use scale space representation to filter one image

Question

Currently I hope to use scale space representation to filter one image. Features in one image can be filtered using an Gaussian smooth filter with one optimal sigma. It means different features in one image can be expressed best in different scale under scale space representation.

For example, I have one image with one tree in it. In the scale space representation, three sigma values are used and they are represented as sigma0, sigma1 and sigma2. The ground is best expressed in the smoothed image with sigma0 because it contains textures mainly. The branches are best expressed in the smoother image with sigma1 and the trunk is with the smoother image with sigma2. If I hope to filter the image, I hope that the filtered pixels for the group is from the smoothed image with sigma0. The filtered pixels for the branches are from the smoothed image with sigma1. The filtered pixels for the trunk are from the smoothed image with sigma2.

It requires that I need to determine in which smoothed image one pixel is expressed best. Is this idea plausible? I am trying to use differece-of-Gaussian of two successive smoothed images to perform the above task. Is there any other way to combine the three smoothed image?

I use Matlab to implement the idea. The values of the three sigmas is 1.0, 2.0 and 3.0. The corresponding size of Gaussian kernel is 3, 5 and 7. I use the function fspecial to generate the kernel. Are the parameter reasonable? Please share your experience with the scale space representation to help me. You can provide some links to useful papers.

Answer 1

your idea is very much plausible! You are just one step away from it. I did something very similar once and it looked like this:

After smoothing your images and extracting the edges for each smoothing step (I used a weighted [to compensate for maxima supression after Gauss filtering] Sobel filter for this since DOG was not quite stable for my aplication), you can proyect (and normalize) your whole stack of edge images into a single image ("cummulative edges") which will contain the characteristic edges. You can then compare the cummulative edges image (using cross-correlation or whatever you wish) with every single image in your edge stack, the biggest value of this comparation is then the smooth-scale in which the pixel is expressed the best.

Hope that makes sense for you after reading it a couple of times.

Also don't be afraid of using much bigger kernel sizes, while it all depends on your application, I ended up using things of 51 and bigger!!! (was working with 40MP images though...)

T. Lindeberg has literally dozens of papers related to this problem. I found this one the most useful, but since you are already in the right track, I don't think reading the 50 pages will make you that much smarter. The most important part of it is maybe this one:

Principle for scale selection: In the absence of other evidence, assume that a scale level, at which some (possibly non-linear) combination of normalized derivatives assumes a local maximum over scales, can be treated as reflecting a characteristic length of a corresponding structure in the data.