The detection of smooth curves in jagged contours

Abstract

Jagged contours with sharp edges, such as those formed by the fractal edge of the Mandelbrot set, have a lower correlation in position and shape between different scales than smooth curves. The more jagged the contour, the lower the correlation. In principle, coarse changes in position of a curve, be it jagged or smooth, can be coded by using operators tuned to low-luminance spatial frequencies; but, to code the fine changes in position of a jagged contour, small operators are required. Since a sharp-luminance- transition contour is visible to both high-spatial-frequency-tuned and low-spatial-frequency-tuned operators, the question arises whether coarse changes in shape are coded via low-spatial-frequency- tuned cells, or via high-spatial-frequency-tuned cells whose outputs are pooled by a coarse-scale higher-order mechanism. We investigated this issue by conducting two experiments. In the first experiment, we show that shape-amplitude detection thresholds of a sinusoidal contour increase with the blur of the contour, and that the threshold functions are parallel over a large range of shape spatial frequencies, implying that high-(luminance)-spatial-frequency-tuned mechanisms that are more shape-and-position sensitive come into play whenever they can be supported. In the second experiment, we measured the threshold for shape-amplitude detection of a low-shape-frequency sinusoidal contour in the presence of shape harmonics of various amplitudes, for both (luminance) spatial-frequency unfiltered, and high-pass spatial-frequency filtered, contours.We found no differ- ence in thresholds for shape-amplitude detection when using filtered and unfiltered stimuli. We conclude that coarse shape information is coded with the smallest operators available. In the context of a model of vision that emphasises the role of self-similar `filters' tuned in spatial frequency, our results are consistent with the idea that contour shape is encoded via high-spatial- frequency-tuned cells, possibly of the highest spatial frequency capable of responding to the contour. [Supported by URC (Hong Kong) and NSERC (Canada).]