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On the topology preservation property of local parallel operations
ABSTRACTS
86
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FOR PUBLICATION
Department of Information Science, Faculty of Engineering, Nagoya University. Furo-cho, Chikusa-ku, Nagoya 464, Japan. Received June 29. 198 I ; revised December 14, 198 I ; accepted February I. 1982. In this paper, the distance transformation of a line pattern (DTLP) is discussed. The DTLP is a transformation of a binary pattern developed for extracting useful features to analyze and recognize a given pictorial data. Its basic type (BDTLP) has already been reported by the authors. This paper presents a modification and a generalization of the BDTLP. The modified DTLP (MDTLP) is derived by defining an inhibited edge point among the edge points of an input line pattern. By applying the MDTLP, information on the length of a line pattern is concentrated on the inhibited edge point instead of the center point as in the case of the BDTLP. The generalized DTLP (GDTLP) is a parallel iterative local operation applied to a line pattern with gray values, whose execution is controlled by the BDTLP or the MDTLP performed on another picture plane containing a binarized version of an input line pattern. It enables us to process a line pattern with arbitrary gray values on it as well as a binary pattern. Experimental results are shown concerning the application of the GDTLP to the processing of ridge and ravine lines extracted from a digitized map data. An application of the type II MDTLP to the extraction of information on the loop structure of a line pattern is also presented with illustrative examples. Segment&on Using Simple Murkoo Field Models. F. R. HANSEN AND H. ELLIOTT. Department of Electrical Engineering, Colorado State University, Fort Collins, Colorado 80523.
Imuge
Received June 29, 1981; revised October 15, 1981 By modelling a picture as a two-state Markov field, MAP estimation techniques are used to develop suboptimal but computationally tractable binary segmentation algorithms. The algorithms are shown to perform well at low signal to noise ratios, and analytical procedures are developed for estimating the Markov field transition probabilities. In addition, extensions of this approach to the multispectral and multiregion cases are discussed. On
the
Topology
Information
Preservution Property of L.ocul Parullel Operations. SATORU KAWAI. Department of Science, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan.
Received July 7, 1981; revised August 17, I98 I Quasi-preservation of topological structures of binary pictures by a group of parallel local operations is considered. The topology is defined in terms of adjacency among binary components. Parallel local operations treated here are allowed to alter the topology only by deleting simply connected components. They also are required to annihilate all components except for the background. The window for these operations is 2 X 2. and asymmetric with respect to the point whose value is to be calculated at the next step of operation. The group of operations are obtained by determining the necessary and sufficient conditions for a parallel operation to satisfy the quasi-preservation property thus defined. Some other considerations are also given. Approximution by the Minimux Merhod. YOSHINJKE KUROZUMI Department of Computer Sciences, Kyoto-Sangyo University, Kyoto 603; Japan, AND WAYNE A. DAVIS, Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2H1, Canada.
PoJvgonul
Received July 15, 1981. This paper is concerned with the problem of approximating digitized pictures by polygons, The digitized picture is represented by a two-dimensional array of points, and it is desired to convert the given array into a set of polygons, such that each polygon has the least number of sides and the error between the initial points and the approximated lines is less than a given constant (E). There are many other solutions to this problem, but to evaluate the error, they use either the least-squares method or the cone-intersection method. In this paper, it is shown that the minimax approximation that minimizes the
86
OF PAPERS ACCEPTED
FOR PUBLICATION
Department of Information Science, Faculty of Engineering, Nagoya University. Furo-cho, Chikusa-ku, Nagoya 464, Japan. Received June 29. 198 I ; revised December 14, 198 I ; accepted February I. 1982. In this paper, the distance transformation of a line pattern (DTLP) is discussed. The DTLP is a transformation of a binary pattern developed for extracting useful features to analyze and recognize a given pictorial data. Its basic type (BDTLP) has already been reported by the authors. This paper presents a modification and a generalization of the BDTLP. The modified DTLP (MDTLP) is derived by defining an inhibited edge point among the edge points of an input line pattern. By applying the MDTLP, information on the length of a line pattern is concentrated on the inhibited edge point instead of the center point as in the case of the BDTLP. The generalized DTLP (GDTLP) is a parallel iterative local operation applied to a line pattern with gray values, whose execution is controlled by the BDTLP or the MDTLP performed on another picture plane containing a binarized version of an input line pattern. It enables us to process a line pattern with arbitrary gray values on it as well as a binary pattern. Experimental results are shown concerning the application of the GDTLP to the processing of ridge and ravine lines extracted from a digitized map data. An application of the type II MDTLP to the extraction of information on the loop structure of a line pattern is also presented with illustrative examples. Segment&on Using Simple Murkoo Field Models. F. R. HANSEN AND H. ELLIOTT. Department of Electrical Engineering, Colorado State University, Fort Collins, Colorado 80523.
Imuge
Received June 29, 1981; revised October 15, 1981 By modelling a picture as a two-state Markov field, MAP estimation techniques are used to develop suboptimal but computationally tractable binary segmentation algorithms. The algorithms are shown to perform well at low signal to noise ratios, and analytical procedures are developed for estimating the Markov field transition probabilities. In addition, extensions of this approach to the multispectral and multiregion cases are discussed. On
the
Topology
Information
Preservution Property of L.ocul Parullel Operations. SATORU KAWAI. Department of Science, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan.
Received July 7, 1981; revised August 17, I98 I Quasi-preservation of topological structures of binary pictures by a group of parallel local operations is considered. The topology is defined in terms of adjacency among binary components. Parallel local operations treated here are allowed to alter the topology only by deleting simply connected components. They also are required to annihilate all components except for the background. The window for these operations is 2 X 2. and asymmetric with respect to the point whose value is to be calculated at the next step of operation. The group of operations are obtained by determining the necessary and sufficient conditions for a parallel operation to satisfy the quasi-preservation property thus defined. Some other considerations are also given. Approximution by the Minimux Merhod. YOSHINJKE KUROZUMI Department of Computer Sciences, Kyoto-Sangyo University, Kyoto 603; Japan, AND WAYNE A. DAVIS, Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2H1, Canada.
PoJvgonul
Received July 15, 1981. This paper is concerned with the problem of approximating digitized pictures by polygons, The digitized picture is represented by a two-dimensional array of points, and it is desired to convert the given array into a set of polygons, such that each polygon has the least number of sides and the error between the initial points and the approximated lines is less than a given constant (E). There are many other solutions to this problem, but to evaluate the error, they use either the least-squares method or the cone-intersection method. In this paper, it is shown that the minimax approximation that minimizes the