Fast Block Matching with Normalized Cross-Correlation using Walsh Transforms

Local image matching (block-matching) is a frequent operation in many image processing tasks, such as MPEG compression and the estimation of optical flow and stereo disparities. Normalized cross-correlation (NCC) is particularly useful since it is insensitive to both signal strength and level. However, NCC is computationally expensive. In this article we attempt to speed up NCC first by transforming each sub-block of the image into the Walsh basis. The Walsh transform expansion can be done very efficiently through a binary tree of filters. Calculating the NCC using the Walsh components requires 2N − 1 operations instead of 4N + 1 in a straightforward implementation. Further, the Walsh transform expansion is shown to have several scales encoded in it. Using only a part of the Walsh components is the same as doing the correlation at a coarser scale. A coarse-to-fine algorithm for doing block-matching using this is presented and tested. The performance of the algorithm is a trade-off between how well the algorithm can find the correct match and how many calculations that are saved. When matching 99% of the blocks correctly the calculations were reduced to 9 − 23% of what a full search would require, depending on the images and the size of the search region. Keywords—Matching, Block matching, Fast normalized crosscorrelation, Walsh functions, Coarse-to-fine