Parallel Region Property Computation by Active Quadtree Networks

Given a binary image stored in a cellular array, a local reconfiguration process can be used to reconnect some of the cells into a quadtree network representing the image. This quadtree can also be ``roped,'' i.e., nodes representing adjacent image blocks of the same size can be joined. Using the roped quadtree network as a parallel (cellular) computer, image properties such as perimeter and genus, as well as the quadtree distance transform, can be computed in O(tree height) = O(log image diameter) time. The area and centroid of the image can be computed in O(height) time without the need for roping.

[1]  P. Rosenstiehl,et al.  INTELLIGENT GRAPHS: NETWORKS OF FINITE AUTOMATA CAPABLE OF SOLVING GRAPH PROBLEMS , 1972 .

[2]  Gn Ubra.  OnSomeOpenProblems intheTheory ofCellular Automata , 1974 .

[3]  Azriel Rosenfeld,et al.  Cellular Graph Automata. I. Basic Concepts, Graph Property Measurement, Closure Properties , 1979, Inf. Control..

[4]  Michael Shneier.  A Path-Length Distance Transform for Quadtrees , 1979 .

[5]  Gregory Michael Hunter,et al.  Efficient computation and data structures for graphics. , 1978 .

[6]  Kenneth Steiglitz,et al.  Operations on Images Using Quad Trees , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Hannan Samet,et al.  Region representation: Quadtrees from binary arrays , 1980 .

[8]  Hanan Samet,et al.  A quadtree medial axis transform , 1983, Commun. ACM.

[9]  S. Rao Kosaraju.  On Some Open Problems in the Theory of Cellular Automata , 1974, IEEE Transactions on Computers.

[10]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .

[11]  Charles R. Dyer,et al.  Experiments on Picture Representation Using Regular Decomposition , 1976 .

[12]  Hanan Samet,et al.  Region Representation: Quadtree-to-Raster Conversion , 1979 .

[13]  Hanan Samet,et al.  Distance Transform for Images Represented by Quadtrees , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  C. Dyer.  Computing the Euler number of an image from its quadtree , 1980 .

[15]  Azriel Rosenfeld,et al.  Region representation: boundary codes from quadtrees , 1980, CACM.

[16]  Nikitas A. Alexandridis,et al.  Picture decomposition, tree data-structures, and identifying directional symmetries as node combinations , 1978 .

[17]  Azriel Rosenfeld,et al.  Picture languages: Formal models for picture recognition , 1979 .

[18]  Hanan Samet,et al.  Connected Component Labeling Using Quadtrees , 1981, JACM.

[19]  Olivier D. Faugeras,et al.  Semantic Description of Aerial Images Using Stochastic Labeling , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Alvy Ray Smith,et al.  Two-Dimensional Formal Languages and Pattern Recognition by Cellular Automata , 1971, SWAT.

[21]  G. M. Hunter,et al.  Linear transformation of pictures represented by quad trees , 1979 .

[22]  Hanan Samet,et al.  Computing Perimeters of Regions in Images Represented by Quadtrees , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Charles R. Dyer.  Memory-Augmented Cellular Automata for Image Analysis. , 1978 .

[24]  Allen Klinger,et al.  Data Structures and Pattern Recognition , 1978 .

[25]  Azriel Rosenfeld,et al.  Local Reconfiguration of Networks of Processors. , 1979 .

[26]  S. Levialdi,et al.  Basics of cellular logic with some applications in medical image processing , 1979, Proceedings of the IEEE.

[27]  Hanan Samet,et al.  Region representation: quadtrees from boundary codes , 1980, CACM.

[28]  Michael L. Rhodes,et al.  Organization and Access of Image Data by Areas , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Hanan Samet,et al.  Region Representation: Raster-to-Quadtree Conversion , 1979 .

[30]  Michael Shneier,et al.  Linear Time Calculations of Geometric Properties Using Quadtrees , 1979 .