The shape-oriented dissimilarity of polygons and its application to the classification of chromosome images

doi:10.1016/0031-3203(74)90007-7

Pattern Recognition

Volume 6, Issue 1, June 1974, Pages 47-60

https://doi.org/10.1016/0031-3203(74)90007-7 Get rights and content

Abstract

Pavlidis in his “analysis of set patterns” proposed three size-oriented similarity measures. In this paper, shape-oriented similarity and dissimilarity measures of triangles and polygons are proposed and investigated. There are three advantages of shape-oriented similarity measures. First, two polygons may have the same shape but differ in area and dimensions and still be similar. Second, shape-oriented similarity and dissimilarity measures can be normalized between zero and one. Third, shape-oriented similarity measures are invariant with respect to rotation, translation, or expansion or contraction in size. The “rubber-mask” technique proposed by Widrow utilized length and width parameters in the classification of chromosomes. In this paper, chromosome images are classified through the use of angular and dimensional proximity measures which are in terms of angle and length parameters. The results obtained in this paper may contribute to processing a picture from the polygonal approximation stage to the final filtering stage in order to recognize or classify a picture.

References (18)

T. Pavlidis
Analysis of set patterns
Pattern Recognition
(1968)
T. Pavlidis
Representation of figures by labeled graphs
Pattern Recognition
(1972)
T. Pavlidis
Computer recognition of figures through decomposition
Inf. Control
(1968)
L.A. Zadeh
Similarity relations and fuzzy ordering
Inf. Sci.
(1971)
D.M. Jackson
An error analysis for functions of qualitative attributes with application to information retrieval
M.F. Dacey
The syntax of a triangle and some other figures
Pattern Recognition
(1970)
P.H. Swain et al.
Stochastic programmed grammars for syntactic pattern recognition
Pattern Recognition
(1972)
B. Widrow
The rubber-mask technique—I: Pattern measurement and analysis
Pattern Recognition
(1973)
B. Widrow
The rubber-mask technique—II: Pattern storage and recognition
Pattern Recognition
(1973)

There are more references available in the full text version of this article.

Cited by (26)

Recognizing shapes in planar binary images
1989, Pattern Recognition
Shape features are described which enable the identification of shapes of simply connected objects in a low resolution planar binary image. Invariance properties of the features are investigated. In the continuous case, a class of general shape measures is introduced. An experiment using low resolution real images to test the effectiveness of the features in discriminating similar shapes in digital images is described. Error-free classification is observed in low noise images.
Algorithms for finding most unsymmetrical chromosome images
1983, Mathematical Biosciences
By using chromosome images as a framework, algorithms for finding most unsymmetrical images are presented and illustrated with examples. Sixteen angularly-not-equal and six angularly-not-equivalent most unsymmetrical chromosome images are found. A state-transition table, a state-transition diagram, and six most unsymmetrical chromosome images are also presented. The results may have useful applications in pattern recognition, picture understanding, information storage and retrieval, artificial intelligence, fuzzy-set theory, and pictorial information systems.
Shape-oriented storage and retrieval of geometric figures and chromosome images
1976, Information Processing and Management
Four advantages of storing and retrieving geometric figures and chromosome images through the use of shape-oriented similarity measures are presented. A complemented but not distributive lattice and a distributive but not complemented lattice are found. Answers to triangle related fuzzy queries such as “retrieve the triangles which are very similar to isosceles triangles but not similar to a given triangle Δx”, and chromosome related fuzzy queries such as “retrieve the chromosomes which are more or less similar to median chromosomes and very very similar to a given chromosome A” are presented and illustrated by examples. For shape-oriented storage of triangles, it is proposed to store the angles of each triangle in decreasing order of the magnitude and logically order all the triangles according to the magnitude of the angles. For shape-oriented storage of chromosomes, it is proposed to logically order all the chromosomes individually and independently according to the angular sums of its exterior biangles and interior biangles. The results may have useful applications in information storage and retrieval, artificial intelligence and pattern recognition.
An application of fuzzy sets to the classification of geometric figures and chromosome images
1976, Information Sciences
The concept of a fuzzy set is applied to the classification of geometric figures and chromosome images through the use of shape-oriented angular and dimensional proximity measures. Various properties of approximate isosceles, approximate equilateral, approximate right, and approximate isosceles right triangles are investigated. A method for classifying a triangle as an “approximate right triangle,” “approximate isosceles triangle,” “approximate isosceles right triangle,” “approximate equilateral triangle,” or “ordinary triangle” is presented. A method used to classify a quadrangle as “approximate square,” “approximate rectangle,” “approximate rhombus,” “approximate parallelogram,” “approximate trapezoid,” or “ordinary quadrangle” is also presented. The measures of proximity employed for this purpose have an intuitive interpretation. The stochastic syntactic analysis technique and the “rubber-mask” technique have, in the past, been applied to the classification of chromosome images. In this paper, chromosome images are classified through the use of angular and dimensional proximity measures. The uttermost dimensional proximity and the least dimensional dissimilarity of chromosome images are defined and investigated. The results obtained in this paper may contribute to processing a picture from the polygonal approximation stage to the final classification stage in order to recognize a picture.
Shape oriented storage and retrieval of geometric figures and chromosome images
1976, INFORM.PROC.MANAGE.
Four advantages of storing and retrieving geometric figures and chromosome images through the use of shape-oriented similarity measures are presented. A complemented but not distributive lattice and a distributive but not complemented lattice are found. Answers to triangle related fuzzy queries such as “retrieve the triangles which are very similar to isosceles triangles but not similar to a given triangle Δx”, and chromosome related fuzzy queries such as “retrieve the chromosomes which are more or less similar to median chromosomes and very very similar to a given chromosome A” are presented and illustrated by examples. For shape-oriented storage of triangles, it is proposed to store the angles of each triangle in decreasing order of the magnitude and logically order all the triangles according to the magnitude of the angles. For shape-oriented storage of chromosomes, it is proposed to logically order all the chromosomes individually and independently according to the angular sums of its exterior biangles and interior biangles. The results may have useful applications in information storage and retrieval, artificial intelligence and pattern recognition.
Emulating human visual perception for measuring difference in images using an SPN graph approach
2002, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

View all citing articles on Scopus

View full text

The shape-oriented dissimilarity of polygons and its application to the classification of chromosome images

Abstract

Pattern Recognition

Pattern Recognition

Inf. Control

Inf. Sci.

Pattern Recognition

Pattern Recognition

Pattern Recognition

Pattern Recognition