By using a combination of the Mellin radial harmonic function and the Mexican-hat wavelet transform, scale- and shift-invariant pattern recognition is reported. Without preprocessing of the input object, this filter is capable of identifying over a wide allowable scale range of 0.25 to 1. The correlation peaks are sharp, and the peak intensity is fairly uniform, with a variance below 30%. Computer simulation is adopted to investigate the performance of the filter. Experimental results implemented using a photorefractive joint-transform correlator, including those obtained under white noise, are also presented.