A new split-and-merge technique for polygonal approximation of chain coded curves
TL;DR: The initial segmentation is done by introducing the concept of rank of a point and the procedure generates polygons that are insensitive to rotation and scales and remains reliable in presence of noise.
About: This article is published in Pattern Recognition Letters.The article was published on 1995-02-01. It has received 69 citations till now. The article focuses on the topics: Distance from a point to a line & Line segment.
Citations
More filters
TL;DR: The experimental results manifest that the proposed discrete PSO is comparable to the genetic algorithm, and it outperforms another discrete implementation of PSO in the literature.
130 citations
Cites background from "A new split-and-merge technique for..."
...Ray and Ray (1995) proposed an orientation-invariant and scale-invariant method by introducing the use of ranks of points and the normalized distances....
[...]
...2) which are broadly used in the literature (Held et al., 1994; Ho and Chen, 2001; Huang and Sun, 1999; Ray and Ray, 1993, 1995; Teh and Chin, 1989; Wall and Danielsson, 1984; Yin, 1999, 2003; Zhu and Chirlian, 1995) and two real image curves (see Figs....
[...]
TL;DR: A bibliography of nearly 1700 references related to computer vision and image analysis, arranged by subject matter is presented, including computational techniques; feature detection and segmentation; image and scene analysis; two-dimensional shape; pattern; color and texture; matching and stereo.
94 citations
TL;DR: The performance of the proposed polygonal approximation method as compared to those of the genetic-based and the tabu search-based approaches is very promising.
90 citations
Cites methods from "A new split-and-merge technique for..."
...Keywords: Polygonal approximation; Genetic algorithm; Tabu search; Ant colony search algorithm; Local optimal solution; Global optimal solution...
[...]
01 Jan 2003
TL;DR: In this article, a polygonal approximation method using ant colony search algorithm is presented, which is represented by a directed graph such that the objective of the original problem becomes to find the shortest closed circuit on the graph under the problem-speci c constraints.
Abstract: This paper presents a new polygonal approximation method using ant colony search algorithm. The problem is represented bya directed graph such that the objective of the original problem becomes to .nd the shortest closed circuit on the graph under the problem-speci.c constraints. A number of arti.cial ants are distributed on the graph and communicate with one another through the pheromone trails which are a form of the long-term memoryguiding the future exploration of the graph. The important properties of the proposed method are thoroughlyinvestigated. The performance of the proposed method as compared to those of the genetic-based and the tabu search-based approaches is verypromising. ? 2003 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.
89 citations
TL;DR: It is shown empirically that the proposed EEA outperforms the existing genetic-algorithm-based method under the same cost conditions in terms of the quality of the best solution, average solution, variance of solutions, and the convergence speed, especially in solving large polygonal approximation problems.
60 citations
References
More filters
14,948 citations
Book•
01 Jan 1973
TL;DR: In this article, a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition is provided, including Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.
Abstract: Provides a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition. The topics treated include Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.
13,647 citations
Book•
01 Aug 1981
TL;DR: This chapter discusses Graphics, Image Processing, and Pattern Recognition, and the Reconstruction techniques used in this program, as well as some of the problems faced in implementing this program.
