This paper presents a theoretical introduction into image structure. The topological structure of scalar and vector images is described. Scale-space is treated in some depth, including the problem of sampling and that of canonical projection. Objects are defined by way of a theory of (physical) measurements. Their properties (shape of the boundary, skeleton, natural subparts) are defined and their topological changes over varying ranges of resolution explored. A short section on the theory of local and global operators in scale-space is provided.
KeywordsImage Space Scale Space Canonical Projection Morse Function Outer Scale
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