A discriminant formulation of top-down visual saliency, intrinsically connected to the recognition problem, is proposed. The new formulation is shown to be closely related to a number of classical principles for the organization of perceptual systems, including infomax, inference by detection of suspicious coincidences, classification with minimal uncertainty, and classification with minimum probability of error. The implementation of these principles with computational parsimony, by exploitation of the statistics of natural images, is investigated. It is shown that Barlow's principle of inference by the detection of suspicious coincidences enables computationally efficient saliency measures which are nearly optimal for classification. This principle is adopted for the solution of the two fundamental problems in discriminant saliency, feature selection and saliency detection. The resulting saliency detector is shown to have a number of interesting properties, and act effectively as a focus of attention mechanism for the selection of interest points according to their relevance for visual recognition. Experimental evidence shows that the selected points have good performance with respect to 1) the ability to localize objects embedded in significant amounts of clutter, 2) the ability to capture information relevant for image classification, and 3) the richness of the set of visual attributes that can be considered salient.