Parallel Connectivity-Preserving Thinning Algorithms

Abstract A variety of approaches to parallel thinning using operators with small supports are reviewed, with emphasis on how one may preserve, and prove one has preserved, connec- tivity. Tests are demonstrated for verifying connectivity preservation; and for fundamental classes of parallel thinning algorithms, including fully parallel, two-subiteration, and two- subfield, conditions are identified using these tests which are sufficient for preservation of connectivity. Thus“design spaces” for connectivity preserving algorithms belonging to these classes are identified. Some fundamental limitations on parallel thinning operators for images with 8-4 connectivity are also reviewed, including constraints on support size and shape. Parallel computation time issues are addressed and it is shown that existing fully parallel thinning algorithms are nearly optimally fast.

[1]  Roland T. Chin,et al.  A one-pass thinning algorithm and its parallel implementation , 1987, Comput. Vis. Graph. Image Process..

[2]  Yung-Sheng Chen,et al.  A comparison of some one-pass parallel thinnings , 1990, Pattern Recognit. Lett..

[3]  Yung-Sheng Chen,et al.  A 1-subcycle parallel thinning algorithm for producing perfect 8-curves and obtaining isotropic skeleton of an L-shape pattern , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  Azriel Rosenfeld,et al.  Connectivity in Digital Pictures , 1970, JACM.

[5]  R. Brubaker.  Models for the perception of speech and visual form: Weiant Wathen-Dunn, ed.: Cambridge, Mass., The M.I.T. Press, I–X, 470 pages , 1968 .

[6]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[7]  Azriel Rosenfeld,et al.  Some Parallel Thinning Algorithms for Digital Pictures , 1971, JACM.

[8]  Stefano Levialdi,et al.  Parallel thinning of binary pictures , 1975 .

[9]  R. W. Hall.  Tests for connectivity preservation for parallel reduction operators , 1992 .

[10]  Terry J. Fountain,et al.  Cellular logic image processing , 1986 .

[11]  Azriel Rosenfeld,et al.  A Characterization of Parallel Thinning Algorithms , 1975, Inf. Control..

[12]  Ulrich Eckhardt,et al.  Parallel reduction of digital sets , 1988 .

[13]  Ching Y. Suen,et al.  A fast parallel algorithm for thinning digital patterns , 1984, CACM.

[14]  Adam Krzyzak,et al.  Computer Vision and Shape Recognition , 1989, World Scientific Series in Computer Science.

[15]  Theodosios Pavlidis.  An asynchronous thinning algorithm , 1982, Comput. Graph. Image Process..

[16]  C. V. Kameswara Rao,et al.  Checking connectivity preservation properties of some types of picture processing operations , 1978 .

[17]  Donald Michie,et al.  Machine Intelligence 4 , 1970 .

[18]  Edward S. Deutsch,et al.  Thinning algorithms on rectangular, hexagonal, and triangular arrays , 1972, Commun. ACM.

[19]  Angel L. DeCegama,et al.  The technology of parallel processing: parallel processing architectures and VLSI hardware (vol. 1) , 1989 .

[20]  Zicheng Guo,et al.  Parallel thinning with two-subiteration algorithms , 1989, Commun. ACM.

[21]  Ching Y. Suen,et al.  Thinning Methodologies - A Comprehensive Survey , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Malcolm J. Shute,et al.  Multiprocessor Computer Architectures , 1990 .

[23]  Patrick Shen-Pei Wang,et al.  A comment on “a fast parallel algorithm for thinning digital patterns” , 1986, CACM.

[24]  Christian Ronse,et al.  A Topological Characterization of Thinning , 1986, Theor. Comput. Sci..

[25]  Christian Ronse,et al.  Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images , 1988, Discret. Appl. Math..

[26]  Yung-Sheng Chen,et al.  Systematic approach for designing 2-subcycle and pseudo 1-subcycle parallel thinning algorithms , 1989, Pattern Recognit..

[27]  NABIL JEAN NACCACHE,et al.  An investigation into the skeletonization approach of hilditch , 1984, Pattern Recognit..

