Haar Wavelets and Image Comparison/Analysis

[alexander]

Ok, so now that i am done with doing some basic searching with GPS data, i think it's time to step up the geekitude a little bit. I've recently been exploring image comparison and image search algorithms, well what i can find anyways, and a particular one struck me as something that might be worth playing with. Basically its the engine behind imgseek, and they use Haar Wavelet decompositions of images of varying resolutions to search across a database for images "like" either another image or a rough sketch of something...

I think i generally understand what they do (without looking at the code, which won't really tell me anything until i understand the concept anyways) they use the discrete wavelet transform to transform image rows into component vectors, and then use the haar transform to compress and stretch the result matrix to obtain varying resolutions...

 

Now can someone actually explain to me what i said above, perhaps with an example? Which will be a starting point, basically at the end of this thread i want to write a function that will take in an image (bitmap) and try to find other images similar to it (or take in 2 images and at least give back some number(s) indicating how similar the other image is to the first one)

 

Unfortunately texts on the subject are pretty expensive, but i figured it shouldn't be too too difficult to figure out the basic principles and have something even rough, working :shrug:

 

You guys up for a trip?

[sanctus]

I work with a development from general wavelet transforms (on the sphere instead of plane and a type of wavelet called needlet due to the form of the needlet function in "harmonic-space") on CMB-data analysis, so I have some background in this, but not really when it comes to image-comparison analysis...

 

If you look for a super-cool and not too advanced tutorial on what (and why) a wavelet transform is, then I would suggest: this one.

 

 

In super-short, the general idea of a wavelet transform is to make a transfrom that tells you both which frequency and when each frequency. This is a big difference from just fourier-transforming, because there you only know which frequency is in the signal, but not when...but then there is always Heisenberg, so you never get a super good resolution of frequency and time at the same moment.

 

If you have specific question on the Haar-wavelets I might be of help, but I have to look it up too.

[sanctus]

Also, in the context of image comparison, I think you can use it (=this wavelet transformed image) in the way that it splits you the image in many images at different scales and so you can compare if they are the same (or better similar) at a given scale.

 

If you have a spherical image (but I think it is similar somehow on the plane, but there monople etc make less sense ;-)) made of a monopole contribution say red (means that the average over the whole image is red) and a dipole contribution say blue (means that one half of the sphere is a bit more blue than the other).

If now you have another spherical image with the same monopole contribution but a green dipole contribution.

What you could do now to compare, is that you decompose the images into monopole and dipole scales and compare...and you find that at the monopole scale they are the same.

 

This is just spherical harmonics decomposition, but then if you compare a combination of scales (which is wavelet-type dependent) you get a wavelet comparison...

 

This is how I image it is done at least...

[alexander]

Sweet.... research tiiime! :shrug:

[sanctus]

So how is it going?

[alexander]

Its in the process of being thought of, i go back and read a little about the wavelet transform then, because of either getting frustrated at math or just needing some time to think, leave it alone, then something sparks my interest again and i go back to it... i may have some questions, or thoughts, i dont know if you are interested in discussing it though...?

[sanctus]

Yeah, we can. And if I can answer I will ;-)