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Sigmoid filter

I found the following text at:

It is very helpful in understanding how to set alpha and beta values for the sigmoid filter.

Page 150 has a nice illustration of the parameters. The Beta value can be thought of the offset on the pixel value that you are trying to isolate. E.g., if the object you are trying to isolate is at a pixel intensity above 150, you would choose a Beta value that is around that value. The Alpha value can be thought of as the scaling or variance of the sigmoid. Lower alpha values will make the pixel range of your intensity sharper. There are quite a few examples in the Level Set chapter on the use of the sigmoid function. Here it is applied to the mapping of the gradient of the image. In this case you would want to choose a Beta value near the intensity of the gradient that you are trying to isolate. E.g., the gradient you are trying to find occurs at an intensity of 5 or more. Perhaps you would notice that most gradients that have an intensity of less than 2 are noise/nonsense objects. You might choose a Beta value that is near your gradient, but would account for some variability, say, 4. Your alpha value would decide how much of the noise you would want to include in your transformation. Smaller alpha values (0.25, 0.5) would zero out most of the noise, but it might make your actual signal thicker and not specific enough. Conversely, larger alpha values (e.g. 3+) might have a smoother signal but might include more noise. Negative alpha values can be thought of as using a positive alpha value and then inverting the image.