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Chapter 13
Geometric Operations
13.1 Introduction
Basic image processing operations include the geometric type that rotate
images and scale them (make them bigger and smaller). The rst edition of
this text included some simple forms of these operations. Those operators
are not in this edition. Instead, this chapter discusses a powerful geometric
operator that displaces, rotates, stretches, and bends images. It also includes
auseful and simple program that stretches images to almost any size.
13.2 Geometric Operations
Geometric operations change the spatial relationships between objects in an
image. They do this by moving objects around and changing the size and
shape of objects. Geometric operations help rearrange an image so we can
see what we want to see a little better.
The three basic geometric operations are displacement, stretching, and
rotation. A fourth operation is the cross product (included here to show how
to distort an image using higher order terms).
Displacement moves or displaces an image in the vertical and horizontal
directions. Stretching enlarges or reduces an image in the vertical and hor-
izontal directions. Rotation turns or rotates an image by any angle. Figure
13.1 shows the basic idea of these three operations.
Equations (13.1) and (13.2) describe mathematically how to perform
these operations [13.1]. The rst two terms in each equation perform the
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