4 ms·
When seen as a [1 3 3 1] (the 4th row of Pascal's Triangle) kernel, it is more easily revealed as a discrete Gaussian kernel, which is for example used in scale
by dognotdog 11y ago
When seen as a [1 3 3 1] (the 4th row of Pascal's Triangle) kernel, it is more easily revealed as a discrete Gaussian kernel, which is for example used in scale-space representations in image processing.
- kentonv 11y agoWhoa. Your one sentence completely demystified this article for me.
- eru 11y agoThe same applies to {0.05, 0.25, 0.4, 0.25, 0.05} mentioned later: it's proportional to 1 5 8 5 1, which is two rows down from 1 3 3 1.
- powera 11y agoThe row is 1 4 6 4 1, but these are the closest 5-cent approximations to the 1/16th that add to 1.
- eru 11y agoThanks for the correction, and additional information.
- mjcohen 11y agoThe rows after 1 3 3 1 are 1 4 6 4 1 and 1 5 10 10 5 1. Where does 1 5 8 5 1 come from?
- eru 11y agoFrom me being bad at arithmetic. Sorry.
- Hydraulix989 11y agoDoing arithmetic in public is dangerous.
- taneq 11y agoThis makes heaps of sense, they say "wow it looks so much like a Gaussian kernel" and my first thought was "is Gaussian not the go-to kernel for image processing?"
- Ono-Sendai 11y agono, gaussian is a bad reconstruction kernel.
- Hydraulix989 11y agoThe argument is that, in practice, it performs better for resampling images than the more correct sinc kernel from sampling and reconstruction theory.
- Ono-Sendai 11y agoWell, you can't actually use sinc in practice because it has an infinite support. But something like windowed sinc will work better than gaussian.
- nimrody 11y agoRight. And the advantages of the Gaussian kernel with respect to image processing: 1. It has no negative coefficients (hence the output will always be a valid color value.) 2. It is circular symmetric, yet separable (X and Y may be filtered independently) -- a property which simplifies the implementation considerably.
- Hydraulix989 11y agoThe Gaussian function is actually the distribution function of the normal distribution, and the normal distribution’s discrete equivalent is the binomial distribution whose coefficients (binomial coefficients) are the rows of Pascal's triangle.