Haar wavelets

Hey /prog/,

I'm confused about Haar wavelet decomposition, the guide I have found:

http://grail.cs.washington.edu/pub/stoll/wavelet1.pdf

Only works if the dimensions of the input image divided are 2^n, otherwise you run out of pairs to average, what do you do in cases where this is not true? add padding? consider only a cropped section of the image?

>>1
I have no idea about wavelet decomposition but you could try to divide the image into fixed-size parts that fulfil that requirement. I'm really not sure but I think you have to do that in video compression: You divide the whole image into fixed-size pieces and the cropping (which hits efficiency) is limited to a few elements on the boundary.

>>2
Actually, wavelet composition is not meant to be used on a block basis. One of the advantages of using haar wavelet decomposition is you don't get the blocking artifacts associated with block-transform based compression methods.

Unfortunately, the haar wavelet transform is only defined for power of 2 signals, so your only choice would be padding if you want to retain the original image.

>>3
I see. You got me interested.

So when I'd like to decompose an image with the dimensions 2049x1025, I would have to pad it to 4096x2048?
This transform doesn't look like it's very useful for compression. Am I missing something? What is it for?

The detail coefficients are a measure of local change in detail so a uniform coloured padding area would deliver long string of 0s which I understand are eminently compressible.

>>4
It's typically not. It's a basic wavelet, one of the very simplest, and is easy to implement and reason about, so it's taught first.

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