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I have been going through few research papers around face recognition and I came across two texture extraction algorithms :

  1. Summed-area table by Crow et al. ("Summed-area tables for texture mapping", 1984)
  2. Integral image by Viola et al. (e.g. "Robust Real-time Object Detection", 2002)

Apologizes if I'm wrong, I found that generating texture map in both these algorithms are same.

i.e., Texture map $I(x,y)$ = Sum of all gray level intensity values who lies left and above $i(x,y)$ of the original image.

Please clarify me, what is the main difference between these two algorithms?

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The Sum-area table (SAT) was introduced in computer graphics, and as far as I know, was popularized in computer vision and image processing under the name Integral image.

Apart from a larger genericity of the SAT to objects of dimensions different to that of images, the concepts are the same to me.

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They are the same concept. Summed Area Tables are typically called Integral Images in the image processing domain. In fact, the Wikipedia entry has the following line:

A summed-area table is a data structure and algorithm for quickly and efficiently generating the sum of values in a rectangular subset of a grid. In the image processing domain, it is also known as an integral image.1

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