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steerableDetector.cpp
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steerableDetector.cpp
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/* [response, orientation, nms, filterBank] = steerableDetector(image, filterOrder, sigma);
*
* Copyright (C) 2011-2012 Francois Aguet
* Adapted from the SteerableJ package, Copyright (C) 2005-2008 Francois Aguet, Biomedical Imaging Group, EPFL.
*
* Last modified: Nov 29, 2012
*
* Compilation:
* Mac/Linux: mex -I/usr/local/include -I../../mex/include /usr/local/lib/libgsl.a /usr/local/lib/libgslcblas.a steerableDetector.cpp
* Windows: mex COMPFLAGS="$COMPFLAGS /TP /MT" -I"..\..\..\extern\mex\include\gsl-1.15" -I"..\..\mex\include" "..\..\..\extern\mex\lib\gsl.lib" "..\..\..\extern\mex\lib\cblas.lib" -output steerableDetector steerableDetector.cpp
*/
#include <string>
#include <math.h>
#include <gsl/gsl_poly.h>
#include <algorithm>
#include "mex.h"
#include "convolver.h"
using namespace std;
#define PI 3.141592653589793
#define TOL 1e-12
static double approxZero(double n) {
if (fabs(n) < TOL) {
return 0.0;
} else {
return n;
}
}
static double opposite(double theta) {
if (theta > 0.0) { // values in (-PI,PI]
return theta - PI;
} else {
return theta + PI;
}
}
static int getTemplateN(int M) {
if (M==1) {
return M*(M+3)/2;
} else {
return M*(M+3)/2 - getTemplateN(M-1);
}
}
double* getWeights(int M, double sigma) {
double* alpha;
double s2 = sigma*sigma;
double s3 = sigma*s2;
switch (M) {
case 1:
alpha = new double[1];
alpha[0] = sqrt(2.0/PI);
break;
case 2:
alpha = new double[2];
// mu = 0
alpha[0] = -sqrt(3.0/(4.0*PI)) * sigma;
alpha[1] = -alpha[0] / 3.0;
// mu = 2
//alpha[0] = -sqrt(2.0/(3.0*PI))*sigma;
//alpha[0] = -sigma; // Hessian
//alpha[1] = 0.0;
break;
case 3: // mu = 0
alpha = new double[3];
alpha[0] = 0.966;
alpha[1] = 0.0;
alpha[2] = 0.256*s2;
break;
case 4: // mu = 0.25
alpha = new double[5];
alpha[0] = -0.392*sigma;
alpha[1] = 0.113*sigma;
alpha[2] = 0.034*s3;
alpha[3] = -0.184*s3;
alpha[4] = 0.025*s3;
break;
case 5:
alpha = new double[5];
alpha[0] = 1.1215;
alpha[1] = 0.018*s2;
alpha[2] = 0.5576*s2;
alpha[3] = 0.0038*s2*s2;
alpha[4] = 0.0415*s2*s2;
break;
default:
alpha = NULL;
}
return alpha;
}
void computeBaseTemplates(double* input, int nx, int ny, int M, int borderCondition, double sigma, double** templates) {
int wWidth = (int)(4.0*sigma);
int nk = wWidth+1;
double* aKernel = new double[nk];
double* bKernel = new double[nk];
double* g = new double[nk];
double* buffer = new double[nx*ny];
double d;
double sigma2 = sigma*sigma;
double sigma4 = sigma2*sigma2;
double sigma6 = sigma4*sigma2;
double sigma8 = sigma4*sigma4;
double sigma10 = sigma6*sigma4;
double sigma12 = sigma8*sigma4;
for (int i=0;i<nk;i++) {
g[i] = exp(-(i*i)/(2.0*sigma2));
}
// set up convolver
Convolver conv = Convolver(input, nx, ny, borderCondition);
if (M == 1 || M == 3 || M == 5) {
d = 2.0*PI*sigma4;
for (int i=0;i<nk;i++) {
aKernel[i] = -i*g[i] / d;
}
// g_x
conv.convolveOddXEvenY(aKernel, nk, g, nk, templates[0]);
// g_y
conv.convolveEvenXOddY(g, nk, aKernel, nk, templates[1]);
