Calculate 2-D integral image

In an *integral image*, each pixel represents the
cumulative sum of a corresponding input pixel with all pixels above and to
the left of the input pixel.

An integral image enables you to rapidly calculate summations over image subregions. Subregion summations can be computed in constant time as a linear combination of only four pixels in the integral image, regardless of the size of the subregion. Use of integral images was popularized by the Viola-Jones algorithm [1].

[1]
Viola, P., and M. J. Jones. "Rapid Object Detection using a
Boosted Cascade of Simple Features". *Proceedings of the 2001 IEEE Computer Society
Conference on Computer Vision and Pattern Recognition*. 2001. Vol. 1, pp.
511–518.

[2] Lienhart, R., and J.
Maydt. "An Extended Set of Haar-like Features for Rapid Object Detection".
*Proceedings of the 2002 IEEE International Conference on
Image Processing*. Sept. 2002. Vol. 1, pp.
900–903.