Résumé : In this report, we consider whether statistical regularities in natural images might be exploited to provide an improved selection criterion for interest points. One approach that has been particularly influential in this domain, is the Harris corner detector. The impetus for the selection criterion for Harris corners, proposed in early work and which remains in use to this day, is based on an intuitive mathematical definition constrained by the need for computational parsimony. In this report, we revisit this selection criterion free of the computational constraints that existed 20 years ago, and also importantly, taking advantage of the regularities observed in natural image statistics. Based on the motivating factors of stability and richness of structure, a selection threshold for Harris corners is proposed that is optimal with respect to the structure observed in natural images. Following the protocol proposed by Mikolajczyk et al. \cite{miko2005} we demonstrate that the proposed approach produces interest points that are more stable across various image deformations and are more distinctive resulting in improved matching scores. Finally, the proposal may be shown to generalize to provide an improved selection criterion for other types of interest points. As a whole, the report affords an improved selection criterion for Harris corners which might foreseeably benefit any system that employs Harris corners as a constituent component, and additionally presents a general strategy for the selection of interest points based on any measure of local image structure.