[28]  Ulrich Eckhardt,et al.  The Structure of Irreducible Digital Sets Obtained by Thinning Algorithms , 1988, ICPR.

[29]  C. J. Hilditch,et al.  Linear Skeletons From Square Cupboards , 1969 .

[30]  J. Sossa.  An improved parallel algorithm for thinning digital patterns , 1989 .

[31]  C. J. Hilditch.  Comparison of thinning algorithms on a parallel processor , 1983, Image Vis. Comput..

[32]  Hungwen Li,et al.  Reconfigurable Massively Parallel Computers , 1991 .

[33]  Richard W. Hall.  Comments on "a parallel-symmetric thinning algorithm" by Bourbakis , 1992, Pattern Recognit..

[34]  Nikolaos G. Bourbakis.  A parallel-symmetric thinning algorithm , 1989, Pattern Recognit..

[35]  Ulrich Eckardt.  A note on Rutovtz' method for parallel thinning , 1988 .

[36]  Zicheng Guo,et al.  Fast fully parallel thinning algorithms , 1991, CVGIP Image Underst..

[37]  Vartkes Goetcherian,et al.  From binary to grey tone image processing using fuzzy logic concepts , 1980, Pattern Recognit..

[38]  T. Pavlidis.  Algorithms for Graphics and Image Processing , 1981, Springer Berlin Heidelberg.

[39]  Gabriella Sanniti di Baja,et al.  Parallel Pattern Compression by Octagonal Propagation , 1993, Int. J. Pattern Recognit. Artif. Intell..

[40]  Keiichi Abe,et al.  Binary picture thinning by an iterative parallel two-subcycle operation , 1987, Pattern Recognit..

[41]  Marcel J. E. Golay,et al.  Hexagonal Parallel Pattern Transformations , 1969, IEEE Transactions on Computers.

[42]  Richard W. Hall.  Optimally Small Operator Supports for Fully Parallel Thinning Algorithms , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[43]  Jeffrey A. Fessler,et al.  PARALLEL IMAGE THINNING AND VECTORIZATION ON PASM. , 1985 .

[44]  Kendall Preston,et al.  Feature Extraction by Golay Hexagonal Pattern Transforms , 1971, IEEE Transactions on Computers.

[45]  Xiaobo Li,et al.  Variable-resolution character thinning , 1991, Pattern Recognit. Lett..

[46]  Ronald H. Perrott,et al.  An improved parallel thinning algorithm , 1987, CACM.

[47]  Lawrence O'Gorman,et al.  K × K Thinning , 1990, Comput. Vis. Graph. Image Process..

[48]  Azriel Rosenfeld,et al.  Thinning Algorithms for Gray-Scale Pictures , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  E. R. Davies,et al.  Thinning algorithms: A critique and a new methodology , 1981, Pattern Recognit..

[50]  Carlo Arcelli,et al.  Pattern thinning by contour tracing , 1981 .

[51]  Richard W. Hall,et al.  Parallel shrinking algorithms using 2-subfields approaches , 1990, Comput. Vis. Graph. Image Process..

[52]  Réjean Plamondon,et al.  Thinning of Digitized Characters from Subjective Experiments: a Proposal for a Systematic Evaluation Protocol of Algorithms , 1989, Computer Vision and Shape Recognition.

[53]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[54]  Jan Olszewski,et al.  A flexible thinning algorithm allowing parallel, sequential, and distributed application , 1992, TOMS.

[55]  S. Heydorn,et al.  Optimization and performance analysis of thinning algorithms on parallel computers , 1991, Parallel Comput..

[56]  Carlo Arcelli.  A condition for digital points removal , 1979 .

[57]  Raymond W. Smith,et al.  Computer processing of line images: A survey , 1987, Pattern Recognit..

[58]  T. Fukumura,et al.  An Analysis of Topological Properties of Digitized Binary Pictures Using Local Features , 1975 .

[59]  Richard W. Hall,et al.  Fast parallel thinning algorithms: parallel speed and connectivity preservation , 1989, CACM.

[60]  Josef Kittler,et al.  Image processing system architectures , 1985 .