Abstract
We studied the visual encoding of edge blur in images. Our previous work (VSS 2001) suggested a model in which the visual system spatially differentiates the luminance profile twice to create the ‘signature’ of the edge, and then evaluates the spatial scale of this signature profile by applying Gaussian derivative templates of different sizes. The scale of the best-fitting template estimates the blur of the edge. Here we refine the model in the light of further blur-matching experiments. A staircase procedure adjusted the blur of a Gaussian comparison edge until it appeared to match the blur of test edges with different spatial profiles, lengths, contrasts and blurs. We also added a linear luminance gradient to blurred test edges. When the added gradient was of opposite polarity to the edge gradient, it made the edge look progressively sharper. Lower contrast edges also looked sharper. Both effects can be explained quantitatively by the action of a half-wave rectifying nonlinearity that sits between the first and second differentiating stages. This rectifier also accounts for a range of other effects on perceived blur. It segments the image into discrete regions of common gradient polarity around each edge. The effect of contrast arises because the rectifier has a threshold: it not only suppresses negative values but also small positive values. At low contrasts, more of the gradient profile falls below threshold and its effective width shrinks, leading to perceived sharpening. The refined template model has few free parameters, but is a remarkably accurate predictor of perceived edge blur and offers some insight into the role of multi-scale filtering by V1 neurons.