#ifndef DLS_H_
#define DLS_H_
#include "precomp.hpp"
#include <iostream>
using namespace std;
using namespace cv;
class dls
{
public:
dls(const cv::Mat& opoints, const cv::Mat& ipoints);
~dls();
bool compute_pose(cv::Mat& R, cv::Mat& t);
private:
// initialisation
template <typename OpointType, typename IpointType>
void init_points(const cv::Mat& opoints, const cv::Mat& ipoints)
{
for(int i = 0; i < N; i++)
{
p.at<double>(0,i) = opoints.at<OpointType>(i).x;
p.at<double>(1,i) = opoints.at<OpointType>(i).y;
p.at<double>(2,i) = opoints.at<OpointType>(i).z;
// compute mean of object points
mn.at<double>(0) += p.at<double>(0,i);
mn.at<double>(1) += p.at<double>(1,i);
mn.at<double>(2) += p.at<double>(2,i);
// make z into unit vectors from normalized pixel coords
double sr = std::pow(ipoints.at<IpointType>(i).x, 2) +
std::pow(ipoints.at<IpointType>(i).y, 2) + (double)1;
sr = std::sqrt(sr);
z.at<double>(0,i) = ipoints.at<IpointType>(i).x / sr;
z.at<double>(1,i) = ipoints.at<IpointType>(i).y / sr;
z.at<double>(2,i) = (double)1 / sr;
}
mn.at<double>(0) /= (double)N;
mn.at<double>(1) /= (double)N;
mn.at<double>(2) /= (double)N;
}
// main algorithm
cv::Mat LeftMultVec(const cv::Mat& v);
void run_kernel(const cv::Mat& pp);
void build_coeff_matrix(const cv::Mat& pp, cv::Mat& Mtilde, cv::Mat& D);
void compute_eigenvec(const cv::Mat& Mtilde, cv::Mat& eigenval_real, cv::Mat& eigenval_imag,
cv::Mat& eigenvec_real, cv::Mat& eigenvec_imag);
void fill_coeff(const cv::Mat * D);
// useful functions
cv::Mat cayley_LS_M(const std::vector<double>& a, const std::vector<double>& b,
const std::vector<double>& c, const std::vector<double>& u);
cv::Mat Hessian(const double s[]);
cv::Mat cayley2rotbar(const cv::Mat& s);
cv::Mat skewsymm(const cv::Mat * X1);
// extra functions
cv::Mat rotx(const double t);
cv::Mat roty(const double t);
cv::Mat rotz(const double t);
cv::Mat mean(const cv::Mat& M);
bool is_empty(const cv::Mat * v);
bool positive_eigenvalues(const cv::Mat * eigenvalues);
cv::Mat p, z, mn; // object-image points
int N; // number of input points
std::vector<double> f1coeff, f2coeff, f3coeff, cost_; // coefficient for coefficients matrix
std::vector<cv::Mat> C_est_, t_est_; // optimal candidates
cv::Mat C_est__, t_est__; // optimal found solution
double cost__; // optimal found solution
};
class EigenvalueDecomposition {
private:
// Holds the data dimension.
int n;
// Stores real/imag part of a complex division.
double cdivr, cdivi;
// Pointer to internal memory.
double *d, *e, *ort;
double **V, **H;
// Holds the computed eigenvalues.
Mat _eigenvalues;
// Holds the computed eigenvectors.
Mat _eigenvectors;
// Allocates memory.
template<typename _Tp>
_Tp *alloc_1d(int m) {
return new _Tp[m];
}
// Allocates memory.
template<typename _Tp>
_Tp *alloc_1d(int m, _Tp val) {
_Tp *arr = alloc_1d<_Tp> (m);
for (int i = 0; i < m; i++)
arr[i] = val;
return arr;
}
// Allocates memory.
template<typename _Tp>
_Tp **alloc_2d(int m, int _n) {
_Tp **arr = new _Tp*[m];
for (int i = 0; i < m; i++)
arr[i] = new _Tp[_n];
return arr;
}
// Allocates memory.
