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The converging squares algorithm is a method for locating peaks in sampled data of two dimensions or higher. There are two primary advantages of this algorithm over conventional methods. First, it is robust with respect to noise and data type. There are no empirical parameters to permit adjustment of the process, so results are completely objective. Second, the method is computationally efficient. The inherent structure of the algorithm is that of a resolution pyramid. This enhances computational efficiency as well as contributing to the quality of noise immunity of the method. The algorithm is detailed for two-dimensional data, and is described for three-dimensional data. Quantitative comparisons of computation are made with two conventional peak picking methods. Applications to biomedical image analysis, and for industrial inspection tasks are discussed.