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 step, peak and roof profiles. Most edge detection schemes ignore the composite nature of these edges, resulting in systematic errors in detection and localization. The problem of detecting and localizing these edges is addressed, along with the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. A class of nonlinear filters, known as quadratic filters, is appropriate for this task, while linear filters are not. Performance criteria are derived for characterizing the SNR, localization and multiple responses of these filters in a manner analogous to Canny's criteria for linear filters. A two-dimensional version of the approach is developed which has the property of being able to represent multiple edges at the same location and determine the orientation of each to any desired precision. This permits junctions to be localized without rounding. Experimental results are presented.
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