template<typename _Tp>
_Tp **alloc_2d(int m, int _n, _Tp val) {
_Tp **arr = alloc_2d<_Tp> (m, _n);
for (int i = 0; i < m; i++) {
for (int j = 0; j < _n; j++) {
arr[i][j] = val;
}
}
return arr;
}
void cdiv(double xr, double xi, double yr, double yi) {
double r, dv;
if (std::abs(yr) > std::abs(yi)) {
r = yi / yr;
dv = yr + r * yi;
cdivr = (xr + r * xi) / dv;
cdivi = (xi - r * xr) / dv;
} else {
r = yr / yi;
dv = yi + r * yr;
cdivr = (r * xr + xi) / dv;
cdivi = (r * xi - xr) / dv;
}
}
// Nonsymmetric reduction from Hessenberg to real Schur form.
void hqr2() {
// This is derived from the Algol procedure hqr2,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
// Initialize
int nn = this->n;
int n1 = nn - 1;
int low = 0;
int high = nn - 1;
double eps = std::pow(2.0, -52.0);
double exshift = 0.0;
double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
// Store roots isolated by balanc and compute matrix norm
double norm = 0.0;
for (int i = 0; i < nn; i++) {
if (i < low || i > high) {
d[i] = H[i][i];
e[i] = 0.0;
}
for (int j = std::max(i - 1, 0); j < nn; j++) {
norm = norm + std::abs(H[i][j]);
}
}
// Outer loop over eigenvalue index
int iter = 0;
while (n1 >= low) {
// Look for single small sub-diagonal element
int l = n1;
while (l > low) {
s = std::abs(H[l - 1][l - 1]) + std::abs(H[l][l]);
if (s == 0.0) {
s = norm;
}
if (std::abs(H[l][l - 1]) < eps * s) {
break;
}
l--;
}
// Check for convergence
// One root found
if (l == n1) {
H[n1][n1] = H[n1][n1] + exshift;
d[n1] = H[n1][n1];
e[n1] = 0.0;
n1--;
iter = 0;
// Two roots found
} else if (l == n1 - 1) {
w = H[n1][n1 - 1] * H[n1 - 1][n1];
p = (H[n1 - 1][n1 - 1] - H[n1][n1]) / 2.0;
q = p * p + w;
z = std::sqrt(std::abs(q));
H[n1][n1] = H[n1][n1] + exshift;
H[n1 - 1][n1 - 1] = H[n1 - 1][n1 - 1] + exshift;
x = H[n1][n1];
// Real pair
if (q >= 0) {
if (p >= 0) {
z = p + z;
} else {
z = p - z;
}
d[n1 - 1] = x + z;
d[n1] = d[n1 - 1];
if (z != 0.0) {
d[n1] = x - w / z;
}
e[n1 - 1] = 0.0;
e[n1] = 0.0;
x = H[n1][n1 - 1];
s = std::abs(x) + std::abs(z);
p = x / s;
q = z / s;
r = std::sqrt(p * p + q * q);
p = p / r;
q = q / r;
// Row modification
for (int j = n1 - 1; j < nn; j++) {
z = H[n1 - 1][j];
H[n1 - 1][j] = q * z + p * H[n1][j];
H[n1][j] = q * H[n1][j] - p * z;
}
// Column modification
for (int i = 0; i <= n1; i++) {
z = H[i][n1 - 1];
H[i][n1 - 1] = q * z + p * H[i][n1];
H[i][n1] = q * H[i][n1] - p * z;
}
// Accumulate transformations
for (int i = low; i <= high; i++) {
z = V[i][n1 - 1];
V[i][n1 - 1] = q * z + p * V[i][n1];
V[i][n1] = q * V[i][n1] - p * z;
}
// Complex pair
} else {
d[n1 - 1] = x + p;
d[n1] = x + p;
e[n1 - 1] = z;
e[n1] = -z;
}
n1 = n1 - 2;
iter = 0;
// No convergence yet
} else {
// Form shift
x = H[n1][n1];
y = 0.0;
w = 0.0;
if (l < n1) {
y = H[n1 - 1][n1 - 1];
w = H[n1][n1 - 1] * H[n1 - 1][n1];
}
// Wilkinson's original ad hoc shift
if (iter == 10) {
exshift += x;
for (int i = low; i <= n1; i++) {
H[i][i] -= x;
}
s = std::abs(H[n1][n1 - 1]) + std::abs(H[n1 - 1][n1 - 2]);
x = y = 0.75 * s;
w = -0.4375 * s * s;
}
// MATLAB's new ad hoc shift
if (iter == 30) {
s = (y - x) / 2.0;
s = s * s + w;
if (s > 0) {
s = std::sqrt(s);
if (y < x) {
s = -s;
}
s = x - w / ((y - x) / 2.0 + s);
for (int i = low; i <= n1; i++) {
H[i][i] -= s;
}
exshift += s;
x = y = w = 0.964;
}
}
iter = iter + 1; // (Could check iteration count here.)
