Edge Detection - Important Concepts in Signal Processing, Image Processing and Data Compression - page 22

data to be processed and may therefore filter out information that may be regarded as less
relevant, while preserving the important structural properties of an image. If the edge
detection step is successful, the subsequent task of interpreting the information contents
in the original image may therefore be substantially simplified. However, it is not always
possible to obtain such ideal edges from real life images of moderate complexity. Edges
extracted from non-trivial images are often hampered by fragmentation , meaning that the
edge curves are not connected, missing edge segments as well as false edges not
corresponding to interesting phenomena in the image - thus complicating the subsequent
task of interpreting the image data.

Edge detection is one of the fundamental steps in image processing, image analysis,
image pattern recognition, and computer vision techniques. During recent years,
however, substantial (and successful) research has also been made on computer vision
methods that do not explicitly rely on edge detection as a pre-processing step.

Edge properties

The edges extracted from a two-dimensional image of a three-dimensional scene can be
classified as either viewpoint dependent or viewpoint independent. A viewpoint
independent edge typically reflects inherent properties of the three-dimensional objects,
such as surface markings and surface shape. A viewpoint dependent edge may change as
the viewpoint changes, and typically reflects the geometry of the scene, such as objects
occluding one another.

A typical edge might for instance be the border between a block of red color and a block
of yellow. In contrast a line (as can be extracted by a ridge detector) can be a small
number of pixels of a different color on an otherwise unchanging background. For a line,
there may therefore usually be one edge on each side of the line.

A simple edge model

Although certain literature has considered the detection of ideal step edges, the edges
obtained from natural images are usually not at all ideal step edges. Instead they are
normally affected by one or several of the following effects:

focal blur caused by a finite depth-of-field and finite point spread function.

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penumbral blur caused by shadows created by light sources of non-zero radius.

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shading at a smooth object

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A number of researchers have used a Gaussian smoothed step edge (an error function) as
the simplest extension of the ideal step edge model for modeling the effects of edge blur
in practical applications. Thus, a one-dimensional image f which has exactly one edge
placed at x = 0 may be modeled as: