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In my group, we have developed an algorithm which shows abstract information from quantum mechanical systems as images. This way, given a quantum system, we obtain an associated image which has the same information and makes some features visible.

One of the important features is obtained using a "cross-correlation matrix": We divide the image into $L\times L$ sub-images and find the "overlap" between all pairs. So, the entry for sub-images $i$ and $j$, $A_{i,j}$ is a number stating how similar they are. The matrix dimension is $L^2\times L^2$.

The question is: is this matrix, or a close relative, used in image-processing? If it does, does it have a name? Does it have any interesting properties, or does it help for any useful algorithms?

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    $\begingroup$ Similar approaches (to analyze the block matching) are used in video processing to understand the motion patterns and or to estimate depth from stereo images. It would be better if we understand more from the property you are looking for or application requirement. $\endgroup$ – Dipan Mehta Nov 4 '11 at 16:09
  • $\begingroup$ Thanks to you all for your ideas. The article is finally in the ArXiv, if you want to take a look :) arxiv.org/abs/1112.3560 $\endgroup$ – Javier Rodriguez Laguna Jan 20 '12 at 16:05
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If you look around for "image patch self-similarity" there are some things that are along those lines, for example the work of Eli Shechtman and Michal Irani

http://www.wisdom.weizmann.ac.il/~vision/SelfSimilarities.html

or the Calvin research centre:

http://www.vision.ee.ethz.ch/~calvin/software.html

(see Global and Efficient Self-Similarity for Object Classification and Detection)

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