Seeing edge blur: receptive fields as multi-scale neural templates

Abstract

Edge blur is an important perceptual cue, but how does vision encode the degree of blur at edges? I examined measurement models and template models. Blur could be measured by the width of the gradient profile, peak-trough separation in the 2nd derivative profile, or the ratio of 1st-to-3rd derivative magnitudes. In template models, vision would store a set of templates of different sizes and find which one best fits the ‘signature’ of the edge. The signature could be the luminance profile itself, or one of its spatial derivatives. In a 2AFC staircase procedure, observers adjusted the blur of Gaussian edges (30% contrast) to match the perceived blur of various test edges. Exp. 1: Test stimuli were mixtures of 2 Gaussian edges (e.g. 10′ and 30′ blur) at the same location, and relative contrast of the 2 component edges was varied while overall contrast was 30%. Exp. 2: Test stimuli were formed from a blurred edge sharpened to different extents by a compressive transformation. Predictions of the various models were tested against the blur-matching data, but only one model was strongly supported. This was the template model in which the input signature is the 2nd derivative of the luminance profile, and the templates are applied to this signature at the zero-crossings. The templates are Gaussian derivative receptive fields that co-vary in width and length to form a self-similar set (i.e. same shape, different sizes). This naturally predicts that shorter edges should look sharper. As edge length gets shorter, responses of longer templates drop more than shorter ones, and so the response distribution shifts towards shorter (smaller) templates, signalling a sharper edge. Our data confirmed this, including the scale-invariance implied by self-similarity, and a good fit was obtained from templates with a length-width ratio of 1.5. The simultaneous analysis of edge blur and edge location may offer a new solution to the multi-scale problem in edge detection.