Abstract: 1: Introduction.- 1.1 Graphics, Image Processing, and Pattern Recognition.- 1.2 Forms of Pictorial Data.- 1.2.1 Class 1: Full Gray Scale and Color Pictures.- 1.2.2 Class 2: Bilevel or "Few Color" pictures.- 1.2.3 Class 3: Continuous Curves and Lines.- 1.2.4 Class 4: Points or Polygons.- 1.3 Pictorial Input.- 1.4 Display Devices.- 1.5 Vector Graphics.- 1.6 Raster Graphics.- 1.7 Common Primitive Graphic Instructions.- 1.8 Comparison of Vector and Raster Graphics.- 1.9 Pictorial Editor.- 1.10 Pictorial Transformations.- 1.11 Algorithm Notation.- 1.12 A Few Words on Complexity.- 1.13 Bibliographical Notes.- 1.14 Relevant Literature.- 1.15 Problems.- 2: Digitization of Gray Scale Images.- 2.1 Introduction.- 2.2 A Review of Fourier and other Transforms.- 2.3 Sampling.- 2.3.1 One-dimensional Sampling.- 2.3.2 Two-dimensional Sampling.- 2.4 Aliasing.- 2.5 Quantization.- 2.6 Bibliographical Notes.- 2.7 Relevant Literature.- 2.8 Problems.- Appendix 2.A: Fast Fourier Transform.- 3: Processing of Gray Scale Images.- 3.1 Introduction.- 3.2 Histogram and Histogram Equalization.- 3.3 Co-occurrence Matrices.- 3.4 Linear Image Filtering.- 3.5 Nonlinear Image Filtering.- 3.5.1 Directional Filters.- 3.5.2 Two-part Filters.- 3.5.3 Functional Approximation Filters.- 3.6 Bibliographical Notes.- 3.7 Relevant Literature.- 3.8 Problems.- 4: Segmentation.- 4.1 Introduction.- 4.2 Thresholding.- 4.3 Edge Detection.- 4.4 Segmentation by Region Growing.- 4.4.1 Segmentation by Average Brightness Level.- 4.4.2 Other Uniformity Criteria.- 4.5 Bibliographical Notes.- 4.6 Relevant Literature.- 4.7 Problems.- 5: Projections.- 5.1 Introduction.- 5.2 Introduction to Reconstruction Techniques.- 5.3 A Class of Reconstruction Algorithms.- 5.4 Projections for Shape Analysis.- 5.5 Bibliographical Notes.- 5.6 Relevant Literature.- 5.7 Problems.- Appendix 5.A: An Elementary Reconstruction Program.- 6: Data Structures.- 6.1 Introduction.- 6.2 Graph Traversal Algorithms.- 6.3 Paging.- 6.4 Pyramids or Quad Trees.- 6.4.1 Creating a Quad Tree.- 6.4.2 Reconstructing an Image from a Quad Tree.- 6.4.3 Image Compaction with a Quad Tree.- 6.5 Binary Image Trees.- 6.6 Split-and-Merge Algorithms.- 6.7 Line Encodings and the Line Adjacency Graph.- 6.8 Region Encodings and the Region Adjacency Graph.- 6.9 Iconic Representations.- 6.10 Data Structures for Displays.- 6.11 Bibliographical Notes.- 6.12 Relevant Literature.- 6.13 Problems.- Appendix 6.A: Introduction to Graphs.- 7: Bilevel Pictures.- 7.1 Introduction.- 7.2 Sampling and Topology.- 7.3 Elements of Discrete Geometry.- 7.4 A Sampling Theorem for Class 2 Pictures.- 7.5 Contour Tracing.- 7.5.1 Tracing of a Single Contour.- 7.5.2 Traversal of All the Contours of a Region.- 7.6 Curves and Lines on a Discrete Grid.- 7.6.1 When a Set of Pixels is not a Curve.- 7.6.2 When a Set of Pixels is a Curve.- 7.7 Multiple Pixels.- 7.8 An Introduction to Shape Analysis.- 7.9 Bibliographical Notes.- 7.10 Relevant Literature.- 7.11 Problems.- 8: Contour Filling.- 8.1 Introduction.- 8.2 Edge Filling.- 8.3 Contour Filling by Parity Check.- 8.3.1 Proof of Correctness of Algorithm 8.3.- 8.3.2 Implementation of a Parity Check Algorithm.- 8.4 Contour Filling by Connectivity.- 8.4.1 Recursive Connectivity Filling.- 8.4.2 Nonrecursive Connectivity Filling.- 8.4.3 Procedures used for Connectivity Filling.- 8.4.4 Description of the Main Algorithm.- 8.5 Comparisons and Combinations.- 8.6 Bibliographical Notes.- 8.7 Relevant Literature.- 8.8 Problems.- 9: Thinning Algorithms.- 9.1 Introduction.- 9.2 Classical Thinning Algorithms.- 9.3 Asynchronous Thinning Algorithms.- 9.4 Implementation of an Asynchronous Thinning Algorithm.- 9.5 A Quick Thinning Algorithm.- 9.6 Structural Shape Analysis.- 9.7 Transformation of Bilevel Images into Line Drawings.- 9.8 Bibliographical Notes.- 9.9 Relevant Literature.- 9.10 Problems.- 10: Curve Fitting and Curve Displaying.- 10.1 Introduction.- 10.2 Polynomial Interpolation.- 10.3 Bezier Polynomials.- 10.4 Computation of Bezier Polynomials.- 10.5 Some Properties of Bezier Polynomials.- 10.6 Circular Arcs.- 10.7 Display of Lines and Curves.- 10.7.1 Display of Curves through Differential Equations.- 10.7.2 Effect of Round-off Errors in Displays.- 10.8 A Point Editor.- 10.8.1 A Data Structure for a Point Editor.- 10.8.2 Input and Output for a Point Editor.- 10.9 Bibliographical Notes.- 10.10 Relevant Literature.- 10.11 Problems.