Learning OpenCV

Integral Images

OpenCV allows you to calculate an integral image easily with the appropriately named cvIntegral() function. An integral image [Viola04] is a data structure that allows rapid summing of subregions. Such summations are useful in many applications; a notable one is the computation of Haar wavelets, which are used in some face recognition and similar algorithms.

void cvIntegral(
   const CvArr* image,
   CvArr*       sum,
   CvArr*       sqsum      = NULL,
   CvArr*       tilted_sum = NULL
);

The arguments to cvIntegral() are the original image as well as pointers to destination images for the results. The argument sum is required; the others, sqsum and tilted_sum, may be provided if desired. (Actually, the arguments need not be images; they could be matrices, but in practice, they are usually images.) When the input image is 8-bit unsigned, the sum or tilted_sum may be 32-bit integer or floating-point arrays. For all other cases, the sum or tilted_sum must be floating-point valued (either 32- or 64-bit). The result "images" must always be floating-point. If the input image is of size W-by-H, then the output images must be of size (W + 1)-by-(H + 1). ^[86]

An integral image sum has the form:

The optional sqsum image is the sum of squares:

and the tilted_sum is like the sum except that it is for the image rotated ...