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This paper formulates the problem encountered in the first stage of two-stage, binary template matching as a set of hypotheses to be tested, including a hypothesis of ``no object.'' Two new statistics R and G are proposed, based on a likelihood ratio, and are compared to the sum of absolute differences and a correlation measure by analytical approximations and Monte Carlo experiments. Statistical power and a measure of sensitivity to the true location of the object are the criteria. Parameters are the numbers of 1's in object and image, subtemplate size, and parameters reflecting intensity distortion between template and object. One of the proposed statistics R is much more computationally intensive than the other G. Although R is more powerful than G and the other statistics, G is generally more sensitive to the true object location. Statistic G is also more powerful than the sum of absolute differences and correlation. All statistics are robust to incomplete knowledge of distortion parameters. Experiments on Landsat images confirm the sensitivity of G and recommend it for application in the first stage.