2) * 9 + 2] = -dy;
a[(i * 3 + 2) * 9 + 3] = dx * sx;
a[(i * 3 + 2) * 9 + 4] = dx * sy;
a[(i * 3 + 2) * 9 + 5] = dx;
a[(i * 3 + 2) * 9 + 6] = a[(i * 3 + 2) * 9 + 7] =
a[(i * 3 + 2) * 9 + 8] = 0;
}
if (SVD(U, S, V, a, np3, 9)) {
free(a);
return 1;
} else {
double minS = 1e12;
mini = -1;
for (i = 0; i < 9; ++i) {
if (S[i] < minS) {
minS = S[i];
mini = i;
}
}
}
for (i = 0; i < 9; i++) mat[i] = V[i * 9 + mini];
denormalizeHomography(mat, T1, T2);
free(a);
if (mat[8] == 0.0) {
return 1;
}
return 0;
}
int findHomographyScale1(const int np, double *pts1, double *pts2,
double *mat) {
// This implementation assumes h33 = 1, but does not seem to give good results
const int np2 = np * 2;
double *a = (double *)malloc(sizeof(double) * np2 * 17);
double *b = a + np2 * 8;
double *temp = b + np2;
int i, j;
double sx, sy, dx, dy;
double T1[9], T2[9];
normalizeHomography(pts1, np, T1);
normalizeHomography(pts2, np, T2);
for (i = 0, j = np; i < np; ++i, ++j) {
dx = *(pts2++);
dy = *(pts2++);
sx = *(pts1++);
sy = *(pts1++);
a[i * 8 + 0] = a[j * 8 + 3] = sx;
a[i * 8 + 1] = a[j * 8 + 4] = sy;
a[i * 8 + 2] = a[j * 8 + 5] = 1;
a[i * 8 + 3] = a[i * 8 + 4] = a[i * 8 + 5] =
a[j * 8 + 0] = a[j * 8 + 1] = a[j * 8 + 2] = 0;
a[i * 8 + 6] = -dx * sx;
a[i * 8 + 7] = -dx * sy;
a[j * 8 + 6] = -dy * sx;
a[j * 8 + 7] = -dy * sy;
b[i] = dx;
b[j] = dy;
}
if (PseudoInverse(temp, a, np2, 8)) {
free(a);
return 1;
}
MultiplyMat(temp, b, &*mat, 8, np2, 1);
mat[8] = 1;
denormalizeHomography(mat, T1, T2);
free(a);
return 0;
}
int ransacTranslation(double *matched_points, int npoints,
int *number_of_inliers,
int *best_inlier_mask, double *bestH) {
return ransac_(matched_points,
npoints,
number_of_inliers,
best_inlier_mask,
bestH,
3,
2,
isDegenerateTranslation,
NULL, // normalizeHomography,
NULL, // denormalizeRotZoom,
findTranslation,
projectPointsTranslation);
}
int ransacRotZoom(double *matched_points, int npoints,
int *number_of_inliers,
int *best_inlier_mask, double *bestH) {
return ransac_(matched_points,
npoints,
number_of_inliers,
best_inlier_mask,
bestH,
3,
4,
isDegenerateAffine,
NULL, // normalizeHomography,
NULL, // denormalizeRotZoom,
findRotZoom,
projectPointsRotZoom);
}
int ransacAffine(double *matched_points, int npoints,
int *number_of_inliers,
int *best_inlier_mask, double *bestH) {
return ransac_(matched_points,
npoints,
number_of_inliers,
best_inlier_mask,
bestH,
3,
6,
isDegenerateAffine,
NULL, // normalizeHomography,
NULL, // denormalizeAffine,
findAffine,
projectPointsAffine);
}
int ransacHomography(double *matched_points, int npoints,
int *number_of_inliers,
int *best_inlier_mask, double *bestH) {
int result =
ransac_(matched_points,
npoints,
number_of_inliers,
best_inlier_mask,
bestH,
4,
8,
isDegenerateHomography,
NULL, // normalizeHomography,
NULL, // denormalizeHomography,
findHomography,
projectPointsHomography);
if (!result) {
// normalize so that H33 = 1
int i;
double m = 1.0 / bestH[8];
for (i = 0; i < 8; ++i)
bestH[i] *= m;
bestH[8] = 1.0;
}
return result;
}
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