if (M == 3 || M == 5) {
d = 2.0*PI*sigma8;
for (int i=0;i<nk;i++) {
aKernel[i] = (3.0*i*sigma2 - i*i*i) * g[i] / d;
}
// g_xxx
conv.convolveOddXEvenY(aKernel, nk, g, nk, templates[2]);
// g_yyy
conv.convolveEvenXOddY(g, nk, aKernel, nk, templates[5]);
for (int i=0;i<nk;i++) {
aKernel[i] = (sigma2 - i*i) * g[i] / d;
bKernel[i] = i*g[i];
}
// gxxy
conv.convolveEvenXOddY(aKernel, nk, bKernel, nk, templates[3]);
// gxyy
conv.convolveOddXEvenY(bKernel, nk, aKernel, nk, templates[4]);
}
if (M == 5) {
d = 2.0*PI*sigma12;
for (int i=0;i<nk;i++) {
aKernel[i] = -i*(i*i*i*i - 10.0*i*i*sigma2 + 15.0*sigma4) * g[i] / d;
}
// gxxxxx
conv.convolveOddXEvenY(aKernel, nk, g, nk, templates[6]);
// gyyyyy
conv.convolveEvenXOddY(g, nk, aKernel, nk, templates[11]);
for (int i=0;i<nk;i++) {
aKernel[i] = (i*i*i*i - 6.0*i*i*sigma2 + 3.0*sigma4) * g[i] / d;
bKernel[i] = -i * g[i];
}
// g_xxxxy
conv.convolveEvenXOddY(aKernel, nk, bKernel, nk, templates[7]);
// g_xyyyy
conv.convolveOddXEvenY(bKernel, nk, aKernel, nk, templates[10]);
for (int i=0;i<nk;i++) {
aKernel[i] = i*(i*i - 3.0*sigma2) * g[i] / d;
bKernel[i] = (sigma2 - i*i) * g[i];
}
// g_xxxyy
conv.convolveOddXEvenY(aKernel, nk, bKernel, nk, templates[8]);
// g_xxyyy
conv.convolveEvenXOddY(bKernel, nk, aKernel, nk, templates[9]);
}
} else { //(M == 2 || M == 4)
d = 2.0*PI*sigma6;
for (int i=0;i<nk;i++) {
aKernel[i] = (i*i - sigma2) * g[i] / d;
}
// g_xx
conv.convolveEvenXEvenY(aKernel, nk, g, nk, templates[0]);
// g_yy
conv.convolveEvenXEvenY(g, nk, aKernel, nk, templates[2]);
for (int i=0;i<nk;i++) {
aKernel[i] = i * g[i];
bKernel[i] = aKernel[i] / d;
}
// g_xy
conv.convolveOddXOddY(aKernel, nk, bKernel, nk, templates[1]);
if (M == 4) {
d = 2.0*PI*sigma10;
for (int i=0;i<nk;i++) {
aKernel[i] = (i*i*i*i - 6.0*i*i*sigma2 + 3.0*sigma4) * g[i] / d;
}
// g_xxxx
conv.convolveEvenXEvenY(aKernel, nk, g, nk, templates[3]);
// g_yyyy
conv.convolveEvenXEvenY(g, nk, aKernel, nk, templates[7]);
for (int i=0;i<nk;i++) {
aKernel[i] = i * (i*i - 3.0*sigma2) * g[i] / d;
bKernel[i] = i * g[i];
}
// g_xxxy
conv.convolveOddXOddY(aKernel, nk, bKernel, nk, templates[4]);
// g_xyyy
conv.convolveOddXOddY(bKernel, nk, aKernel, nk, templates[6]);
for (int i=0;i<nk;i++) {
aKernel[i] = (sigma2 - i*i) * g[i];
bKernel[i] = aKernel[i] / d;
}
// g_xxyy
conv.convolveEvenXEvenY(aKernel, nk, bKernel, nk, templates[5]);
}
}
// free memory
delete[] aKernel;
delete[] bKernel;
delete[] g;
delete[] buffer;
}
// Point responses
double pointRespM1(int i, double angle, double* alpha, double** templates) {
double cosT = cos(angle);
double sinT = sin(angle);
double gxi = templates[0][i];
double gyi = templates[1][i];
double a11 = alpha[0];
double result = a11 * (cosT*gxi + sinT*gyi);
return result;
}
double pointRespM2(int i, double angle, double* alpha, double** templates) {
double cosT = cos(angle);
double sinT = sin(angle);
double gxxi = templates[0][i];
double gxyi = templates[1][i];
double gyyi = templates[2][i];
double a20 = alpha[0];
double a22 = alpha[1];
double result = sinT*sinT * (a20*gyyi+a22*gxxi)
