22-06-2012, 04:52 PM
A Computational Approach to Edge Detection
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INTRODUCTION
EDGE detectors of some kind, particularly step edge
detectors, have been an essential part of many computer
vision systems. The edge detection process serves
to simplify the analysis of images by drastically reducing
the amount of data to be processed, while at the same time
preserving useful structural information about object
boundaries. There is certainly a great deal of diversity in
the applications of edge detection, but it is felt that many
applications share a common set of requirements. These
requirements yield an abstract edge detection problem, the
solution of which can be applied in any of the original
problem domains.
Eliminating Multiple Responses
In our specification of the edge detection problem, we
decided that edges would be marked at local maxima in
the response of a linear filter applied to the image. The
detection criterion given in the last section measures the
effectiveness of the filter in discriminating between signal
and noise at the center of an edge. It does not take into
account the behavior of the filter nearby the edge center.
FINDING OPTIMAL DETECTORS BY NUMERICAL
OPTIMIZATION
In general it will be difficult (or impossible) to find a
closed form for the functionfwhich maximizes (10) subject
to the multiple response constraint. Even when G has
a particularly simple form (e.g., it is a step edge), the
form off may be complicated. However, if we are given
a candidate function f, evaluation of (10) and (12) is
straightforward. In particular, if the function f is represented
by a discrete time sequence, evaluation of (10)
requires only the computation of four inner products
between sequences. This suggests that numerical optimization
can be done directly on the sampled operator impulse
response.
NOISE ESTIMATION AND THRESHOLDING
To estimate noise from an operator output, we need to
be able to separate its response to noise from the response
due to step edges. Since the performance of the system
will be critically dependent on the accuracy of this estimate,
it should also be formulated as an optimization.
Wiener filtering is a method for optimally estimating one
component of a two-component signal, and can be used
to advantage in this application. It requires knowledge of
the autocorrelation functions of the two components and
of the combined signal. Once the noise component has
been optimally separated, we form a global histogram of
noise amplitude, and estimate the noise strength from
some fixed percentile of the noise signal.
Two OR MORE DIMENSIONS
In one dimension we can characterize the position of a
step edge in space with one position coordinate. In two
dimensions an edge also has an orientation. In this section
we will use the term "edge direction" to mean the direction
of the tangent to the contour that the edge defines in
two dimensions. Suppose we wish to detect edges of a
particular orientation. We create a two-dimensional mask
for this orientation by convolving a linear edge detection
CANNY: COMPUTATIONAL APPROACH TO EDGE DETECTION
function aligned normal to the edge direction with a projection
function parallel to the edge direction.