Integral Images for Block Matching

Abstract

The integral image representation is a remarkable idea that permits to evaluate the sum of image values over rectangular regions of the image with four operations, regardless of the size of the region. It was first proposed under the name of summed area table in the computer graphics community by Crow'84, in order to efficiently filter texture maps. It was later popularized in the computer vision community by Viola & Jones'04 with its use in their real-time object detection framework. In this article we describe the integral image algorithm and study its application in the context of block matching. We investigate tradeoffs and the limits of the performance gain with respect to exhaustive block matching.

Parameter-Free Fast Pixelwise Non-Local Means Denoising

“…Another problem may occur even in the simple case of NLM-P: when image size as well as patch distances are large, some values of the integral image (14) may become so huge that the accuracy of the final result may drop, even when using a double precision representation (see [10] for a discussion of this phenomenon). Therefore this fast algorithm can hardly be used to implement NLM-Pa, unlike the two ones that will be now presented.…”

“…The method is known as integral images [24] (or summed area tables [6] in the context of texture mapping) and it allows to efficiently compute the sum of values of any image in a rectangular subset of a grid. A recent review of the integral image algorithm and its application is proposed in [10].…”

“…Note that in [4] and unlike [1,3], the authors do subtract 2σ 2 to the square of the norm. In the discrete setting, the Gaussian Euclidean norm writes (10) and d s = (d − 1)/2 being the patch side half-length, d being an odd number. In the right-hand of Equation (9) the symbol v(x) 2 must be understood as the Euclidean norm of v(x), which is simply the absolute value of v(x) in the case of a gray-level image.…”

BM3D image denoising using heterogeneous computing platforms

“…In the integral images the pixel differences for each search window offset are calculated beforehand into buffers, and then the patch difference can be calculated with only four addition operations [36]. But because the integral images stored into buffers require much memory and also the buffer values are cumulating and possibly overflowing, using integral images is only feasible for small images where it could improve the performance.…”

“…The results that are missing from the table denotes a failure in the execution of the application in question. The failures in the implementation by Lebrun occurred because it uses integral images [36] to speed up the patch distance evaluation, and this uses memory excessively. Therefore it was not possible to run most of the larger resolution image tests at all due to running out of memory.…”