Reliable polygonal approximations of imaged real objects through dominant point detection

Abstract The problem of dominant point detection is posed, taking into account what usually happens in practice. The algorithms found in the literature often prove their performance with laboratory contours, but the shapes in real images present noise, quantization, and high inter and intra-shape variability. These effects are analyzed and solutions to them are proposed. We will also focus on the conditions for an efficient (few points) and precise (low error) dominant point extraction that preserves the original shape. A measurement of the committed error (optimization error, E 0 ) that takes into account both aspects is defined for studying this feature.

[1]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[2]  Theodosios Pavlidis,et al.  Segmentation of Plane Curves , 1974, IEEE Transactions on Computers.

[3]  James George Dunham,et al.  Optimum Uniform Piecewise Linear Approximation of Planar Curves , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Mandyam D. Srinath,et al.  Partial Shape Classification Using Contour Matching in Distance Transformation , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Edward J. Delp,et al.  On detecting dominant points , 1991, Pattern Recognit..

[6]  P. Sankar,et al.  A parallel procedure for the detection of dominant points on a digital curve , 1978 .

[7]  H. Lynn Beus,et al.  An improved corner detection algorithm based on chain-coded plane curves , 1987, Pattern Recognit..

[8]  Jack Sklansky,et al.  Fast polygonal approximation of digitized curves , 1980, Pattern Recognit..

[9]  Charles M. Williams,et al.  An Efficient Algorithm for the Piecewise Linear Approximation of Planar Curves , 1978 .

[10]  James C. Bezdek,et al.  Curvature and Tangential Deflection of Discrete Arcs: A Theory Based on the Commutator of Scatter Matrix Pairs and Its Application to Vertex Detection in Planar Shape Data , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Larry S. Davis,et al.  A Corner-Finding Algorithm for Chain-Coded Curves , 1977, IEEE Transactions on Computers.

[12]  Theodosios Pavlidis,et al.  A Hierarchical Syntactic Shape Analyzer , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Jia-Guu Leu.  Computing a shape's moments from its boundary , 1991, Pattern Recognit..

[14]  Trond Melen,et al.  A Fast Algorithm for Dominant Point Detection on Chain-Coded Contours , 1993, CAIP.

[15]  Godfried T. Toussaint,et al.  On Approximating Polygonal Curves in Two and Three Dimensions , 1994, CVGIP Graph. Model. Image Process..

[16]  Theodosios Pavlidis,et al.  A review of algorithms for shape analysis , 1978 .

[17]  John A. Saghri,et al.  Analysis of the Precision of Generalized Chain Codes for the Representation of Planar Curves , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Ralph Roskies,et al.  Fourier Descriptors for Plane Closed Curves , 1972, IEEE Transactions on Computers.

[19]  M. Fischler,et al.  Perceptual organization and curve partitioning , 1987 .

[20]  Hiroshi Imai,et al.  Computational-geometric methods for polygonal approximations of a curve , 1986, Comput. Vis. Graph. Image Process..

[21]  Azriel Rosenfeld,et al.  An Improved Method of Angle Detection on Digital Curves , 1975, IEEE Transactions on Computers.

[22]  BIMAL KUMAR RAY,et al.  Determination of optimal polygon from digital curve using L1 norm , 1993, Pattern Recognit..

[23]  Yazid M. Sharaiha,et al.  An Optimal Algorithm for the Straight Segment Approximation of Digital Arcs , 1993, CVGIP Graph. Model. Image Process..

[24]  James Robergé.  A data reduction algorithm for planar curves , 1985, Comput. Vis. Graph. Image Process..

[25]  Roland T. Chin,et al.  On the Detection of Dominant Points on Digital Curves , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Carlo Arcelli,et al.  Finding contour-based abstractions of planar patterns , 1993, Pattern Recognit..

[27]  Jhing-Fa Wang,et al.  An Adaptive Reduction Procedure for the Piecewise Linear Approximation of Digitized Curves , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Yukio Sato,et al.  Piecewise linear approximation of plane curves by perimeter optimization , 1992, Pattern Recognit..

[29]  Paul L. Rosin,et al.  Techniques for segmenting image curves into meaningful descriptions , 1991, Pattern Recognit..

[30]  F. Attneave.  Some informational aspects of visual perception. , 1954, Psychological review.

[31]  Juan Carlos Pérez-Cortes,et al.  Optimum polygonal approximation of digitized curves , 1994, Pattern Recognit. Lett..

[32]  A. Melkman,et al.  On Polygonal Chain Approximation , 1988 .

[33]  F. Badi'i,et al.  Functional approximation of planar curves via adaptive segmentation , 1982 .

[34]  Filiberto Pla,et al.  Recognition of Partial Circular Shapes from Segmented Contours , 1996, Comput. Vis. Image Underst..

[35]  Nirwan Ansari,et al.  Non-parametric dominant point detection , 1991, Pattern Recognition.

[36]  George K. Papakonstantinou,et al.  Optimal polygonal approximation of digital curves , 1985 .

[37]  Azriel Rosenfeld,et al.  Angle Detection on Digital Curves , 1973, IEEE Transactions on Computers.