# Summed-area table vs Integral image?

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?

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.

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