Digital topology: introduction and survey

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback
Take a look at the new version of this page: [ beta version ]. Tell us what you think.

Digital topology: introduction and survey

Source

Computer Vision, Graphics, and Image Processing archive
Volume 48 , Issue 3 (December 1989) table of contents

Pages: 357 - 393

Year of Publication: 1989

ISSN:0734-189X

Authors

T. Y. Kong
A. Rosenfeld

Publisher

Academic Press Professional, Inc. San Diego, CA, USA

Bibliometrics

Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 93

Additional Information:

cited by index terms collaborative colleagues

Tools and Actions:	Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	10.1016/0734-189X(89)90147-3

CITED BY 93

	Stephan Winter, Bridging vector and raster representation in GIS, Proceedings of the 6th ACM international symposium on Advances in geographic information systems, p.57-62, November 02-07, 1998, Washington, D.C., United States
	Li Chen , Jianping Zhang, Digital manifolds: an intuitive definition and some properties, Proceedings on the second ACM symposium on Solid modeling and applications, p.459-460, May 19-21, 1993, Montreal, Quebec, Canada
	Jasit S. Suri , Sameer Singh , S. K. Setarehdan , Rakesh Sharma , Keir Bovis , Dorin Comaniciu , Laura Reden, A note on future research in segmentation techniques applied to neurology, cardiology, mammography and pathology, Advanced algorithmic approaches to medical image segmentation: state-of-the-art application in cardiology, neurology, mammography and pathology, Springer-Verlag New York, Inc., New York, NY, 2001
	Atul Sudhalkar , Levent Gürsöz , Fritz Prinz, Continuous skeletons of discrete objects, Proceedings on the second ACM symposium on Solid modeling and applications, p.85-94, May 19-21, 1993, Montreal, Quebec, Canada
	D. Ayala , J. Rodríguez , A. Aguilera, Connected component labeling based on the EVM model, Proceedings of the 18th spring conference on Computer graphics, April 24-27, 2002, Budmerice, Slovakia
	Yan Gérard, Periodic graphs and connectivity of the rational digital hyperplanes, Theoretical Computer Science, v.283 n.1, p.171-182, June 11 2002
	Markus Schneider, Design and implementation of finite resolution crisp and fuzzy spatial objects, Data & Knowledge Engineering, v.44 n.1, p.81-108, January 2003
	Eladio Domínguez , Angel R. Francés, An axiomatic approach to digital topology, Digital and image geometry: advanced lectures, Springer-Verlag New York, Inc., New York, NY, 2001
	Steffen Prohaska , Hans Christian Hege, Fast visualization of plane-like structures in voxel data, Proceedings of the conference on Visualization '02, October 27-November 01, 2002, Boston, Massachusetts
	Isabelle Bloch , Jérémie Pescatore , Line Garnero, A new characterization of simple elements in a tetrahedral mesh, Graphical Models, v.67 n.4, p.260-284, July 2005
	Cherng-Min Ma , Shu-Yen Wan , Her-Kun Chang, Extracting medial curves on 3D images, Pattern Recognition Letters, v.23 n.8, p.895-904, June 2002
	Andreas Alpers, Digital Topology: Regular Sets and Root Images of the Cross-Median Filter, Journal of Mathematical Imaging and Vision, v.17 n.1, p.7-14, July 2002
	Yang Wang , Prabir Bhattacharya, Using connected components to guide image understanding and segmentation, Machine Graphics & Vision International Journal, v.12 n.2, p.163-186, February 2003
	R. Ayala , E. Domínguez , A. R. Francés , A. Quintero, Weak lighting functions and strong 26-surfaces, Theoretical Computer Science, v.283 n.1, p.29-66, June 11 2002
	Antony Galton, A generalized topological view of motion in discrete space, Theoretical Computer Science, v.305 n.1-3, p.111-134, 18 August 2003
	J. Šlapal, Closure operations for digital topology, Theoretical Computer Science, v.305 n.1-3, p.457-471, 18 August 2003
	P. K. Saha , B. B. Chaudhuri, Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.16 n.10, p.1028-1032, October 1994
	Longin Jan Latecki , Christopher Conrad , Ari Gross, Preserving Topology by a Digitization Process, Journal of Mathematical Imaging and Vision, v.8 n.2, p.131-159, March, 1998
	Michel Couprie , Gilles Bertrand , Yukiko Kenmochi, Discretization in 2D and 3D orders, Graphical Models, v.65 n.1-3, p.77-91, January 2003
	Guillaume Damiand , Yves Bertrand , Christophe Fiorio, Topological model for two-dimensional image representation: definition and optimal extraction algorithm, Computer Vision and Image Understanding, v.93 n.2, p.111-154, February 2004
	S. C. Lu , A. B. Rebello , D. H. Cui , R. Yagel , R. A. Miller , G. L. Kinzel, A visualization tool for mechanical design, Proceedings of the 7th conference on Visualization '96, p.401-ff., October 28-29, 1996, San Francisco, California, United States
	R. W. Hall, Optimally Small Operator Supports for Fully Parallel Thinning Algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.15 n.8, p.828-833, August 1993
	Jian Huang , Roni Yagel , Vassily Filippov , Yair Kurzion, An accurate method for voxelizing polygon meshes, Proceedings of the 1998 IEEE symposium on Volume visualization, p.119-126, October 19-20, 1998, Research Triangle Park, North Carolina, United States
	Jasmine Burguet , Rémy Malgouyres, Strong thinning and polyhedric approximation of the surface of a voxel object, Discrete Applied Mathematics, v.125 n.1, p.93-114, 15 January 2003
	Christophe Lohou , Gilles Bertrand, A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Applied Mathematics, v.139 n.1-3, p.171-195, 30 April 2004
	Jean-Charles Pinoli, The Logarithmic Image Processing Model: Connections with Human Brightness Perception and Contrast Estimators, Journal of Mathematical Imaging and Vision, v.7 n.4, p.341-358, Oct. 1997
	Jocelyn Marchadier , Didier Arquès , Sylvain Michelin, Thinning grayscale well-composed images, Pattern Recognition Letters, v.25 n.5, p.581-590, 5 April 2004
	R. Ayala , E. Domínguez , A. R. Francés , A. Quintero, Digital homotopy with obstacles, Discrete Applied Mathematics, v.139 n.1-3, p.5-30, 30 April 2004
	Louisa Lam , Seong-Whan Lee , Ching Y. Suen, Thinning Methodologies-A Comprehensive Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.14 n.9, p.869-885, September 1992
	Gilles Bertrand, On Topological Watersheds, Journal of Mathematical Imaging and Vision, v.22 n.2-3, p.217-230, May 2005
	Stina Svensson , Gabriella Sanniti di Baja, Simplifying curve skeletons in volume images, Computer Vision and Image Understanding, v.90 n.3, p.242-257, June 2003
	Yukiko Kenmochi , Atsushi Imiya, Discrete polyhedrization of a lattice point set, Digital and image geometry: advanced lectures, Springer-Verlag New York, Inc., New York, NY, 2001
	Cherng-Min Ma , Shu-Yen Wan , Jiann-Der Lee, Three-Dimensional Topology Preserving Reduction on the 4-Subfields, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.24 n.12, p.1594-1605, December 2002
	J. Šlapal, A digital analogue of the Jordan curve theorem, Discrete Applied Mathematics, v.139 n.1-3, p.231-251, 30 April 2004
	David Brunner , Guido Brunnett, An extended concept of voxel neighborhoods for correct thinning in mesh segmentation, Proceedings of the 21st spring conference on Computer graphics, May 12-14, 2005, Budmerice, Slovakia
	Xavier Daragon , Michel Couprie , Gilles Bertrand, Derived neighborhoods and frontier orders, Discrete Applied Mathematics, v.147 n.2-3, p.227-243, 15 April 2005
	Ralph Kopperman, On storage of topological information, Discrete Applied Mathematics, v.147 n.2-3, p.287-300, 15 April 2005
	Mohammed Khachan , Patrick Chenin , Hafsa Deddi, Digital pseudomanifolds, digital weakmanifolds and Jordan-Brouwer separation theorem, Discrete Applied Mathematics, v.125 n.1, p.45-57, 15 January 2003
	Michel Couprie , Laurent Najman , Gilles Bertrand, Quasi-Linear Algorithms for the Topological Watershed, Journal of Mathematical Imaging and Vision, v.22 n.2-3, p.231-249, May 2005
	Rueiher Tsaur , Michael B. Smyth, "Continuous" multifunctions in discrete spaces with applications to fixed point theory, Digital and image geometry: advanced lectures, Springer-Verlag New York, Inc., New York, NY, 2001
	Sébastien Fourey , Rémy Malgouyres, A concise characterization of 3D simple points, Discrete Applied Mathematics, v.125 n.1, p.59-80, 15 January 2003
	C. Lincke , C. A. Wüthrich, Surface digitizations by dilations which are tunnel-free, Discrete Applied Mathematics, v.125 n.1, p.81-91, 15 January 2003
	Ben K. Jang , Roland T. Chin, One-Pass Parallel Thinning: Analysis, Properties, and Quantitative Evaluation, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.14 n.11, p.1129-1140, November 1992
	Stephan Bischoff , Darko Pavic , Leif Kobbelt, Automatic restoration of polygon models, ACM Transactions on Graphics (TOG), v.24 n.4, p.1332-1352, October 2005
	Reiner Schulz , James A. Reggia, Predicting nearest agent distances in artificial worlds, Artificial Life, v.8 n.3, p.247-264, 2002
	Rémy Malgouyres , Malika More, On the computational complexity of reachability in 2D binary images and some basic problems of 2D digital topology, Theoretical Computer Science, v.283 n.1, p.67-108, June 11 2002
	Xavier Daragon , Michel Couprie , Gilles Bertrand, Discrete Surfaces and Frontier Orders, Journal of Mathematical Imaging and Vision, v.23 n.3, p.379-399, November 2005
	Christophe Lohou , Gilles Bertrand, A 3D 6-subiteration curve thinning algorithm based on P-simple points, Discrete Applied Mathematics, v.151 n.1-3, p.198-228, 1 October 2005
	Kaleem Siddiqi , Sylvain Bouix , Allen Tannenbaum , Steven W. Zucker, Hamilton-Jacobi Skeletons, International Journal of Computer Vision, v.48 n.3, p.215-231, July-August 2002
	Punam Kumar Saha, Tensor scale: a local morphometric parameter with applications to computer vision and image processing, Computer Vision and Image Understanding, v.99 n.3, p.384-413, September 2005
	Michel Couprie , David Coeurjolly , Rita Zrour, Discrete bisector function and Euclidean skeleton in 2D and 3D, Image and Vision Computing, v.25 n.10, p.1543-1556, October, 2007
	Bruce H. McCormick , Brad Busse , Purna Doddapaneni , Zeki Melek , John Keyser, Compression, segmentation, and modeling of filamentary volumetric data, Proceedings of the ninth ACM symposium on Solid modeling and applications, June 09-11, 2004, Genoa, Italy
	Michael H. F. Wilkinson, Attribute-space connectivity and connected filters, Image and Vision Computing, v.25 n.4, p.426-435, April, 2007
	Vladimir Kovalevsky, Axiomatic Digital Topology, Journal of Mathematical Imaging and Vision, v.26 n.1-2, p.41-58, November 2006
	T. Yung Kong , Punam Kumar Saha , Azriel Rosenfeld, Strongly normal sets of contractible tiles in N dimensions, Pattern Recognition, v.40 n.2, p.530-543, February, 2007
	Christophe Lohou , Gilles Bertrand, Two symmetrical thinning algorithms for 3D binary images, based on P-simple points, Pattern Recognition, v.40 n.8, p.2301-2314, August, 2007
	Carmen Escribano , Antonio Giraldo , María Asunción Sastre , Mario Trotta, Digital topology java applet, Proceedings of the 13th annual conference on Innovation and technology in computer science education, June 30-July 02, 2008, Madrid, Spain
	L. G. Nonato , M. A. S. Lizier , J. Batista , M. C. F. de Oliveira , A. Castelo, Topological triangle characterization with application to object detection from images, Image and Vision Computing, v.26 n.8, p.1081-1093, August, 2008
	Sang-Eon Han, Digital fundamental group and Euler characteristic of a connected sum of digital closed surfaces, Information Sciences: an International Journal, v.177 n.16, p.3314-3326, August, 2007
	Punam Kumar Saha , Bipul Das , Felix W. Wehrli, An object class-uncertainty induced adaptive force and its application to a new hybrid snake, Pattern Recognition, v.40 n.10, p.2656-2671, October, 2007
	Guillaume Damiand, Topological model for 3D image representation: Definition and incremental extraction algorithm, Computer Vision and Image Understanding, v.109 n.3, p.260-289, March, 2008
	Gilles Bertrand , Rémy Malgouyres, Some Topological Properties of Surfaces in Z3, Journal of Mathematical Imaging and Vision, v.11 n.3, p.207-221, Dec. 1999
	Frederic H. Mabin , Catherine Mongenet, A Parallel Algorithm to Reconstruct Bounding Surfaces in 3D Images, The Journal of Supercomputing, v.12 n.1-2, p.137-155, Jan./Feb., 1998
	Sándor Fejes , Azriel Rosenfeld, Migration Processes II: The Discrete Case, Journal of Mathematical Imaging and Vision, v.8 n.1, p.27-40, Jan. 1998
	Bruce H. McCormick , Purna Doddapaneni , David Mayerich , Zeki Melek , John Keyser, Compression, Segmentation, and Modeling of Large-Scale Filamentary Volumetric Data, Proceedings of the conference on Visualization '04, p.598.31, October 10-15, 2004
	Zhilin Li , Yongli Li , Yong-Qi Chen, Basic Topological Models for Spatial Entities in 3-Dimensional Space, Geoinformatica, v.4 n.4, p.419-433, December 2000
	Stephan Winter , Andrew U. Frank, Topology in Raster and Vector Representation, Geoinformatica, v.4 n.1, p.35-65, March 2000
	Joe Kniss , Warren Hunt , Kristin Potter , Pradeep Sen, IStar: A Raster Representation for Scalable Image and Volume Data, IEEE Transactions on Visualization and Computer Graphics, v.13 n.6, p.1424-1431, November 2007
	Xiaojun Wu , Weijun Liu , Michael Yu Wang, A CAD modeling system for heterogeneous object, Advances in Engineering Software, v.39 n.5, p.444-453, May, 2008
	Christophe Lohou, Detection of the non-topology preservation of Ma's 3D surface-thinning algorithm, by the use of P-simple points, Pattern Recognition Letters, v.29 n.6, p.822-827, April, 2008
	G. Bertrand , M. Couprie, Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels, Journal of Mathematical Imaging and Vision, v.31 n.1, p.35-56, May 2008
	Erik Melin, Continuous digitization in Khalimsky spaces, Journal of Approximation Theory, v.150 n.1, p.96-116, January, 2008
	Giuseppe Di Maio , Jesús Rodríguez-López , José Manuel Sánchez-Álvarez, Weak inclusions and digital spaces, Pattern Recognition Letters, v.30 n.1, p.39-45, January, 2009
	N. Passat , M. Couprie , G. Bertrand, Minimal Simple Pairs in the 3-D Cubic Grid, Journal of Mathematical Imaging and Vision, v.32 n.3, p.239-249, November 2008
	Kálmán Palágyi, A 3D fully parallel surface-thinning algorithm, Theoretical Computer Science, v.406 n.1-2, p.119-135, October, 2008
	Georgios K. Ouzounis , Michael H. F. Wilkinson, Mask-Based Second-Generation Connectivity and Attribute Filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.29 n.6, p.990-1004, June 2007
	Jean Cousty , Michel Couprie , Laurent Najman , Gilles Bertrand, Weighted fusion graphs: Merging properties and watersheds, Discrete Applied Mathematics, v.156 n.15, p.3011-3027, August, 2008
	Nicu D. Cornea , Deborah Silver , Patrick Min, Curve-Skeleton Properties, Applications, and Algorithms, IEEE Transactions on Visualization and Computer Graphics, v.13 n.3, p.530-548, May 2007
	Sébastien Fourey , Rémy Malgouyres, Technical Section: Normals estimation for digital surfaces based on convolutions, Computers and Graphics, v.33 n.1, p.2-10, February, 2009
	Carlo Arcelli , Gabriella Sanniti di Baja , Luca Serino, A parallel algorithm to skeletonize the distance transform of 3D objects, Image and Vision Computing, v.27 n.6, p.666-672, May, 2009
	Xiao Han , Chenyang Xu , Jerry L. Prince, A Moving Grid Framework for Geometric Deformable Models, International Journal of Computer Vision, v.84 n.1, p.63-79, August 2009
	Jean-François Dufourd, An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps, Journal of Automated Reasoning, v.43 n.1, p.19-51, June 2009
	Jean Cousty , Gilles Bertrand, Uniqueness of the Perfect Fusion Grid on Z^d, Journal of Mathematical Imaging and Vision, v.34 n.3, p.291-306, July 2009
	J. Cousty , G. Bertrand , M. Couprie , L. Najman, Fusion Graphs: Merging Properties and Watersheds, Journal of Mathematical Imaging and Vision, v.30 n.1, p.87-104, January 2008
	Ying Bai , Xiao Han , Jerry L. Prince, Digital Topology on Adaptive Octree Grids, Journal of Mathematical Imaging and Vision, v.34 n.2, p.165-184, June 2009
	Gilles Bertrand , Michel Couprie, On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels, Journal of Mathematical Imaging and Vision, v.35 n.1, p.23-35, September 2009
	Geoffrey Fudenberg , Liam Paninski, Bayesian image recovery for dendritic structures under low signal-to-noise conditions, IEEE Transactions on Image Processing, v.18 n.3, p.471-482, March 2009
	Marcin Iwanowski, Morphological classification of binary image's pixels, Machine Graphics & Vision International Journal, v.18 n.2, p.155-173, January 2009
	Samuel Peltier , Sylvie Alayrangues , Laurent Fuchs , Jacques-Olivier Lachaud, Computation of homology groups and generators, Computers and Graphics, v.30 n.1, p.62-69, February, 2006
	Nicolas Passat , Loïc Mazo, An introduction to simple sets, Pattern Recognition Letters, v.30 n.15, p.1366-1377, November, 2009
	Jean-Pierre Braquelaire , Jean-Philippe Domenger, Geometrical, topological, and hierarchical structuring of overlapping 2-D discrete objects, Computers and Graphics, v.21 n.5, p.587-597, September, 1997
	Punam Kumar Saha, Tensor scale: A local morphometric parameter with applications to computer vision and image processing, Computer Vision and Image Understanding, v.99 n.3, p.384-413, September 2005
	Prosenjit Bose , Vida Dujmović , Ferran Hurtado , Pat Morin, Connectivity-preserving transformations of binary images, Computer Vision and Image Understanding, v.113 n.10, p.1027-1038, October, 2009