The Weight-Shape decomposition of density estimates: A framework for clustering and image analysis algorithms.

•Every Parzen estimate of a probability distribution can be decomposed into Weight and Shape components in a unique fashion.•This decomposition allows for a fresh classification of clustering algorithms, based on Probability (mean-shift), on Shape (quantum clustering), or on Weight (entropy maximization).•These concepts can be applied to image analysis, with Shape providing novel aspects of generalized edge detection.