Digital geometry is the study of geometrical properties of subsets of digital images. If the digitization is sufficiently fine-grained, such properties can be regarded as approximations to the corresponding properties of the "real" sets that gave rise, by digitization, to the digital sets; but it is also important to define how the properties can be computed for the digital sets themselves. Questions of particular interest include how images and image subsets are digitized; how geometric properties are defined for digitized sets; the computational complexity of computing them--in particular, whether they can be computed using simple (e.g., local) operations; characterizing image operations that preserve them; and characterizing digital objects that could be the digitizations of real objects that have given geometric properties. Concepts that have been extensively studied include topological properties (connected components, boundaries); curves and surfaces; straightness, curvature, convexity, and elongatedness; distance, extent, length, area, surface area, volume, and moments; shape description, similarity, symmetry, and relative position; shape simplification and skeletonization.

Digital geometry

Logarithmic spiral grids for image processing and display

A digital arc is called 'straight' if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.

Digital straightness: a review

The author suggests that bus automata (BAs) may serve as better brain models than sequential computers of cellular automata. He proposes to view self-simulationability, together with the use of status flags and the like, as a primitive model of self-consciousness, analogous to viewing a regulator as exhibiting rudimentary purposive behavior. A discussion of what meanings might be ascribed in a BA context to terms like intelligence, pattern, theory, and meaning itself is also given. It is concluded that the BA-UTM (universal Turing machine) is a promising candidate for a brain model whose operation may actually be relevant to mental processes. Prospects for actual BA-UTM realization are briefly discussed. >

Carl Weiman

Papers

Parallel and sequential specification of a context sensitive language for straight lines on grids