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Boundary detection using quadratic filters: performance criteria and experimental assessment

It is well known that the projection of depth or orientation discontinuities in a physical scene results in image intensity edges which are not ideal step edges but are more typically a combination of steps, peak, and roof profiles. However, most edge detection schemes ignore the composite nature of intensity edges, resulting in systematic errors in detection and localization. We have addressed the problem of detecting and localizing these edges, while at the same time solving the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. We have shown that a class of nonlinear filters, known as quadratic filters are appropriate for this task, while linear filters are not. In this paper a series of performance criteria are derived for characterizing the SNR, localization, and multiple responses of these quadratic filters in a manner analogous to Canny's criteria for linear filters. Additionally, we show experiments on a series of images varying systematically the parameters of the edge detector.