// Look for two consecutive small sub-diagonal elements
int m = n1 - 2;
while (m >= l) {
z = H[m][m];
r = x - z;
s = y - z;
p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
q = H[m + 1][m + 1] - z - r - s;
r = H[m + 2][m + 1];
s = std::abs(p) + std::abs(q) + std::abs(r);
p = p / s;
q = q / s;
r = r / s;
if (m == l) {
break;
}
if (std::abs(H[m][m - 1]) * (std::abs(q) + std::abs(r)) < eps * (std::abs(p)
* (std::abs(H[m - 1][m - 1]) + std::abs(z) + std::abs(
H[m + 1][m + 1])))) {
break;
}
m--;
}
for (int i = m + 2; i <= n1; i++) {
H[i][i - 2] = 0.0;
if (i > m + 2) {
H[i][i - 3] = 0.0;
}
}
// Double QR step involving rows l:n and columns m:n
for (int k = m; k <= n1 - 1; k++) {
bool notlast = (k != n1 - 1);
if (k != m) {
p = H[k][k - 1];
q = H[k + 1][k - 1];
r = (notlast ? H[k + 2][k - 1] : 0.0);
x = std::abs(p) + std::abs(q) + std::abs(r);
if (x != 0.0) {
p = p / x;
q = q / x;
r = r / x;
}
}
if (x == 0.0) {
break;
}
s = std::sqrt(p * p + q * q + r * r);
if (p < 0) {
s = -s;
}
if (s != 0) {
if (k != m) {
H[k][k - 1] = -s * x;
} else if (l != m) {
H[k][k - 1] = -H[k][k - 1];
}
p = p + s;
x = p / s;
y = q / s;
z = r / s;
q = q / p;
r = r / p;
// Row modification
for (int j = k; j < nn; j++) {
p = H[k][j] + q * H[k + 1][j];
if (notlast) {
p = p + r * H[k + 2][j];
H[k + 2][j] = H[k + 2][j] - p * z;
}
H[k][j] = H[k][j] - p * x;
H[k + 1][j] = H[k + 1][j] - p * y;
}
// Column modification
for (int i = 0; i <= std::min(n1, k + 3); i++) {
p = x * H[i][k] + y * H[i][k + 1];
if (notlast) {
p = p + z * H[i][k + 2];
H[i][k + 2] = H[i][k + 2] - p * r;
}
H[i][k] = H[i][k] - p;
H[i][k + 1] = H[i][k + 1] - p * q;
}
// Accumulate transformations
for (int i = low; i <= high; i++) {
p = x * V[i][k] + y * V[i][k + 1];
if (notlast) {
p = p + z * V[i][k + 2];
V[i][k + 2] = V[i][k + 2] - p * r;
}
V[i][k] = V[i][k] - p;
V[i][k + 1] = V[i][k + 1] - p * q;
}
} // (s != 0)
} // k loop
} // check convergence
} // while (n1 >= low)
// Backsubstitute to find vectors of upper triangular form
if (norm == 0.0) {
return;
}
for (n1 = nn - 1; n1 >= 0; n1--) {
p = d[n1];
q = e[n1];
// Real vector
if (q == 0) {
int l = n1;
H[n1][n1] = 1.0;
for (int i = n1 - 1; i >= 0; i--) {
w = H[i][i] - p;
r = 0.0;
for (int j = l; j <= n1; j++) {
r = r + H[i][j] * H[j][n1];
}
if (e[i] < 0.0) {
z = w;
s = r;
} else {
l = i;
if (e[i] == 0.0) {
if (w != 0.0) {
H[i][n1] = -r / w;
} else {
H[i][n1] = -r / (eps * norm);
}
// Solve real equations
} else {
x = H[i][i + 1];
y = H[i + 1][i];
q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
t = (x * s - z * r) / q;
H[i][n1] = t;
if (std::abs(x) > std::abs(z)) {
H[i + 1][n1] = (-r - w * t) / x;
