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Partial computation elimination techniques are often used for fast template matching. At a particular search location, computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location. Due to the nonmonotonic growth pattern of the correlation-based similarity measures, partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures. In this paper, we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation, and we propose basic-mode and extended-mode partial correlation elimination algorithms for fast template matching. The basic-mode algorithm is more efficient on small template sizes, whereas the extended mode is faster on medium and larger templates. We also propose a strategy to decide which algorithm to use for a given data set. To achieve a high speedup, elimination algorithms require an initial guess of the peak correlation value. We propose two initialization schemes including a coarse-to-fine scheme for larger templates and a two-stage technique for small- and medium-sized templates. Our proposed algorithms are exact, i.e., having exhaustive equivalent accuracy, and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes. While the actual speedups are data dependent, in most cases, our proposed algorithms have been found to be significantly faster than the other algorithms.