+ sinT*cosT*2.0*(a20-a22)*gxyi
+ cosT*cosT * (a20*gxxi+a22*gyyi);
return result;
}
double pointRespM3(int i, double angle, double* alpha, double** templates) {
double cosT = cos(angle);
double sinT = sin(angle);
double cosT2 = cosT*cosT;
double sinT2 = sinT*sinT;
double gxi = templates[0][i];
double gyi = templates[1][i];
double gxxxi = templates[2][i];
double gxxyi = templates[3][i];
double gxyyi = templates[4][i];
double gyyyi = templates[5][i];
double a10 = alpha[0];
double a30 = alpha[1];
double a32 = alpha[2];
double result = a10*(sinT*gyi + cosT*gxi)
+ sinT2*sinT*(a30*gyyyi + a32*gxxyi)
+ cosT*sinT2*(a32*gxxxi + (3.0*a30-2.0*a32)*gxyyi)
+ cosT2*sinT*(a32*gyyyi + (3.0*a30-2.0*a32)*gxxyi)
+ cosT2*cosT*(a32*gxyyi + a30*gxxxi);
return result;
}
double pointRespM4(int i, double angle, double* alpha, double** templates) {
double cosT = cos(angle);
double sinT = sin(angle);
double sinTcosT = cosT*sinT;
double cosT2 = cosT*cosT;
double sinT2 = sinT*sinT;
double gxxi = templates[0][i];
double gxyi = templates[1][i];
double gyyi = templates[2][i];
double gxxxxi = templates[3][i];
double gxxxyi = templates[4][i];
double gxxyyi = templates[5][i];
double gxyyyi = templates[6][i];
double gyyyyi = templates[7][i];
double a20 = alpha[0];
double a22 = alpha[1];
double a40 = alpha[2];
double a42 = alpha[3];
double a44 = alpha[4];
double result = sinT2*(a20*gyyi + a22*gxxi)
+ sinT*cosT*2.0*(a20-a22)*gxyi
+ cosT2*(a20*gxxi + a22*gyyi)
+ sinT2*sinT2*(a40*gyyyyi + a42*gxxyyi + a44*gxxxxi)
+ sinT2*sinTcosT*2.0*((2.0*a40-a42)*gxyyyi + (a42-2.0*a44)*gxxxyi)
+ sinT2*cosT2*(a42*gyyyyi + (6.0*a40 - 4.0*a42 + 6.0*a44)*gxxyyi + a42*gxxxxi)
+ sinTcosT*cosT2*2.0*((2.0*a40-a42)*gxxxyi + (a42-2.0*a44)*gxyyyi)
+ cosT2*cosT2*(a44*gyyyyi + a42*gxxyyi + a40*gxxxxi);
return result;
}
double pointRespM5(int i, double angle, double* alpha, double** templates) {
double cosT = cos(angle);
double sinT = sin(angle);
double cosT2 = cosT*cosT;
double sinT2 = sinT*sinT;
double cosT3 = cosT2*cosT;
double sinT3 = sinT2*sinT;
double sinT4 = sinT2*sinT2;
double cosT4 = cosT2*cosT2;
double sinT5 = sinT2*sinT3;
double cosT5 = cosT2*cosT3;
double gxi = templates[0][i];
double gyi = templates[1][i];
double gxxxi = templates[2][i];
double gxxyi = templates[3][i];
double gxyyi = templates[4][i];
double gyyyi = templates[5][i];
double gxxxxxi = templates[6][i];
double gxxxxyi = templates[7][i];
double gxxxyyi = templates[8][i];
double gxxyyyi = templates[9][i];
double gxyyyyi = templates[10][i];
double gyyyyyi = templates[11][i];
double a10 = alpha[0];
double a30 = alpha[1];
double a32 = alpha[2];
double a52 = alpha[3];
double a54 = alpha[4];
double result = a10*(sinT*gyi + cosT*gxi)
+ sinT3*(a30*gyyyi + a32*gxxyi)
+ sinT2*cosT*((3.0*a30-2.0*a32)*gxyyi + a32*gxxxi)
+ cosT2*sinT*((3.0*a30-2.0*a32)*gxxyi + a32*gyyyi)
+ cosT3*(a32*gxyyi + a30*gxxxi)
+ sinT5*(a52*gxxyyyi + a54*gxxxxyi)
+ sinT4*cosT*(-2.0*a52*gxyyyyi + (3.0*a52-4.0*a54)*gxxxyyi + a54*gxxxxxi)
+ sinT3*cosT2*(a52*gyyyyyi + 6.0*(a54-a52)*gxxyyyi + (3.0*a52-4.0*a54)*gxxxxyi)
+ sinT2*cosT3*(a52*gxxxxxi + 6.0*(a54-a52)*gxxxyyi + (3.0*a52-4.0*a54)*gxyyyyi)
