Computational geometry: Recent results relevant to pattern recognition

In this paper we survey recent results in computational geometry relevant to the problem of shape description and recognition by machines. In particular we consider the medial axis of a polygon, shape hulls of sets of points, decomposition of polygons into perceptually meaningful components, smoothing and approximating polygonal curves, and computing geodesic and visibility properties of polygons.

[1]  D. T. Lee,et al.  Computational Geometry—A Survey , 1984, IEEE Transactions on Computers.

[2]  D. Avis,et al.  REMARKS ON THE SPHERE OF INFLUENCE GRAPH , 1985 .

[3]  David G. Kirkpatrick,et al.  Efficient computation of continuous skeletons , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[4]  Robert E. Tarjan,et al.  A linear-time algorithm for triangulating simple polygons , 1986, STOC '86.

[5]  Bernard Chazelle,et al.  A theorem on polygon cutting with applications , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[6]  D. Kirkpatrick,et al.  A Framework for Computational Morphology , 1985 .

[7]  Leonidas J. Guibas,et al.  Linear time algorithms for visibility and shortest path problems inside simple polygons , 2011, SCG '86.

[8]  P. V. de Souza,et al.  Computer location of medial axes. , 1977, Computers and biomedical research, an international journal.

[9]  Ugo Montanari,et al.  A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance , 1968, J. ACM.

[10]  F. Bookstein The line-skeleton , 1979 .

[11]  Kenneth J. Supowit,et al.  The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees , 1983, JACM.

[12]  Godfried T. Toussaint,et al.  PATTERN RECOGNITION AND GEOMETRICAL COMPLEXITY. , 1980 .

[13]  H. Blum Biological shape and visual science (part I) , 1973 .

[14]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[15]  W. E. Hartnett,et al.  Shape Recognition, Prairie Fires, Convex Deficiencies and Skeletons , 1968 .

[16]  D. T. Lee Relative neighborhood graphs in the Li-metric , 1985, Pattern Recognit..

[17]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[18]  D. T. Lee,et al.  Euclidean shortest paths in the presence of rectilinear barriers , 1984, Networks.

[19]  B. Chazelle,et al.  Optimal Convex Decompositions , 1985 .

[20]  D. T. Lee,et al.  Medial Axis Transformation of a Planar Shape , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Hossam Ahmed Elgindy,et al.  Hierarchical decomposition of polygons with applications , 1985 .

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

[23]  D. T. Lee,et al.  Generalization of Voronoi Diagrams in the Plane , 1981, SIAM J. Comput..

[24]  G. Matheron Random Sets and Integral Geometry , 1976 .

[25]  Godfried T. Toussaint Shortest Path Solves Translation Separability of Polygons , 1986, IAS.

[26]  Gustav Bernroider,et al.  The Foundation of Computational Geometry: Theory and Application of the Point-Lattice-Concept within Modern Structure Analysis , 1978 .

[27]  Azriel Rosenfeld,et al.  Computer representation of planar regions by their skeletons , 1967, CACM.

[28]  J. Reif,et al.  Shortest Paths in Euclidean Space with Polyhedral Obstacles. , 1985 .

[29]  Godfried T. Toussaint,et al.  Computational Geometric Problems in Pattern Recognition , 1982 .

[30]  Joseph O'Rourke Computing the relative neighborhood graph in the L1 and Linfinity metrics , 1982, Pattern Recognit..

[31]  Leonidas J. Guibas,et al.  Visibility and intersectin problems in plane geometry , 1985, SCG '85.

[32]  Franco P. Preparata,et al.  The Medial Axis of a Simple Polygon , 1977, MFCS.

[33]  D'arcy W. Thompson On Growth and Form , 1945 .

[34]  Václav Medek On the boundary of a finite set of points in the plane , 1981 .

[35]  Matthew T. Mason,et al.  Robot Motion: Planning and Control , 1983 .

[36]  Godfried T. Toussaint,et al.  NEW RESULTS IN COMPUTATIONAL GEOMETRY RELEVANT TO PATTERN RECOGNITION IN PRACTICE , 1986 .

[37]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[38]  F. Bookstein,et al.  The Measurement of Biological Shape and Shape Change. , 1980 .

[39]  D. T. Lee,et al.  Computing the visibility polygon from an edge , 1986, Comput. Vis. Graph. Image Process..

[40]  Joseph O'Rourke,et al.  Worst-case optimal algorithms for constructing visibility polygons with holes , 1986, SCG '86.

[41]  Roderick Urquhart,et al.  Some properties of the planar Euclidean relative neighbourhood graph , 1983, Pattern Recognit. Lett..

[42]  Manabu Ichino,et al.  The relative neighborhood graph for mixed feature variables , 1985, Pattern Recognit..

[43]  Godfried T. Toussaint A linear-time algorithm for solving the strong hidden-line problem in a simple polygon , 1986, Pattern Recognit. Lett..

[44]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[45]  Godfried T. Toussaint,et al.  Computing the Relative Neighbour Decomposition of a Simple Polygon , 1988 .

[46]  Godfried T. Toussaint,et al.  Shortest path solves edge-to-edge visibility in a polygon , 1986, Pattern Recognit. Lett..

[47]  J. Sack,et al.  Minimum Decompositions of Polygonal Objects , 1985 .

[48]  J M Kennedy,et al.  Illusory Contours Can Arise in Dot Figures , 1978, Perception.

[49]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[50]  Godfried T. Toussaint,et al.  Computational Geometry and Morphology , 1986 .

[51]  HARRY BLUM,et al.  Shape description using weighted symmetric axis features , 1978, Pattern Recognit..

[52]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[53]  J. O'Rourke,et al.  Connect-the-dots: a new heuristic , 1987 .

[54]  Christian Lantuéjoul,et al.  Geodesic methods in quantitative image analysis , 1984, Pattern Recognit..

[55]  Leonidas J. Guibas,et al.  Visibility-polygon search and euclidean shortest paths , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[56]  G. Toussaint,et al.  Computing the Geodesic Center of a Simple Polygon , 1987 .

[57]  Ugo Montanari,et al.  Continuous Skeletons from Digitized Images , 1969, JACM.