Diagnosis of melanoma is fraught with uncertainty, and discordance rates among physicians remain high because of the lack of a definitive criterion. Motivated by this challenge, this paper first introduces the Patch Weyl transform (PWT), a 2-dimensional variant of the Weyl transform. It then presents a method for classifying pump-probe images of melanocytic lesions based on the PWT coefficients. Performance of the PWT coefficients is shown to be superior to classification based on baseline intensity, on standard descriptors such as the Histogram of Oriented Gradients (HOG) and Local Binary Patterns (LBP), and on coefficients derived from PCA and Fourier representations of the data.