## Integral computations: A framework to compute fast region based features

Doretto, G. and Wang, X.**Integral computations: A framework to compute fast region based features**

Technical Report 2007GRC593, GE Global Research, 2007. Visualization and Computer Vision Laboratory

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### Abstract

The integral image and the integral histogram are very popular image representations in Computer Vision. After a pre-computation step (an O(N^2) operation for an NxN image), they allow the computation of image statistics such as mean, covariance, and histogram of the image pixels of given rectangular image regions in constant time, regardless of the dimension of such regions. In this report, while focusing on the case of the integral image, we show that it is possible to establish very simple rules that allow extending the computational benefits of the integral representations to image regions of any shape. Based on this framework, it is possible to derive a very efficient algorithm for computing the co-occurrence of image values, or labels, lowering the computational complexity of such an operation to O(N^2). Several aspects of the implementation of the proposed algorithms are also reported.

### BibTeX

@TechReport{dorettoW07tr, Title = {Integral computations: {A} framework to compute fast region based features}, Author = {Doretto, G. and Wang, X.}, Institution = {GE Global Research}, Year = {2007}, Address = {Niskayuna, NY, USA}, Month = {June}, Note = {Visualization and Computer Vision Laboratory}, Number = {2007GRC593}, Abstract = {The integral image and the integral histogram are very popular image representations in Computer Vision. After a pre-computation step (an O(N^2) operation for an NxN image), they allow the computation of image statistics such as mean, covariance, and histogram of the image pixels of given rectangular image regions in constant time, regardless of the dimension of such regions. In this report, while focusing on the case of the integral image, we show that it is possible to establish very simple rules that allow extending the computational benefits of the integral representations to image regions of any shape. Based on this framework, it is possible to derive a very efficient algorithm for computing the co-occurrence of image values, or labels, lowering the computational complexity of such an operation to O(N^2). Several aspects of the implementation of the proposed algorithms are also reported.}, Bib2html_pubtype = {Tech Reports}, Bib2html_rescat = {Video Surveillance, Integral Image Computations}, File = {dorettoW07tr.pdf:doretto\\report\\dorettoW07tr.pdf:PDF;dorettoW07tr.pdf:doretto\\report\\dorettoW07tr.pdf:PDF}, Keywords = {integral image, integral histogram, integral computation, co-occurrence matrix, correlogram}, Owner = {doretto}, Timestamp = {2007.04.30} }