Approximating Polygons and Subdivisions with Minimum Link Paths

We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We also discuss additional topological constraints such as simplicity.

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

[2]  Robert B McMaster,et al.  The Integration Of Simplification And Smoothing Algorithms In Line Generalization , 1989 .

[3]  Rephael Wenger,et al.  Ordered stabbing of pairwise disjoint convex sets in linear time , 1991, Discret. Appl. Math..

[4]  Robert B McMaster,et al.  Automated Line Generalization , 1987 .

[5]  Azriel Rosenfeld,et al.  Axial representations of shape , 1986, Computer Vision Graphics and Image Processing.

[6]  Robert B McMaster,et al.  A Statistical Analysis of Mathematical Measures for Linear Simplification , 1986 .

[7]  S. Suri.  A linear time algorithm with minimum link paths inside a simple polygon , 1986 .

[8]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[9]  John Hershberger,et al.  Computing Minimum Length Paths of a Given Homotopy Class (Extended Abstract) , 1991, WADS.

[10]  Subir Kumar Ghosh.  Computing the Visibility Polygon from a Convex Set and Related Problems , 1991, J. Algorithms.

[11]  Micha Sharir,et al.  On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles , 1986, Discret. Comput. Geom..

[12]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[13]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[14]  Hiroshi Imai,et al.  An optimal algorithm for approximating a piecewise linear function , 1986 .

[15]  B. Buttenfield.  TREATMENT OF THE CARTOGRAPHIC LINE , 1985 .

[16]  Michael Blakemore,et al.  Part 4: Mathematical, Algorithmic and Data Structure Issues: Generalisation and Error in Spatial Data Bases , 1984 .

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

[18]  Leonidas J. Guibas,et al.  A kinetic framework for computational geometry , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[19]  M. Iri,et al.  Polygonal Approximations of a Curve — Formulations and Algorithms , 1988 .

[20]  Micha Sharir,et al.  Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences , 1989, J. Comb. Theory A.

[21]  James R. Munkres,et al.  Topology; a first course , 1974 .

[22]  S. Louis Hakimi,et al.  Fitting polygonal functions to a set of points in the plane , 1991, CVGIP Graph. Model. Image Process..

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

[24]  Joseph O'Rourke,et al.  An on-line algorithm for fitting straight lines between data ranges , 1981, CACM.

[25]  Helmut Alt,et al.  Approximation of Convex Polygons , 1990, ICALP.