} else {
H[i + 1][n1] = (-s - y * t) / z;
}
}
// Overflow control
t = std::abs(H[i][n1]);
if ((eps * t) * t > 1) {
for (int j = i; j <= n1; j++) {
H[j][n1] = H[j][n1] / t;
}
}
}
}
// Complex vector
} else if (q < 0) {
int l = n1 - 1;
// Last vector component imaginary so matrix is triangular
if (std::abs(H[n1][n1 - 1]) > std::abs(H[n1 - 1][n1])) {
H[n1 - 1][n1 - 1] = q / H[n1][n1 - 1];
H[n1 - 1][n1] = -(H[n1][n1] - p) / H[n1][n1 - 1];
} else {
cdiv(0.0, -H[n1 - 1][n1], H[n1 - 1][n1 - 1] - p, q);
H[n1 - 1][n1 - 1] = cdivr;
H[n1 - 1][n1] = cdivi;
}
H[n1][n1 - 1] = 0.0;
H[n1][n1] = 1.0;
for (int i = n1 - 2; i >= 0; i--) {
double ra, sa;
ra = 0.0;
sa = 0.0;
for (int j = l; j <= n1; j++) {
ra = ra + H[i][j] * H[j][n1 - 1];
sa = sa + H[i][j] * H[j][n1];
}
w = H[i][i] - p;
if (e[i] < 0.0) {
z = w;
r = ra;
s = sa;
} else {
l = i;
if (e[i] == 0) {
cdiv(-ra, -sa, w, q);
H[i][n1 - 1] = cdivr;
H[i][n1] = cdivi;
} else {
// Solve complex equations
x = H[i][i + 1];
y = H[i + 1][i];
double vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
double vi = (d[i] - p) * 2.0 * q;
if (vr == 0.0 && vi == 0.0) {
vr = eps * norm * (std::abs(w) + std::abs(q) + std::abs(x)
+ std::abs(y) + std::abs(z));
}
cdiv(x * r - z * ra + q * sa,
x * s - z * sa - q * ra, vr, vi);
H[i][n1 - 1] = cdivr;
H[i][n1] = cdivi;
if (std::abs(x) > (std::abs(z) + std::abs(q))) {
H[i + 1][n1 - 1] = (-ra - w * H[i][n1 - 1] + q
* H[i][n1]) / x;
H[i + 1][n1] = (-sa - w * H[i][n1] - q * H[i][n1
- 1]) / x;
} else {
cdiv(-r - y * H[i][n1 - 1], -s - y * H[i][n1], z,
q);
H[i + 1][n1 - 1] = cdivr;
H[i + 1][n1] = cdivi;
}
}
// Overflow control
t = std::max(std::abs(H[i][n1 - 1]), std::abs(H[i][n1]));
if ((eps * t) * t > 1) {
for (int j = i; j <= n1; j++) {
H[j][n1 - 1] = H[j][n1 - 1] / t;
H[j][n1] = H[j][n1] / t;
}
}
}
}
}
}
// Vectors of isolated roots
for (int i = 0; i < nn; i++) {
if (i < low || i > high) {
for (int j = i; j < nn; j++) {
V[i][j] = H[i][j];
}
}
}
// Back transformation to get eigenvectors of original matrix
for (int j = nn - 1; j >= low; j--) {
for (int i = low; i <= high; i++) {
z = 0.0;
for (int k = low; k <= std::min(j, high); k++) {
z = z + V[i][k] * H[k][j];
}
V[i][j] = z;
}
}
}
// Nonsymmetric reduction to Hessenberg form.
void orthes() {
// This is derived from the Algol procedures orthes and ortran,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutines in EISPACK.
int low = 0;
int high = n - 1;
for (int m = low + 1; m <= high - 1; m++) {
// Scale column.
double scale = 0.0;
for (int i = m; i <= high; i++) {
scale = scale + std::abs(H[i][m - 1]);
}
if (scale != 0.0) {
// Compute Householder transformation.
