An Image Algebra

This chapter describes an image algebra, which is based on symbolic projection, including a limited extension of the original set of relational operators. In the algebra a generalized empty space object is also introduced, which supports general descriptions and manipulations of images. The concept of “empty space” is used not only to describe the complete image but also to make it possible to describe space outside the objects of interest. The term “empty space” was first used in this sense by Lozano–Perez partly, to build up a structure that can be used to describe the space of an image. Among the alternative approaches to pictorial data structures, hierarchical structures of various kinds such as the quad-tree have been subject to particular interest.

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