Fast Template Matching

Although it is well known that cross correlation can be efficiently implemented in the transform domain, the normalized form of cross correlation preferred for template matching applications does not have a simple frequency domain expression. Normalized cross correlation is usually computed in the spatial domain for this reason. This short paper shows that unnormalized cross correlation can be efficiently normalized using precomputed tables containing the integral of the image and image over the search window. 1 Template Matching by Cross Correlation Correlation is an important tool in image processing, pattern recognition, and other fields. The correlation between two signals (cross correlation) is a standard approach to feature detection [1, 2] as well as a building block for more sophisticated recognition techniques (e.g. [3]). Textbook presentations of correlation commonly mention the convolution theorem and the attendant possibility of efficiently computing correlation in the frequency domain via the fast Fourier transform. Unfortunately the normalized form of correlation (correlation coefficient) preferred in many applications does not have a correspondingly simple and efficient frequency domain expression, and spatial domain implementation is recommended instead (e.g. [2], p. 585; also see e.g. [4] sections 13.2 and 14.5). This paper shows that the unnormalized correlation can be efficiently normalized using using precomputed tables of the integral of the signal and signal, i.e., summed-area tables [5]. Template matching techniques [1] attempt to answer some variation of the following question: Does the image contain a specified view of some feature, and if so, where? The use of cross correlation for template matching is motivated by the distance measure (squared Euclidean distance)