double h = 0.0;
for (int i = high; i >= m; i--) {
ort[i] = H[i][m - 1] / scale;
h += ort[i] * ort[i];
}
double g = std::sqrt(h);
if (ort[m] > 0) {
g = -g;
}
h = h - ort[m] * g;
ort[m] = ort[m] - g;
// Apply Householder similarity transformation
// H = (I-u*u'/h)*H*(I-u*u')/h)
for (int j = m; j < n; j++) {
double f = 0.0;
for (int i = high; i >= m; i--) {
f += ort[i] * H[i][j];
}
f = f / h;
for (int i = m; i <= high; i++) {
H[i][j] -= f * ort[i];
}
}
for (int i = 0; i <= high; i++) {
double f = 0.0;
for (int j = high; j >= m; j--) {
f += ort[j] * H[i][j];
}
f = f / h;
for (int j = m; j <= high; j++) {
H[i][j] -= f * ort[j];
}
}
ort[m] = scale * ort[m];
H[m][m - 1] = scale * g;
}
}
// Accumulate transformations (Algol's ortran).
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
V[i][j] = (i == j ? 1.0 : 0.0);
}
}
for (int m = high - 1; m >= low + 1; m--) {
if (H[m][m - 1] != 0.0) {
for (int i = m + 1; i <= high; i++) {
ort[i] = H[i][m - 1];
}
for (int j = m; j <= high; j++) {
double g = 0.0;
for (int i = m; i <= high; i++) {
g += ort[i] * V[i][j];
}
// Double division avoids possible underflow
g = (g / ort[m]) / H[m][m - 1];
for (int i = m; i <= high; i++) {
V[i][j] += g * ort[i];
}
}
}
}
}
// Releases all internal working memory.
void release() {
// releases the working data
delete[] d;
delete[] e;
delete[] ort;
for (int i = 0; i < n; i++) {
delete[] H[i];
delete[] V[i];
}
delete[] H;
delete[] V;
}
// Computes the Eigenvalue Decomposition for a matrix given in H.
void compute() {
// Allocate memory for the working data.
V = alloc_2d<double> (n, n, 0.0);
d = alloc_1d<double> (n);
e = alloc_1d<double> (n);
ort = alloc_1d<double> (n);
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
// Copy eigenvalues to OpenCV Matrix.
_eigenvalues.create(1, n, CV_64FC1);
for (int i = 0; i < n; i++) {
_eigenvalues.at<double> (0, i) = d[i];
}
// Copy eigenvectors to OpenCV Matrix.
_eigenvectors.create(n, n, CV_64FC1);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
_eigenvectors.at<double> (i, j) = V[i][j];
// Deallocate the memory by releasing all internal working data.
release();
}
public:
EigenvalueDecomposition()
: n(0) { }
// Initializes & computes the Eigenvalue Decomposition for a general matrix
// given in src. This function is a port of the EigenvalueSolver in JAMA,
// which has been released to public domain by The MathWorks and the
// National Institute of Standards and Technology (NIST).
EigenvalueDecomposition(InputArray src) {
compute(src);
}
// This function computes the Eigenvalue Decomposition for a general matrix
// given in src. This function is a port of the EigenvalueSolver in JAMA,
// which has been released to public domain by The MathWorks and the
// National Institute of Standards and Technology (NIST).
void compute(InputArray src)
{
/*if(isSymmetric(src)) {
// Fall back to OpenCV for a symmetric matrix!
cv::eigen(src, _eigenvalues, _eigenvectors);
} else {*/
Mat tmp;
// Convert the given input matrix to double. Is there any way to
// prevent allocating the temporary memory? Only used for copying
// into working memory and deallocated after.
src.getMat().convertTo(tmp, CV_64FC1);
// Get dimension of the matrix.
this->n = tmp.cols;
// Allocate the matrix data to work on.
this->H = alloc_2d<double> (n, n);
// Now safely copy the data.
for (int i = 0; i < tmp.rows; i++) {
for (int j = 0; j < tmp.cols; j++) {
this->H[i][j] = tmp.at<double>(i, j);
}
}
// Deallocates the temporary matrix before computing.
tmp.release();
// Performs the eigenvalue decomposition of H.
compute();
// }
}
~EigenvalueDecomposition() {}
// Returns the eigenvalues of the Eigenvalue Decomposition.
Mat eigenvalues() { return _eigenvalues; }
// Returns the eigenvectors of the Eigenvalue Decomposition.
Mat eigenvectors() { return _eigenvectors; }
};
#endif // DLS_H