- 11: Curve Fitting with Splines.- 11.1 Introduction.- 11.2 Fundamental Definitions.- 11.3 B-Splines.- 11.4 Computation with B-Splines.- 11.5 Interpolating B-Splines.- 11.6 B-Splines in Graphics.- 11.7 Shape Description and B-splines.- 11.8 Bibliographical Notes.- 11.9 Relevant Literature.- 11.10 Problems.- 12: Approximation of Curves.- 12.1 Introduction.- 12.2 Integral Square Error Approximation.- 12.3 Approximation Using B-Splines.- 12.4 Approximation by Splines with Variable Breakpoints.- 12.5 Polygonal Approximations.- 12.5.1 A Suboptimal Line Fitting Algorithm.- 12.5.2 A Simple Polygon Fitting Algorithm.- 12.5.3 Properties of Algorithm 12.2.- 12.6 Applications of Curve Approximation in Graphics.- 12.6.1 Handling of Groups of Points by a Point Editor.- 12.6.2 Finding Some Simple Approximating Curves.- 12.7 Bibliographical Notes.- 12.8 Relevant Literature.- 12.9 Problems.- 13: Surface Fitting and Surface Displaying.- 13.1 Introduction.- 13.2 Some Simple Properties of Surfaces.- 13.3 Singular Points of a Surface.- 13.4 Linear and Bilinear Interpolating Surface Patches.- 13.5 Lofted Surfaces.- 13.6 Coons Surfaces.- 13.7 Guided Surfaces.- 13.7.1 Bezier Surfaces.- 13.7.2 B-Spline Surfaces.- 13.8 The Choice of a Surface Partition.- 13.9 Display of Surfaces and Shading.- 13.10 Bibliographical Notes.- 13.11 Relevant Literature.- 13.12 Problems.- 14: The Mathematics of Two-Dimensional Graphics.- 14.1 Introduction.- 14.2 Two-Dimensional Transformations.- 14.3 Homogeneous Coordinates.- 14.3.1 Equation of a Line Defined by Two Points.- 14.3.2 Coordinates of a Point Defined as the Intersection of Two Lines.- 14.3.3 Duality.- 14.4 Line Segment Problems.- 14.4.1 Position of a Point with respect to a Line.- 14.4.2 Intersection of Line Segments.- 14.4.3 Position of a Point with respect to a Polygon.- 14.4.4 Segment Shadow.- 14.5 Bibliographical Notes.- 14.6 Relevant Literature.- 14.7 Problems.- 15: Polygon Clipping.- 15.1 Introduction.- 15.2 Clipping a Line Segment by a Convex Polygon.- 15.3 Clipping a Line Segment by a Regular Rectangle.- 15.4 Clipping an Arbitrary Polygon by a Line.- 15.5 Intersection of Two Polygons.- 15.6 Efficient Polygon Intersection.- 15.7 Bibliographical Notes.- 15.8 Relevant Literature.- 15.9 Problems.- 16: The Mathematics of Three-Dimensional Graphics.- 16.1 Introduction.- 16.2 Homogeneous Coordinates.- 16.2.1 Position of a Point with respect to a Plane.- 16.2.2 Intersection of Triangles.- 16.3 Three-Dimensional Transformations.- 16.3.1 Mathematical Preliminaries.- 16.3.2 Rotation around an Axis through the Origin.- 16.4 Orthogonal Projections.- 16.5 Perspective Projections.- 16.6 Bibliographical Notes.- 16.7 Relevant Literature.- 16.8 Problems.- 17: Creating Three-Dimensional Graphic Displays.- 17.1 Introduction.- 17.2 The Hidden Line and Hidden Surface Problems.- 17.2.1 Surface Shadow.- 17.2.2 Approaches to the Visibility Problem.- 17.2.3 Single Convex Object Visibility.- 17.3 A Quad Tree Visibility Algorithm.- 17.4 A Raster Line Scan Visibility Algorithm.- 17.5 Coherence.- 17.6 Nonlinear Object Descriptions.- 17.7 Making a Natural Looking Display.- 17.8 Bibliographical Notes.- 17.9 Relevant Literature.- 17.10 Problems.- Author Index.- Algorithm Index.
1,395 citations
TL;DR: An approximation algorithm is presented which uses an iterative method to produce polygons with a small—but not minimum—number of vertices that lie on the given curve that justifies the abandonment of the minimum-vertices criterion.
1,323 citations
TL;DR: A new fast algorithm is proposed which allows for a variable number of segments iniecewise approximation as a way of feature extraction, data compaction, and noise filtering of boundaries of regions of pictures and waveforms.
Abstract: Piecewise approximation is described as a way of feature extraction, data compaction, and noise filtering of boundaries of regions of pictures and waveforms. A new fast algorithm is proposed which allows for a variable number of segments. After an arbitrary initial choice, segments are split or merged in order to drive the error norm under a prespecified bound. Results of computer experiments with cell outlines and electrocardiograms are reported.
589 citations