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.

@TECHREPORT{dorettoW07tr,
  author = {Doretto, G. and Wang, X.},
  title = {Integral computations: {A} framework to compute fast region based
	features},
  institution = {GE Global Research},
  year = {2007},
  number = {2007GRC593},
  address = {Niskayuna, NY, USA},
  month = {June},
  note = {Visualization and Computer Vision Laboratory},
  bib2html_pubtype = {Tech Reports},
  bib2html_rescat = {Video Surveillance, Integral Image Computations},
  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.},
  file = {dorettoW07tr.pdf:doretto\\report\\dorettoW07tr.pdf:PDF},
  keywords = {integral image, integral histogram, integral computation, co-occurrence
	matrix, correlogram},
  owner = {doretto},
  pdf = {doretto\report\dorettoW07tr.pdf},
  timestamp = {2007.04.30}
}

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