Re: Laplacian of Gaussian - Mask size, normalisation factor
- From: Martin Leese <please@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 11 Jul 2005 14:28:05 -0600
jedi200581@xxxxxxxxxxx wrote:
Hey,
I'm looking to implement an edge detector based on a LoG. I found some documentation, but all this seems very theorical.
First, look at : http://www.cee.hw.ac.uk/hipr/html/log.html (first page on google). I you try to apply the formula for sigma = 1,4 and x = 0, you don't find what they have figure 3 at all!!! Is this a huge scam or something ? They talk about this sonka, hlavac and boyle's book (Image Processing, Analysis and Machine Vision). It's good, but they don't talk about the details!
Anyway, from this formula, how to you determine a normalisation factor ? The normalization factor depends on the mask size you want. But how the mask size influence the LoG operator. It gives the algorithm the power to raise bigger edges in the image and ignoring smaller ones if I'm not stupid. But the mask size is also influenced by the sigma you're choosing!
If anybody have any directions to give me, a paper, or some links on internet which talk about a real-world implementation of a LoG, let me know.
I don't have any real-world examples. In theory, the filter weights approach zero, but never reach it. In practice, therefore, you choose a mask size and sigma such that the filter weights at the edges of the filter are small. So, sigma is fixed, although the actual value is a matter of choice. As you point out, mask size determines the size of feature being selected; essentially, how much low-pass filtering to apply before taking the Laplacian.
Note that at www.cww.hw.ac.uk they state Figure 3 is a "Discrete approximation"; it was not derived by straight application of the formula. Figure 3 looks about right, given that they have restricted themselves to integer filter weights; you may or may not have this restriction.
The normalization factor is usually chosen so that the result fills the range 0 to 255; this, of course, depends on the input image. Note that the filter output from a flat image is zero, so a bias of 127 is usually added. If your image processing software can handle negative pixel values and, even better, floating point values then such scaling and bias will not be necessary.
-- Regards, Martin Leese E-mail: please@xxxxxxxxxxxxxxxxxxxxxxxxxx Web: http://members.tripod.com/martin_leese/ .
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