355 строки
9.6 KiB
C
355 строки
9.6 KiB
C
/*
|
|
* Copyright (c) 2017, 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.
|
|
*/
|
|
|
|
#include <memory.h>
|
|
#include <math.h>
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <assert.h>
|
|
|
|
static const double TINY_NEAR_ZERO = 1.0E-16;
|
|
|
|
// Solves Ax = b, where x and b are column vectors of size nx1 and A is nxn
|
|
static INLINE int linsolve(int n, double *A, int stride, double *b, double *x) {
|
|
int i, j, k;
|
|
double c;
|
|
// Forward elimination
|
|
for (k = 0; k < n - 1; k++) {
|
|
// Bring the largest magitude to the diagonal position
|
|
for (i = n - 1; i > k; i--) {
|
|
if (fabs(A[(i - 1) * stride + k]) < fabs(A[i * stride + k])) {
|
|
for (j = 0; j < n; j++) {
|
|
c = A[i * stride + j];
|
|
A[i * stride + j] = A[(i - 1) * stride + j];
|
|
A[(i - 1) * stride + j] = c;
|
|
}
|
|
c = b[i];
|
|
b[i] = b[i - 1];
|
|
b[i - 1] = c;
|
|
}
|
|
}
|
|
for (i = k; i < n - 1; i++) {
|
|
if (fabs(A[k * stride + k]) < TINY_NEAR_ZERO) return 0;
|
|
c = A[(i + 1) * stride + k] / A[k * stride + k];
|
|
for (j = 0; j < n; j++) A[(i + 1) * stride + j] -= c * A[k * stride + j];
|
|
b[i + 1] -= c * b[k];
|
|
}
|
|
}
|
|
// Backward substitution
|
|
for (i = n - 1; i >= 0; i--) {
|
|
if (fabs(A[i * stride + i]) < TINY_NEAR_ZERO) return 0;
|
|
c = 0;
|
|
for (j = i + 1; j <= n - 1; j++) c += A[i * stride + j] * x[j];
|
|
x[i] = (b[i] - c) / A[i * stride + i];
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////////////////
|
|
// Least-squares
|
|
// Solves for n-dim x in a least squares sense to minimize |Ax - b|^2
|
|
// The solution is simply x = (A'A)^-1 A'b or simply the solution for
|
|
// the system: A'A x = A'b
|
|
static INLINE int least_squares(int n, double *A, int rows, int stride,
|
|
double *b, double *scratch, double *x) {
|
|
int i, j, k;
|
|
double *scratch_ = NULL;
|
|
double *AtA, *Atb;
|
|
if (!scratch) {
|
|
scratch_ = (double *)aom_malloc(sizeof(*scratch) * n * (n + 1));
|
|
scratch = scratch_;
|
|
}
|
|
AtA = scratch;
|
|
Atb = scratch + n * n;
|
|
|
|
for (i = 0; i < n; ++i) {
|
|
for (j = i; j < n; ++j) {
|
|
AtA[i * n + j] = 0.0;
|
|
for (k = 0; k < rows; ++k)
|
|
AtA[i * n + j] += A[k * stride + i] * A[k * stride + j];
|
|
AtA[j * n + i] = AtA[i * n + j];
|
|
}
|
|
Atb[i] = 0;
|
|
for (k = 0; k < rows; ++k) Atb[i] += A[k * stride + i] * b[k];
|
|
}
|
|
int ret = linsolve(n, AtA, n, Atb, x);
|
|
if (scratch_) aom_free(scratch_);
|
|
return ret;
|
|
}
|
|
|
|
// Matrix multiply
|
|
static INLINE 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;
|
|
}
|
|
}
|
|
}
|
|
|
|
//
|
|
// The functions below are needed only for homography computation
|
|
// Remove if the homography models are not used.
|
|
//
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// svdcmp
|
|
// Adopted from Numerical Recipes in C
|
|
|
|
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 INLINE 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 INLINE 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;
|
|
}
|