+ cosT4*sinT*(-2.0*a52*gxxxxyi + (3.0*a52-4.0*a54)*gxxyyyi + a54*gyyyyyi)
+ cosT5*(a54*gxyyyyi + a52*gxxxyyi);
return result;
}
int getRealRoots(double* z, int nz, double* roots) {
int nr = nz/2; // total roots
int nrr = 0; // real roots
for (int k=0;k<nr;++k) {
if (z[2*k+1]==0.0)
nrr++;
}
roots = new double[nrr];
nrr = 0;
for (int k=0;k<nr;++k) {
if (z[2*k+1]==0.0)
roots[nrr++] = z[2*k];
}
return nrr;
}
void filterM1(double** templates, int nx, int ny, double* alpha, double* response, double* orientation) {
double* gx = templates[0];
double* gy = templates[1];
double a11 = alpha[0];
double* tRoots = new double[2];
double gxi, gyi;
for (int i=0;i<nx*ny;++i) {
gxi = approxZero(gx[i]);
gyi = approxZero(gy[i]);
orientation[i] = atan2(gyi,gxi);
response[i] = a11*sqrt(gxi*gxi + gyi*gyi);
}
delete[] tRoots;
}
// quadratic root solution
void filterM2(double** templates, int nx, int ny, double* alpha, double* response, double* orientation) {
double* gxx = templates[0];
double* gxy = templates[1];
double* gyy = templates[2];
double a20 = alpha[0];
double a22 = alpha[1];
double A, B, C;
double a = a22-a20;
double temp;
for (int i=0;i<nx*ny;++i) {
A = a*gxy[i];
B = a*(gxx[i]-gyy[i]);
C = -A;
if (A == 0.0) { // -> linear
if (B == 0.0) { // -> null, solve
orientation[i] = 0.0;
response[i] = pointRespM2(i, 0.0, alpha, templates);
} else { // solve linear
if (C == 0.0) {
orientation[i] = 0.0;
response[i] = pointRespM2(i, 0.0, alpha, templates);
temp = pointRespM2(i, PI/2.0, alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] = PI/2.0;
}
} else {
orientation[i] = atan(-C/B);
response[i] = pointRespM2(i, orientation[i], alpha, templates);
temp = pointRespM2(i, orientation[i]+PI/2.0, alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] += PI/2.0;
}
}
}
} else { // solve quadratic
double* xRoots = new double[2];
gsl_poly_solve_quadratic (A, B, C, &xRoots[0], &xRoots[1]);
double* tRoots = new double[2];
tRoots[0] = atan(xRoots[0]);
tRoots[1] = atan(xRoots[1]);
response[i] = pointRespM2(i, tRoots[0], alpha, templates);
orientation[i] = tRoots[0];
temp = pointRespM2(i, tRoots[1], alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] = tRoots[1];
}
delete[] xRoots;
delete[] tRoots;
}
}
}
void filterM3(double** templates, int nx, int ny, double* alpha, double* response, double* orientation) {
double* gx = templates[0];
double* gy = templates[1];
double* gxxx = templates[2];
double* gxxy = templates[3];
double* gxyy = templates[4];
double* gyyy = templates[5];
double a10 = alpha[0];
double a30 = alpha[1];
double a32 = alpha[2];
double A, B, C, D;
int nr, nt, deg;
for (int i=0;i<nx*ny;++i) {
A = -a10*gx[i] + (2.0*a32-3.0*a30)*gxyy[i] - a32*gxxx[i]; // sin^3
B = a10*gy[i] + (3.0*a30-2.0*a32)*gyyy[i] + (7.0*a32-6.0*a30)*gxxy[i]; // sin^2 cos
C = -a10*gx[i] + (2.0*a32-3.0*a30)*gxxx[i] + (6.0*a30-7.0*a32)*gxyy[i];
D = a10*gy[i] + (3.0*a30-2.0*a32)*gxxy[i] + a32*gyyy[i];
A = approxZero(A);
B = approxZero(B);
C = approxZero(C);
D = approxZero(D);
double* roots;
double* z;
if (A == 0.0) { // -> quadratic
if (B == 0.0) { // -> linear
if (C == 0.0) {// -> null, fixed solution
deg = 1;
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
} else {
deg = 1;
double a[2] = {D, C};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // B!=0
deg = 2;
double a[3] = {D, C, B};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // solve cubic
deg = 3;
double a[4] = {D, C, B, A};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0)
nr++;
}
roots = new double[nr];
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0) {
roots[nr++] = z[2*k];
}
}
double* tRoots;
if (nr == 0) {
nt = 4;
tRoots = new double[nt];
tRoots[0] = -PI/2.0;
tRoots[1] = 0.0;
tRoots[2] = PI/2.0;
tRoots[3] = PI;
} else {
nt = 2*nr;
tRoots = new double[nt];
for (int k=0;k<nr;k++) {
tRoots[k] = atan(roots[k]);
tRoots[k+nr] = opposite(tRoots[k]);
}
}
delete[] roots;
response[i] = pointRespM3(i, tRoots[0], alpha, templates);
orientation[i] = tRoots[0];
double temp;
for (int k=1;k<nt;k++) {
temp = pointRespM3(i, tRoots[k], alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] = tRoots[k];
}
}
delete[] tRoots;
delete[] z;
}
}
void filterM4(double** templates, int nx, int ny, double* alpha, double* response, double* orientation) {
double* gxx = templates[0];
double* gxy = templates[1];
double* gyy = templates[2];
double* gxxxx = templates[3];
double* gxxxy = templates[4];
double* gxxyy = templates[5];
double* gxyyy = templates[6];
double* gyyyy = templates[7];
double a20 = alpha[0];
double a22 = alpha[1];
double a40 = alpha[2];
double a42 = alpha[3];
double a44 = alpha[4];
double A, B, C, D, E;
int nr, deg;
double delta;
for (int i=0;i<nx*ny;i++) {
A = (a22-a20)*gxy[i] + (a42-2.0*a40)*gxyyy[i] + (2.0*a44-a42)*gxxxy[i];
B = (a20-a22)*gyy[i] + (a22-a20)*gxx[i] + (2.0*a40-a42)*gyyyy[i] + 6.0*(a42-a40-a44)*gxxyy[i] + (2.0*a44-a42)*gxxxx[i];
C = 6.0*((a40-a42+ a44)*gxyyy[i] + (a42-a40-a44)*gxxxy[i]);
D = (a20-a22)*gyy[i] + (a22-a20)*gxx[i] + (a42-2.0*a44)*gyyyy[i] + 6.0*(a40-a42+a44)*gxxyy[i] + (a42-2.0*a40)*gxxxx[i];
E = (a20-a22)*gxy[i] + (a42-2.0*a44)*gxyyy[i] + (2.0*a40-a42)*gxxxy[i];
A = approxZero(A);
C = approxZero(C);
E = approxZero(E);
double* roots;
double* z;
if (A == 0.0) { // -> cubic
if (B == 0.0) { // -> quadratic
if (C == 0.0) { // -> linear
if (D == 0.0) { // solve null
deg = 1;
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
} else { // solve linear
deg = 1;
double a[2] = {E, D};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // solve quadratic
deg = 2;
double a[3] = {E, D, C};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // solve cubic
if ( (C == 0.0) && (E == 0.0) ) {
delta = -D/B;
if (delta > 0.0) {
deg = 3;
delta = sqrt(delta);
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
z[2] = delta;
z[3] = 0.0;
z[4] = -delta;
z[5] = 0.0;
} else {
deg = 1;
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
}
} else {
deg = 3;
double a[4] = {E, D, C, B};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
}
} else { // solve quartic
deg = 4;
double a[5] = {E, D, C, B, A};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
// # real roots
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0)
nr++;
}
roots = new double[nr];
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0) {
roots[nr++] = z[2*k];
}
}
double* tRoots;
if (nr == 0) { //orientation[i] = 0.0;
nr = 2;
tRoots = new double[nr];
tRoots[0] = 0.0;
tRoots[1] = PI/2.0;
} else {
if (roots[0] == 0.0) {
nr++;
tRoots = new double[nr];
for (int k=0;k<nr-1;k++) {
tRoots[k] = atan(roots[k]);
}
tRoots[nr-1] = PI/2;
} else {
tRoots = new double[nr];
for (int k=0;k<nr;k++) {
tRoots[k] = atan(roots[k]);
}
}
}
delete[] roots;
response[i] = pointRespM4(i, tRoots[0], alpha, templates);
orientation[i] = tRoots[0];
double temp;
for (int k=1;k<nr;k++) {
temp = pointRespM4(i, tRoots[k], alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] = tRoots[k];
}
}
delete[] z;
delete[] tRoots;
}
}
void filterM5(double** templates, int nx, int ny, double* alpha, double* response, double* orientation) {
double* gx = templates[0];
double* gy = templates[1];
double* gxxx = templates[2];
double* gxxy = templates[3];
double* gxyy = templates[4];
double* gyyy = templates[5];
double* gxxxxx = templates[6];
double* gxxxxy = templates[7];
double* gxxxyy = templates[8];
double* gxxyyy = templates[9];
double* gxyyyy = templates[10];
double* gyyyyy = templates[11];
double a10 = alpha[0];
double a30 = alpha[1];
double a32 = alpha[2];
double a52 = alpha[3];
double a54 = alpha[4];
double A, B, C, D, E, F;
int nr, nt, deg;
double delta;
for (int i=0;i<nx*ny;++i) {
A = -a10*gx[i] + (2.0*a32-3.0*a30)*gxyy[i] - a32*gxxx[i] + (4.0*a54-3.0*a52)*gxxxyy[i] + 2.0*a52*gxyyyy[i] -a54*gxxxxx[i];
B = a10*gy[i] + (3.0*a30-2.0*a32)*gyyy[i] + (7.0*a32-6.0*a30)*gxxy[i] - 2.0*a52*gyyyyy[i] + (17.0*a52-12.0*a54)*gxxyyy[i] + (13.0*a54-6.0*a52)*gxxxxy[i];
C = -2.0*a10*gx[i] + (3.0*a30-5.0*a32)*gxyy[i] + (a32-3.0*a30)*gxxx[i] + (12.0*a54-17.0*a52)*gxyyyy[i] + (30.0*a52-34.0*a54)*gxxxyy[i] + (4.0*a54-3.0*a52)*gxxxxx[i];
D = 2.0*a10*gy[i] + (5.0*a32-3.0*a30)*gxxy[i] + (3.0*a30-a32)*gyyy[i] + (17.0*a52-12.0*a54)*gxxxxy[i] + (34.0*a54-30.0*a52)*gxxyyy[i] + (3.0*a52-4.0*a54)*gyyyyy[i];
E = -a10*gx[i] + (2.0*a32-3.0*a30)*gxxx[i] + (6.0*a30-7.0*a32)*gxyy[i] + 2.0*a52*gxxxxx[i] + (12.0*a54-17.0*a52)*gxxxyy[i] + (6.0*a52-13.0*a54)*gxyyyy[i];
F = a10*gy[i] + (3.0*a30-2.0*a32)*gxxy[i] + a32*gyyy[i] + (3.0*a52-4.0*a54)*gxxyyy[i] - 2.0*a52*gxxxxy[i]+ a54*gyyyyy[i];
A = approxZero(A);
B = approxZero(B);
C = approxZero(C);
D = approxZero(D);
E = approxZero(E);
F = approxZero(F);
double* roots;
double* z;
if (A == 0.0) { // quartic
if (B == 0.0) { // cubic
if (C == 0.0) { // quadratic
if (D == 0.0) { // linear
if (E == 0.0) { // null
deg = 1;
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
} else {
deg = 1;
double a[2] = {E, D};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // solve quadratic
deg = 2;
double a[3] = {E, D, C};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else { // solve cubic
if ( (D == 0.0) && (F == 0.0) ) {
delta = -E/C;
if (delta > 0.0) {
deg = 3;
delta = sqrt(delta);
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
z[2] = delta;
z[3] = 0.0;
z[4] = -delta;
z[5] = 0.0;
} else {
deg = 1;
z = new double[2*deg];
