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 these edges, resulting
in systematic errors in detection and localization. We
address the problem of detecting and localizing these
edges, while at the same time also solving the problem
of false responses in smoothly shaded regions with
constant gradient of the image brightness. We show
that a class of nonlinear filters, known as quadratic
filters, are appropriate for this task, while linear filters
are not. A series of 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