Showing papers by "Azriel Rosenfeld published in 1970"

Connectivity in Digital Pictures

Abstract: Natural concepts of connectedness and simple-connectedness are defined for subsets of a digital picture. It is shown that every simply-connected object (with more than one element) in such a picture has elements which can be deleted without destroying its simple- connectedness. This makes it easy to prove that a well-known "shrinking" algorithm always works--that is, shrinks any simply-connected object down to a single element. It also becomes easy to show that the natural "edge-following" algorithm, in which one "keeps one's hand on the wall," follows completely around the edge of any simply-connected object; this result in turn can be used to show that a well-known "border-following" algorithm (in which one follows the border elements of the object rather than the "cracks" between the object and its comple- ment) always works. Various related questions are also treated, among them, that of whether there can exist a "parallel" shrinking algorithm.

Visual texture analysis

Abstract: Differentiation between the coarsenesses of samples of a given texture may be successfully effected using any of the following measures: (1) Amount of edge per unit area, (2) Self-match (as measured by sum of absolute differences) over a unit shift, (3) Gray value dependency, and (4) Number of relative extrema per unit area.

A note on grammars with coordinates.

Abstract: : Anderson has defined the notion of a 'graphical rewriting grammar', in which each production has an associated set of functions that compute coordinates for the symbols in the production's right member in terms of given coordinates of the symbols in its left member. It is shown that any such 'Anderson grammar' (AG) is equivalent to a 'one-dimensional' AG whose productions are all 'left-linear'; thus the power of an AG can be restricted only by restricting its coordinate-computing functions. On the other hand, even if the productions of an AG are left-linear and its functions are all computable by finite automata, its language need not be finite-state or even context-free. (Author)

Picture grammars

Abstract: In recent years there has been considerable interest in applying the methods of mathematical linguistics to picture generation and description [1]. In this approach, pictures are regarded as combinations of subpictures, which are in turn built up out of still smaller parts, in analogy with the way that sentences can be broken down into phrases and words. Conventionally, however, mathematical linguistics deals with strings (of words, etc.), whereas pictures do not usually have natural representations as strings of subpictures. This suggests that it would be desirable to generalize the tools of mathematical linguistics so as to allow combining parts into wholes by methods more general than string concatenation.

Shape synthesis, i,

Abstract: : The project is concerned with the computer synthesis of classes of natural shapes and patterns. The goal is to gain an understanding of the types of mathematical models that can be used to specify such classes. In this initial study, an approach based on medial axis transformations was used, and the synthesis of leaf shapes was taken as a test problem. A computer program was written to implement the chosen approach, and a mathematical model for this approach - in effect, a picture grammar for the leaf shapes - was formulated. Explicit use of coordinates appears to be desirable in grammars of this type. (Author)