[ptx] Image fusion success (wavelet based)

[Sebastian Nowozin]

Hello all,

as we lately discussed image fusion to extend the focus of overlapping images,
I have been studying the approach described in this paper (it was recommended
on the list):

	http://bigwww.epfl.ch/preprints/forster0401p.html

The paper describes an algorithm that first decomposes a number of images into
their wavelet pyramids and then selects the largest wavelet coefficients among
all images. From all the selected coefficients one image is created by
inverting the wavelet transform back to one image.

I implemented a small prototype that basically does everything described in the
paper, but so far only in the real number wavelet domain using a standard DWT
(Discrete Wavelet Transform) with a standard wavelet (Daubechies 6).

I implemented complex wavelets but even for just one dimensional transforms I
only get a very rough signal (compared to the original signal) when inverting
the wavelet representation. This is most likely a misunderstanding of the
complex wavelet transform on my side (I just replaced every real operation with
complex numbers) and I have tried to find a detailed algorithmic description of
the complex wavelet transform, but failed.

So, this is why I mail to the list, of which I know there are lots of
intelligent mathematicians on it :-) Would anyone like to help me check my
complex wavelet implementation? Its just very short code and an almost exact
copy of the real version, which works just great.

The final program will be released under the GPL. The implementation is in C#.


bye,
Sebastian

PS: The attached screenshot is the output of fusing the three example images
given in the paper using my program. The top three images are the input images,
the fourth is the fused grey image, below there is the topology map (which
pixel is choosen) and at the bottom the color fused image is shown.

-- 
nowozin at cs.tu-berlin.de --- http://user.cs.tu-berlin.de/~nowozin/
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