7.2.4 Digital Topology

Yokoi, S., Toriwaki, J.I., and Fukumura, T.,
An Analysis of Topological Properties of Digital Binary Pictures Using Local Features,
CGIP(4), March 1975, pp. 63-xx. BibRef 7503

Dyer, C.R.,
Computing the Euler Number of an Image from its Quadtree,
CGIP(13), No. 3, July 1980, pp. 270-276.
WWW Version. BibRef 8007

Bribiesca, E., Guzman, A.,
How to Describe Pure Form and How to Measure Differences in Shapes Using Shape Numbers,
PR(12), No. 2, 1980, pp. 101-112.
WWW Version. BibRef 8000
Earlier:
Shape Description and Shape Similarity Measurement for Two-Dimensional Regions,
ICPR78(608-612). BibRef

Mantyla, M.,
A Note on the Modeling Space of Euler Operators,
CVGIP(26), No. 1, April 1984, pp. 45-60.
WWW Version. BibRef 8404

Kawai, S.[Satoru],
On the topology preservation property of local parallel operations,
CGIP(19), No. 3, July 1982, pp. 265-280.
WWW Version. BibRef 8207

Kawai, S.,
Topology Quasi-Preservation by Local Parallel Operations,
CVGIP(23), No. 3, September 1983, pp. 353-365.
WWW Version. BibRef 8309

Shoukry, A., Amin, A.,
Topological and Statistical Analysis of Line Drawings,
PRL(1), No. 5-6, 1983, pp. 365-374. BibRef 8300

Bieri, H., Nef, W.,
Algorithms for the Euler Characteristic and Related Additive Functionals of Digital Objects,
CVGIP(28), No. 2, November 1984, pp. 166-175. BibRef 8411

Bieri, H.,
Computing the Euler Characteristic and Related Additive Functionals of Digital Objects from Their Bintree Representation,
CVGIP(40), No. 1, October 1987, pp. 115-126.
WWW Version. BibRef 8710

Kovalevsky, V.A.,
Discrete Topology and Contour Definition,
PRL(2), 1984, pp. 281-288. BibRef 8400

Massone, L., Sandini, G., Tagliasco, V.,
'Form-Invariant' Topological Mapping Strategy for 2D Shape Recognition,
CVGIP(30), No. 2, May 1985, pp. 169-188.
WWW Version. BibRef 8505

Rosenfeld, A.,
Fuzzy Digital Topology,
InfoControl(40), No. 1, January 1979, pp. 76-87. BibRef 7901

Rosenfeld, A.,
Digital Topology,
AMM(86), 1979, pp. 621-630. BibRef 7900

Rosenfeld, A.[Azriel],
Digital geometry: Introduction and bibliography,
UMD--TR3753, February 1997.
WWW Version.
WWW Version. BibRef 9702

Kong, T.Y., and Rosenfeld, A.,
Digital Topology: Introduction and Survey,
CVGIP(48), No. 3, December 1989, pp. 357-393.
WWW Version. Survey, Digital Topology. Digital Topology, Survey. Study of properties of image arrays to provide a basis for image processing operations. See also Three-Dimensional Digital Topology. BibRef 8912

Kong, T.Y., and Rosenfeld, A., (Eds.),
Topological Algorithms for Digital Image Processing,
North-HollandAmsterdam, 1996. BibRef 9600

Lee, C.N.[Chung-Nim], Poston, T.[Timothy], Rosenfeld, A.[Azriel],
Holes and Genus of 2D and 3D Digital Images,
GMIP(55), No. 1, January 1993, pp. 20-yy. BibRef 9301

Lee, C.N., Rosenfeld, A.,
Computing the Euler Number of a 3D Image,
ICCV87(567-571). BibRef 8700

Atkinson, H.H., Gargantini, I., and Walsh, T.R.S.,
Counting Regions, Holes, and Their Nesting Level in Time Proportional to the Border,
CVGIP(29), No. 2, February 1985, pp. 196-215. (Univ of Western Ont.) Representation of the image with a linear quadtree, then the time is border*number of regions. BibRef 8502

Suzuki, S., and Abe, K.,
Topological Structural Analysis of Digitized Binary Images by Border Following,
CVGIP(30), No. 1, April 1985, pp. 32-46.
WWW Version. (Shizuoka U., Japan) Border following seems standard (e.g. See also Analysis of Natural Scenes. ), but they build up a region/hole structure from the sequence of borders. BibRef 8504

Chen, M.H., Yan, P.F.,
A Fast Algorithm to Calculate the Euler Number for Binary Images,
PRL(8), 1988, pp. 295-297. BibRef 8800

Latecki, L.J.[Longin J.],
Topological Connectedness and 8-Connectedness in Digital Pictures,
CVGIP(57), No. 2, March 1993, pp. 261-262.
WWW Version. BibRef 9303

Chiavetta, F., di Gesu, V.,
Parallel Computation of the Euler Number via Connectivity Graph,
PRL(14), 1993, pp. 849-859. BibRef 9300

Kong, T.Y., Rosenfeld, A.,
If We Use 4- or 8-Connectedness for Both the Objects and the Background, the Euler Characteristic Is Not Locally Computable,
PRL(11), 1990, pp. 231-232. BibRef 9000

Saha, P.K., Chaudhuri, B.B.,
A New Approach to Computing the Euler Characteristic,
PR(28), No. 12, December 1995, pp. 1955-1963.
WWW Version. BibRef 9512

Qian, K., and Bhattacharya, P.,
Determining Holes and Connectivity in Binary Images,
Computers&Graphics(16), 1992, pp. 283-288. BibRef 9200

Gross, A., Latecki, L.J.,
Digitizations Preserving Topological and Differential Geometric-Properties,
CVIU(62), No. 3, November 1995, pp. 370-381.
WWW Version. What digitizations preserve topological properties. See also Modelling Digital Straight Lines. BibRef 9511

McAndrew, A., and Osborne, C.,
A Survey of Algebraic Methods in Digital Topology,
JMIV(6), No. 2-3, June 1996, pp. 139-159. 9608 Survey, Digital Topology. BibRef

Aharoni, R., Herman, G.T., Loebl, M.,
Jordan Graphs,
GMIP(58), No. 4, July 1996, pp. 345-359. 9609Digital topology. Attempt to avoid the problems of different adjacency on the plane (1 and 0 treated differently). BibRef

Diaz de Leon S., J.L., Sossa-Azuela, J.H.,
On the Computation of the Euler Number of a Binary Object,
PR(29), No. 3, March 1996, pp. 471-476.
WWW Version. BibRef 9603

Malladi, R., Sethian, J.A., Vemuri, B.C.,
A Fast Level Set Based Algorithm For Topology-Independent Shape Modeling,
JMIV(6), No. 2-3, June 1996, pp. 269-289. 9608 See also Shape Modeling with Front Propagation: A Level Set Approach. BibRef

Nogly, D., Schladt, M.,
Digital-Topology on Graphs,
CVIU(63), No. 2, March 1996, pp. 394-396.
WWW Version. BibRef 9603

Lin, J.C., Tsai, W.H., Chen, J.A.,
Detecting Number of Folds by a Simple Mathematical Property,
PRL(15), No. 11, November 1994, pp. 1081-1088. BibRef 9411

Lin, J.C.,
A Simplified Fold Number Detector for Shapes with Monotonic Radii,
PR(29), No. 6, June 1996, pp. 997-1005.
WWW Version. 9606 BibRef

Gotsman, C., Lindenbaum, M.,
On the metric properties of discrete space-filling curves,
IP(5), No. 5, May 1996, pp. 794-797.
WWW Version. 0402 BibRef
Earlier: ICPR94(C:98-102).
WWW Version. 9410 BibRef

McAndrew, A., Osborne, C.,
The Euler Characteristic on the Face-Centered-Cubic Lattice,
PRL(18), No. 3, March 1997, pp. 229-237. 9706 BibRef

Agrawal, R.C., Sahasrabudhe, S.C., Shevgaonkar, R.K.,
Preservation of Topological Properties of a Simple Closed Curve under Digitalization,
CVIU(67), No. 2, August 1997, pp. 99-111. 9708
WWW Version. BibRef

Latecki, L.J., Conrad, C., Gross, A.,
Preserving Topology by a Digitization Process,
JMIV(8), No. 2, March 1998, pp. 131-159.
WWW Version. 9803 BibRef

Latecki, L.J.[Longin J.], Gross, A.[Ari],
Digitization Constraints That Preserve Topology and Geometry,
SCV95(127-132).
IEEE Top Reference. U. of Hamburg. Graduate Center and Queens College CUNY. Camera constraints to preserve the properties. BibRef 9500

Gross, A.[Ari], Latecki, L.J.[Longin J.],
Digital Geometric Invariance and Shape Representation,
SCV95(121-126).
IEEE Top Reference. Graduate Center and Queens College CUNY. U. of Hamburg. Studies the issue of what features are preserved with digitization. BibRef 9500

Kopperman, R.[Ralph],
The Khalimsky Line as a Foundation for Digital Topology,
MDSG94(3). BibRef 9400

Ronse, C.,
Set-Theoretical Algebraic Approaches to Connectivity in Continuous Or Digital Spaces,
JMIV(8), No. 1, January 1998, pp. 41-58.
WWW Version. 9803 BibRef

Rosenfeld, A.[Azriel], Nakamura, A.[Akira],
Local Deformations of Digital Curves,
PRL(18), No. 7, July 1997, pp. 613-620. 9711 BibRef
Earlier: UMDTR3650, June 1996
WWW Version.
WWW Version. Preservation of topology for some deformations. BibRef

Rosenfeld, A.[Azriel], Kong, T.Y.[T. Yung], Nakamura, A.[Akira],
Topology-Preserving Deformations of Two-Valued Digital Pictures,
GMIP(60), No. 1, January 1998, pp. 24-34. BibRef 9801
Earlier: (Gave A2 as Y.T.K): UMD--TR3781R, June 1997.
Postscript Version. BibRef

Nakamura, A.[Akira], Rosenfeld, A.[Azriel],
Digital knots,
PR(33), No. 9, September 2000, pp. 1541-1553.
WWW Version. 0005 BibRef

Nakamura, A.[Akira],
Magnification in Digital Topology,
IWCIA04(260-275).
WWW Version. 0505 BibRef

Saha, P.K., Majumder, D.D.[D. Dutta], Rosenfeld, A.[Azriel],
Local Topological Parameters in a Tetrahedral Representation,
GMIP(60), No. 6, November 1998, pp. 423-436. BibRef 9811
And: UMD--TR3826, August 1997. Tetrahedral Representation.
WWW Version.
WWW Version. BibRef

Saha, P.K.[Punam K.], Rosenfeld, A.[Azriel],
The Digital Topology of Sets of Convex Voxels,
GM(62), No. 5, September 2000, pp. 343-352. 0010 BibRef
And: UMD--TR3899, April 1998 Topology with arbitrary convex voxels.
WWW Version.
WWW Version. BibRef

Saha, P.K.[Punam K.], Rosenfeld, A.[Azriel],
Local and Global Topology Preservation in Locally Finite Sets of Tiles,
UMD-- TR3926, September 1998.
WWW Version.
WWW Version. BibRef 9809

Serra, J.[Jean],
Connectivity on Complete Lattices,
JMIV(9), No. 3, November 1998, pp. 231-251.
WWW Version. BibRef 9811

Serra, J.[Jean],
Viscous Lattices,
JMIV(22), No. 2-3, May 2005, pp. 269-282.
WWW Version. 0505 BibRef

Boxer, L.[Laurence],
A Classical Construction for the Digital Fundamental Group,
JMIV(10), No. 1, January 1999, pp. 51-62.
WWW Version. Digital Topology BibRef 9901

Boxer, L.[Laurence],
Properties of Digital Homotopy,
JMIV(22), No. 1, January 2005, pp. 19-26.
WWW Version. 0501Study a variety of digitally-continuous functions that preserve homotopy types or homotopy-related properties such as the digital fundamental group. BibRef

Boxer, L.[Laurence],
Homotopy Properties of Sphere-Like Digital Images,
JMIV(24), No. 2, March 2006, pp. 167-175.
WWW Version. 0605 BibRef

Boxer, L.[Laurence],
Digital Products, Wedges, and Covering Spaces,
JMIV(25), No. 2, September 2006, pp. 159-171.
WWW Version. 0610 BibRef

Boxer, L.[Laurence],
Fundamental Groups of Unbounded Digital Images,
JMIV(27), No. 2, February 2007, pp. 121-127.
WWW Version. 0704 BibRef

Boxer, L.[Laurence], Karaca, I.[Ismet],
The Classification of Digital Covering Spaces,
JMIV(32), No. 1, September 2008, pp. xx-yy.
WWW Version. 0804 BibRef

Imiya, A.[Atsushi], Eckhardt, U.[Ulrich],
The Euler Characteristics of Discrete Objects and Discrete Quasi-Objects,
CVIU(75), No. 3, September 1999, pp. 307-318.
WWW Version. BibRef 9909

Imiya, A.[Atsushi], Eckhardt, U.[Ulrich],
Discrete Mean Curvature Flow,
ScaleSpace99(477-482). BibRef 9900

Winter, S.[Stephan], Frank, A.U.[Andrew U.],
Topology in Raster and Vector Representation,
GeoInfo(4), No. 1, March 2000, pp. 35-65.
WWW Version. 0002 BibRef

Bretto, A.[Alain],
Comparability Graphs and Digital Topology,
CVIU(82), No. 1, April 2001, pp. 33-41.
WWW Version. 0104 BibRef

Xia, F.[Franck],
Normal vector and winding number in 2D digital images with application for hole detection,
PR(34), No. 11, November 2001, pp. 2253-2258.
WWW Version. 0108 BibRef

Xia, F.[Franck],
Normal vector and winding number in 2D digital images with their application for hole detection,
PR(36), No. 6, June 2003, pp. 1383-1395.
WWW Version. 0304 BibRef

Xia, F.[Franck],
On a new basic concept and topological invariant,
CIAP95(341-346).
WWW Version. 9509 BibRef

Kong, T.Y.[T. Yung],
Digital Topology,
FIU01(Chapter 3). BibRef 0100

Alpers, A.[Andreas],
Digital Topology: Regular Sets and Root Images of the Cross-Median Filter,
JMIV(17), No. 1, July 2002, pp. 7-14.
WWW Version. 0211 BibRef

Rosenfeld, A.[Azriel], Nakamura, A.[Akira],
Two simply connected sets that have the same area are IP-equivalent,
PR(35), No. 2, February 2002, pp. 537-541.
WWW Version. 0201 BibRef

Eckhardt, U.[Ulrich], Latecki, L.J.[Longin Jan],
Topologies for the digital spaces Z2 and Z3,
CVIU(90), No. 3, June 2003, pp. 295-312.
WWW Version. 0307 BibRef

Gau, C.J., Kong, T.Y.[T. Yung],
Minimal non-simple sets in 4D binary images,
GM(65), No. 1-3, May 2003, pp. 112-130.
WWW Version. 0309 BibRef

Kong, T.Y.[T. Yung], Gau, C.J.[Chyi-Jou],
Minimal Non-simple Sets in 4-Dimensional Binary Images with (8,80)-Adjacency,
IWCIA04(318-333).
WWW Version. 0505 BibRef

Damiand, G.[Guillaume], Bertrand, Y.[Yves], Fiorio, C.[Christophe],
Topological Model for Two-Dimensional Image Representation: Definition and Optimal Extraction Algorithm,
CVIU(93), No. 2, February 2004, pp. 111-154.
WWW Version. 0402Topoloical map at top of hierarchy of definitions based on object boundary. See also Split-and-merge algorithms defined on topological maps for 3D image segmentation. BibRef

Berthe, V.[Valerie], Fiorio, C.[Christophe], Jamet, D.[Damien], Philippe, F.[Fabrice],
On some applications of generalized functionality for arithmetic discrete planes,
IVC(25), No. 10, 1 October 2007, pp. 1671-1684.
WWW Version. 0709Digital planes; Arithmetic planes; Local configurations; Functionality of discrete planes BibRef

Jonker, P.P.[Pieter P.],
Discrete topology on N-dimensional square tessellated grids,
IVC(23), No. 2, 1 February 2004, pp. 213-225.
WWW Version. 0412 BibRef

Godoy, F.[Francisco], Rodríguez, A.[Andrea],
Defining and Comparing Content Measures of Topological Relations,
GeoInfo(8), No. 4, December 2004, pp. 347-371.
WWW Version. 0501 BibRef

Kiderlen, M.[Markus],
Estimating the Euler Characteristic of a planar set from a digital image,
JVCIR(17), No. 6, December 2006, pp. 1237-1255.
WWW Version. 0711Euler characteristic; Digital morphology; Convex ring; Digitized image; Multigrid convergence; Betti number BibRef

Allili, M.[Madjid], Corriveau, D.,
Topological analysis of shapes using Morse theory,
CVIU(105), No. 3, March 2007, pp. 188-199.
WWW Version. 0704Shape representation; Shape similarity; Morse theory; Computational homology BibRef

Allili, M.[Madjid], Corriveau, D., Ziou, D.,
Morse homology descriptor for shape characterization,
ICPR04(IV: 27-30).
WWW Version. 0409 BibRef

Carlsson, G.[Gunnar], Ishkhanov, T.[Tigran], de Silva, V.[Vin], Zomorodian, A.[Afra],
On the Local Behavior of Spaces of Natural Images,
IJCV(76), No. 1, January 2008, pp. 1-12.
WWW Version. 0712Qualitative topological analysis. BibRef

Ishkhanov, T.[Tigran],
A topological method for shape comparison,
NORDIA08(1-4).
WWW Version. 0806 BibRef

Han, S.E.[Sang-Eon],
The k-Homotopic Thinning and a Torus-Like Digital Image in Z n,
JMIV(31), No. 1, May 2008, pp. xx-yy.
WWW Version. 0804 BibRef

Han, S.E.[Sang-Eon],
Discrete Homotopy of a Closed k-Surface,
IWCIA06(214-225).
WWW Version. 0606 BibRef

Fuchs, L.[Laurent], Largeteau-Skapin, G.[Gaëlle], Wallet, G.[Guy], Andres, E.[Eric], Chollet, A.[Agathe],
A First Look into a Formal and Constructive Approach for Discrete Geometry Using Nonstandard Analysis,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Nempont, O., Atif, J., Angelini, E., Bloch, I.[Isabelle],
A New Fuzzy Connectivity Class Application to Structural Recognition in Images,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Zhu, G.B.[Guo-Bin], Liu, X.L.[Xiao-Li], Jia, Z.G.[Zhi-Ge], Li, Q.Q.[Qing-Quan],
A Multi-Level Image Description Model Based on Digital Topology,
PIA07(185).
PDF Version. 0711 BibRef

Kropatsch, W.G.[Walter G.], Haxhimusa, Y.[Yll], Lienhardt, P.[Pascal],
Hierarchies Relating Topology and Geometry,
CogVis03(199-220).
WWW Version. 0310 BibRef

Klette, G.[Gisela],
Simple Points in 2D and 3D Binary Images,
CAIP03(57-64).
WWW Version. 0311A point is simple if the change of its value does not change the topology of the image. BibRef

Wang, S.[Song], Ji, J.X.[Jim Xiuquan], Liang, Z.P.[Zhi-Pei],
Landmark-based shape deformation with topology-preserving constraints,
ICCV03(923-930).
WWW Version. 0311 BibRef

Klette, R.,
Switches may solve adjacency problems,
ICPR02(III: 907-910).
WWW Version. 0211 BibRef

Klette, R.,
Topologies on the planar orthogonal grid,
ICPR02(II: 354-357).
WWW Version. 0211 BibRef

Imiya, A.[Atsushi], Ootani, H., Tatara, K.[Ken],
Medial Set, Boundary, and Topology of Random Point Sets,
WTRCV02(303-318). 0204 BibRef

Köthe, U.[Ullrich],
What Can We Learn from Discrete Images about the Continuous World?,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Köthe, U.[Ullrich],
Deriving Topological Representations from Edge Images,
WTRCV02(21-42). 0204 BibRef

Comic, L.[Lidija], de Floriani, L.[Leila],
Cancellation of Critical Points in 2D and 3D Morse and Morse-Smale Complexes,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Danovaro, E.[Emanuele], De Floriani, L.[Leila], Mesmoudi, M.M.[Mohammed Mostefa],
Topological Analysis and Characterization of Discrete Scalar Fields,
WTRCV02(65-85). 0204 BibRef

Barth, E.[Erhardt], Ferraro, M.[Mario], Zetzsche, C.[Christoph],
Global Topological Properties of Images Derived from Local Curvature Features,
VF01(285 ff.).
HTML Version. 0209 BibRef

Kofler, H.[Helmut],
A Topological Net Structure and a Topological Graph,
ICPR98(Vol II: 1449-1454).
WWW Version. 9808 BibRef

Sukanya, P., Tanuma, H., Takamatsu, R., Sato, M.,
A New Operator for Describing Topographical Image Structure,
ICPR96(I: 50-54).
WWW Version. 9608(Tokyo Institute of Technology, J) BibRef

Sukanya, P., Takamatsu, R., Sato, I.,
A new operator for image structure analysis,
ICIP96(III: 615-618).
WWW Version. 9610 BibRef

Hall, R.W., Hu, C.Y.[Chih-Yuan],
Time-efficient computations for topological functions in 3D images,
ICIP95(II: 97-100).
WWW Version. 9510 BibRef

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Waveform and Contour Analysis .