fspecial -Disk filter -Algorithm

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Nicholas
Nicholas 2014-9-19
评论： Image Analyst 2014-9-23
I'm trying to understand how matlab creates its disk filter function. In a continuous domain, a disk is just 1 inside some radius and 0 outside that radius.
The tricky part about making the disk function with an image is that the edge pixels may be partially inside the disk and partially outside the disk. It appears that the matlab function assigns the edge pixels a value equal to the area of the pixel contained in the disk.
I've been trying to derive the algorithm for how one would do that, but it seems that this isn't straight forward. Is there a paper or textbook detailing how to create the disk function seen in the fspecial function? Is this problem much easier than I think it is?

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Image Analyst
Image Analyst 2014-9-19
Because it's a digital computer, the circle has to be digitized/quantized. See the FAQ for an algorithm: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F
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Nicholas
Nicholas 2014-9-23
I can see the algorithm, but the algorithm is complicated and I'd like an explanation of the geometry. I wasn't able to derive the algorithm. I'm after a reference or a derivation.
Image Analyst
Image Analyst 2014-9-23
It probably is a typical anti-aliasing routine where you "feather" the edges according to how much of the square tile circle would be taken up by a perfect circle. So if the circle would cover 30% of the square, it will have 30% of the solid, interior value.

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