Graphics Reference
In-Depth Information
Chapter 19
Images
In Chapters 17 and 18 you learned how images are used to store regular arrays
of data, typically representing samples of some continuous function like “the
light energy falling on this region of a synthetic camera's image plane.” You also
learned a lot of theoretical information about how you can understand such sam-
pled representations of functions by examining their Fourier transforms. In this
chapter, we apply this knowledge to the problems of adjusting image sizes (scaling
images up and down, as shown in Figure 19.1, which are synonyms for “enlarg-
ing” and “shrinking”), and performing various operations such as edge detection.
Scale up
Scale down
We assume that the values stored in an image array form a signal that is
real-valued,
not
discrete; nothing we say here applies to an object-ID image, for
example.
Just as we did in Chapter 18, in this chapter we study primarily grayscale
images. Scaling up or down a grayscale image entails all the main ideas without
the complications of three color channels. Furthermore, we continue to study the
effects of transformations on a single row of image pixels, because the extension to
two dimensions really has no important properties beyond those of one dimension,
but the notation is substantially more complex. We do, however, return to two
dimensions when providing code for scaling up and down, and when we analyze
the efficiency of computing convolutions.
In this chapter, we use the following ideas from Chapter 18.
Figure
19.1:
Terminology
for
image scaling.
• Sampling and convolution operations on a signal can be profitably viewed
in both the value and the frequency domains.
• The convolution-multiplication theorem. Convolution in the value domain
corresponds to multiplication in the frequency domain, and vice versa.
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