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Unformatted text preview: t an edge (transition from dark to
light) is modeled as a smooth, rather than as an abrupt, change of gray level. This model reflects
the fact that edges in digital images are generally slightly blurred as a result of sampling. Fig 4
(a) shows that the first derivative of the gray level profile is positive at the leading edge of a
transition, negative at the trailing edge, and, as expected, zero in areas of constant gray level.
The second derivative is positive for that part of the transition associated with the dark side of
the edge, negative for that part of the transition associated with the light side of the edge, and
zero in areas of constant gray level. Hence t he magnitude of the first derivative can be used to
detect the presence of an edge in an image, and the sign of the second derivative can be used to
determine whether an edge pixel lies on the dark or light side of an edge. Note that the second
derivative has a zero crossing at the midpoint of a transition in gray level. Zero crossings
provide a powerful approach for locating edges in an image.
Although discussion so far limited to a 1-D horizontal profile, a similar argument applies to an
edge of any orientation in an image. We simply define a profile perpendicular to the edge
direction at any desired point and interpret the results as in the preceding discussion. The first
derivative at any point in an image is obtained by using the magnitude of the gradient at that
point. The second derivative is similarly obtained by using the Laplacian. Complete segmentation
• set of disjoint regions uniquely corresponding with objects in the input image
cooperation with higher processing levels which use specific knowledge of the problem
domain is necessary Partial segmentation
• regions do not correspond directly with image objects
image is divided into separate regions that are homogeneous with respect to a chosen
property such as brightness, color, reflectivity, texture, etc.
in a complex scene, a set of possibly overlapping homogeneous regions may result. The
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This document was uploaded on 03/12/2014 for the course MECHANICAL 214 at University of Manchester.
- Spring '14