// Compute the minimum eigenvalue of the matrix [a b; b d]
static final double minEig(double a, double b, double d) {
// 2a^2 + 4b^2 + 2d^2 - 2*(a+d)sqrt(a^2 - 2ad + d^2 + 4b^2)
double SA = (a + d) * (a + d) * (a * a - 2 * a * d + d * d + 4 * b * b);
assert (SA >= 0);
SA = Math.sqrt(SA);
double SB = 2 * a * a + 4 * b * b + 2 * d * d - 2 * SA;
if (SB < 0) // can be negative due to numerical precision.
return 0;
SB = Math.sqrt(SB);
return 0.5 * SB;
}
/**
* Compute the corner response, except each pixel also has a confidence mask. Pixels with small
* confidences do not contribute to the gradients. *
*/
public FloatImage computeResponse(FloatImage data, FloatImage conf) {
int width = data.width;
int height = data.height;
///////////////////////////////////////////////
// Compute gradients at every pixel.
FloatImage response = new FloatImage(width, height);
FloatImage fimIx2 = new FloatImage(width, height);
FloatImage fimIxIy = new FloatImage(width, height);
FloatImage fimIy2 = new FloatImage(width, height);
for (int y = scale; y + scale < height; y++) {
for (int x = scale; x + scale < width; x++) {
float vp0 = data.d[y * width + x + scale];
float vn0 = data.d[y * width + x - scale];
float v0p = data.d[y * width + x + scale * width];
float v0n = data.d[y * width + x - scale * width];
float Ix = (vp0 - vn0);
float Iy = (v0p - v0n);
if (conf != null) {
float cp0 = conf.d[y * width + x + scale];
float cn0 = conf.d[y * width + x - scale];
float c0p = conf.d[y * width + x + scale * width];
float c0n = conf.d[y * width + x - scale * width];
Ix *= Math.min(cp0, cn0);
Iy *= Math.min(c0p, c0n);
}
fimIx2.set(x, y, Ix * Ix);
fimIxIy.set(x, y, Ix * Iy);
fimIy2.set(x, y, Iy * Iy);
}
}
///////////////////////////////////////////////
// Convolve with gaussian. This makes it rotationally invariant.
int fsz = ((int) Math.max(3, 3 * sigma)) | 1;
float gaussian[] = SigProc.makeGaussianFilter(sigma, fsz);
fimIx2 = fimIx2.filterFactoredCentered(gaussian, gaussian);
fimIxIy = fimIxIy.filterFactoredCentered(gaussian, gaussian);
fimIy2 = fimIy2.filterFactoredCentered(gaussian, gaussian);
///////////////////////////////////////////////
// Compute filter response.
for (int y = 1; y + 1 < height; y++) {
for (int x = 1; x + 1 < width; x++) {
double A = fimIx2.get(x, y), B = fimIxIy.get(x, y), D = fimIy2.get(x, y);
// The ellipse (autocorrelation matrix) is [A B; C D]
// = [A B; B D]. We're really interested in the
// minimum eigenvalue, but this is slower to
// compute. Instead, we can get some relevant
// information by considering the determinant (product
// of the eigenvalues) and trace (sum of the
// eigenvalues).
response.set(x, y, (float) minEig(A, B, D));
}
}
return response;
}