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∇ 2 (g * f )
= ( ∇ 2 g ) * f.
With g(x, y) = ( 1 / 2 π σ 2 ) exp [ - (x 2 + y 2 ) / 2 σ 2 ], vide expression
(17.6), we can now evaluate ∇ 2 (g * f ) , which will be non-zero at the
pixels lying on edges in an image and will be zero as we go off the edges. The
present method of edge determination, thus, is a two step process that involves
smoothing and then application of Laplacian over the resulting image.
We now say a few words on texture of an image before closing this section.
17.2.3 Texture of an Image
A texture [6] is a repeated pattern of elementary shapes occurring on an
object’s surface. It may be regular and periodic, random, or partially periodic.
For instance, consider the image of a heap of pebbles. It is partially periodic
as the pebbles are not identical in shape. But a heap of sand must have a
regular and periodic texture. Textures are useful information to determine the
objects from their images. Currently, fractals are being employed to model
textures and then the nature of the texture is evaluated from the function
describing the fractals. Various pattern recognition techniques are also used to
classify objects from the texture of their surfaces.
17.3 Medium Level Vision
After the edges in an image are identified, the next major task is to segregate
the image into modules of interest. The process of partitioning the image into
modules of interest is informally called segmentation. The modules in the
image are generally segmented based on the homogeneous features of the
pixel regions and/ or the boundaries created by the connected edges in low
level processing. The intermediate level requires combining the pieces of
edges of contiguous regions to determine the object boundaries and then
attaching a label to each of these boundaries. We now discuss some of the
well-known techniques of image segmentation and labeling.
17.3.1 Segmentation of Images
The most common type of segmentation is done by a specialized plot of
frequency versus intensity levels of an image, called a histogram. Fig. 17.5
describes a typical histogram. The peaks in the histogram correspond to
regions of the same gray levels. The regions of same intensity levels, thus,
can be easily isolated by judiciously selecting a threshold such that the gray