z[0] = 0.0;
z[1] = 0.0;
}
} else {
deg = 3;
double a[4] = {F, E, D, C};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
}
} else { // solve quartic
deg = 4;
double a[5] = {F, E, D, C, B};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
} else {
deg = 5;
double a[6] = {F, E, D, C, B, A};
z = new double[2*deg];
gsl_poly_complex_workspace* w = gsl_poly_complex_workspace_alloc(deg+1);
gsl_poly_complex_solve(a, deg+1, w, z);
gsl_poly_complex_workspace_free(w);
}
// # real roots
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0)
nr++;
}
roots = new double[nr];
nr = 0;
for (int k=0;k<deg;++k) {
if (z[2*k+1]==0.0) {
roots[nr++] = z[2*k];
}
}
double* tRoots;
if (nr == 0) { //orientation[i] = 0.0;
nt = 4;
tRoots = new double[nt];
tRoots[0] = -PI/2.0;
tRoots[1] = 0.0;
tRoots[2] = PI/2.0;
tRoots[3] = PI;
} else {
nt = 2*nr;
tRoots = new double[nt];
for (int k=0;k<nr;k++) {
tRoots[k] = atan(roots[k]);
tRoots[k+nr] = opposite(tRoots[k]);
}
}
delete[] roots;
response[i] = pointRespM5(i, tRoots[0], alpha, templates);
orientation[i] = tRoots[0];
double temp;
for (int k=1;k<nt;k++) {
temp = pointRespM5(i, tRoots[k], alpha, templates);
if (temp > response[i]) {
response[i] = temp;
orientation[i] = tRoots[k];
}
}
delete[] z;
delete[] tRoots;
}
}
// Mirror position in image domain for interpolation
int mirror(int x, int nx) {
if (x >= 0 && x < nx) {
return x;
} else if (x < 0) {
return -x;
} else {
return 2*nx-2-x;
}
}
double interp(double* image, int nx, int ny, double x, double y) {
int xi = (int)x;
int yi = (int)y;
int x0, x1, y0, y1;
double dx = x-xi;
double dy = y-yi;
if (x < 0) { dx = -dx; x1 = mirror(xi-1, nx); } else { x1 = mirror(xi+1, nx); }
if (y < 0) { dy = -dy; y1 = mirror(yi-1, ny); } else { y1 = mirror(yi+1, ny); }
x0 = mirror(xi, nx);
y0 = mirror(yi, ny);
return (1.0-dy)*(dx*image[x1+y0*nx] + (1.0-dx)*image[x0+y0*nx]) + dy*(dx*image[x1+y1*nx] + (1.0-dx)*image[x0+y1*nx]);
}
void computeNMS(double* response, double* orientation, double* nms, int nx, int ny) {
double ux, uy, v1, v2;
div_t divRes;
for (int i=0;i<nx*ny;++i) {
divRes = div(i, nx);
ux = cos(orientation[i]);
uy = sin(orientation[i]);
v1 = interp(response, nx, ny, divRes.rem+ux, divRes.quot+uy);
v2 = interp(response, nx, ny, divRes.rem-ux, divRes.quot-uy);
if (v1 > response[i] || v2 > response[i]) {
nms[i] = 0.0;
} else {
nms[i] = response[i];
}
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
// check # inputs
if (nrhs < 3 || nrhs > 5)
mexErrMsgTxt("Required inputs arguments: image, filter order, sigma.\nOptional: # angles for rotations output; border condition (see help).");
if (nlhs > 4)
mexErrMsgTxt("Too many output arguments.");
// check image
if (!mxIsDouble(prhs[0]) || mxGetNumberOfDimensions(prhs[0]) != 2)
mexErrMsgTxt("Input image must be a 2-D array.");
int nx = (int)mxGetN(prhs[0]); // cols
int ny = (int)mxGetM(prhs[0]);
int N = nx*ny;
double* input = mxGetPr(prhs[0]);
// check for NaNs in input, as these will result in a crash
for (int i=0;i<N;++i) {
if (mxIsNaN(input[i])) {
mexErrMsgTxt("Input image contains NaNs.");
break;
}
}
// check order