I am using Laplacian of Gaussian for edge detection using a combination of what is described in http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm and http://wwwmath.tau.ac.il/~turkel/notes/Maini.pdf
Simply put, I'm using this equation :
for(int i = -(kernelSize/2); i<=(kernelSize/2); i++)
{
for(int j = -(kernelSize/2); j<=(kernelSize/2); j++)
{
double L_xy = -1/(Math.PI * Math.pow(sigma,4))*(1 - ((Math.pow(i,2) + Math.pow(j,2))/(2*Math.pow(sigma,2))))*Math.exp(-((Math.pow(i,2) + Math.pow(j,2))/(2*Math.pow(sigma,2))));
L_xy*=426.3;
}
}
and using up the L_xy variable to build the LoG kernel.
The problem is, when the image size is larger, application of the same kernel is making the filter more sensitive to noise. The edge sharpness is also not the same.
Let me put an example here...
Suppose we've got this image:
Using a value of sigma = 0.9 and a kernel size of 5 x 5 matrix on a 480 × 264 pixel version of this image, we get the following output:
However, if we use the same values on a 1920 × 1080 pixels version of this image (same sigma value and kernel size), we get something like this:
[Both the images are scaled down version of an even larger image. The scaling down was done using a photo editor, which means the data contained in the images are not exactly similar. But, at least, they should be very near.]
Given that the larger image is roughly 4 times the smaller one... I also tried scaling the sigma by factor of 4 (sigma*=4) and the output was... you guessed it right, a black canvas.
Could you please help me realize how to implement a LoG edge detector that finds the same features from an input signal, even if the incoming signal is scaled up or down (scaling factor will be given).
