7.2.4 Digital Topology

Chapter Contents (Back)
Euler Number. Topology. Digital Topology. See also Three Dimensional Geometry and Topology, Computational Geometry.

Yokoi, S.[Shigeki], Toriwaki, J.I.[Jun-Ichiro], Fukumura, T.[Teruo],
An Analysis of Topological Properties of Digitized Binary Pictures Using Local Features,
CGIP(4), No. 1, March 1975, pp. 63-73.
Elsevier DOI 0501
Connectivity number, coefficient of curvature. BibRef

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

Bribiesca, E.[Ernesto], Guzman, A.[Adolfo],
How to Describe Pure Form and How to Measure Differences in Shapes Using Shape Numbers,
PR(12), No. 2, 1980, pp. 101-112.
Elsevier DOI BibRef 8000
Earlier:
Shape Description and Shape Similarity Measurement for Two-Dimensional Regions,
ICPR78(608-612). Shape number. 2D non-intersecting closed curve. BibRef

Mantyla, M.[Martti],
A Note on the Modeling Space of Euler Operators,
CVGIP(26), No. 1, April 1984, pp. 45-60.
Elsevier DOI BibRef 8404

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

Kawai, S.[Satoru],
Topology Quasi-Preservation by Local Parallel Operations,
CVGIP(23), No. 3, September 1983, pp. 353-365.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 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 Link. BibRef 9702

Kong, T.Y., Rosenfeld, A.,
Digital Topology: Introduction and Survey,
CVGIP(48), No. 3, December 1989, pp. 357-393.
Elsevier DOI 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., 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., 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.
Elsevier DOI (Univ of Western Ont.) Representation of the image with a linear quadtree, then the time is border*number of regions. BibRef 8502

Suzuki, S., Abe, K.,
Topological Structural Analysis of Digitized Binary Images by Border Following,
CVGIP(30), No. 1, April 1985, pp. 32-46.
Elsevier DOI (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.
DOI Link Chassery theorem simplification. See also Connectivity and Consecutivity in Digital Pictures. 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.
Elsevier DOI BibRef 9512

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

McAndrew, A., 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. 9609
Digital topology. Attempt to avoid the problems of different adjacency on the plane (1 and 0 treated differently). BibRef

Díaz-de-León S., J.L.[Juan L.], Sossa-Azuela, J.H.[Juan Humberto],
On the Computation of the Euler Number of a Binary Object,
PR(29), No. 3, March 1996, pp. 471-476.
Elsevier DOI Euler number via its skeleton. Terminal points and 3-edge points. 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.
DOI Link 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.[Ja-Chen],
A Simplified Fold Number Detector for Shapes with Monotonic Radii,
PR(29), No. 6, June 1996, pp. 997-1005.
Elsevier DOI 9606
BibRef

Gotsman, C., Lindenbaum, M.,
On the metric properties of discrete space-filling curves,
IP(5), No. 5, May 1996, pp. 794-797.
IEEE DOI 0402
BibRef
Earlier: ICPR94(C:98-102).
IEEE DOI 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.
DOI Link 9708
BibRef

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

Ronse, C.[Christian],
Set-Theoretical Algebraic Approaches to Connectivity in Continuous Or Digital Spaces,
JMIV(8), No. 1, January 1998, pp. 41-58.
DOI Link 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 Link. 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.
PS File. BibRef

Nakamura, A.[Akira], Rosenfeld, A.[Azriel],
Digital knots,
PR(33), No. 9, September 2000, pp. 1541-1553.
Elsevier DOI 0005
6-Knots in Z3 relate to polygonal Knots in R3. BibRef

Nakamura, A.[Akira],
Magnification in Digital Topology,
IWCIA04(260-275).
Springer DOI 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 Link. 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 Link. 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 Link. BibRef 9809

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

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

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

Boxer, L.[Laurence],
Properties of Digital Homotopy,
JMIV(22), No. 1, January 2005, pp. 19-26.
Springer DOI 0501
Study 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.
Springer DOI 0605
BibRef

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

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

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

Boxer, L.[Laurence], Karaca, I.[Ismet],
Some Properties of Digital Covering Spaces,
JMIV(37), No. 1, May 2010, pp. xx-yy.
Springer DOI 1003
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.
DOI Link 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.
DOI Link 0002
BibRef

Bretto, A.[Alain],
Comparability Graphs and Digital Topology,
CVIU(82), No. 1, April 2001, pp. 33-41.
DOI Link 0104
See also Hypergraph Imaging: An Overview. 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.
Elsevier DOI 0304
BibRef
Earlier: Abstract:
Normal vector and winding number in 2D digital images with application for hole detection,
PR(34), No. 11, November 2001, pp. 2253-2258.
Elsevier DOI 0108
See also Holes and Genus of 2D and 3D Digital Images. BibRef

Xia, F.[Franck],
On a new basic concept and topological invariant,
CIAP95(341-346).
Springer DOI 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.
DOI Link 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.
Elsevier DOI 0201
Prove for arbitrary cases the conjectre from: See also Interchangeable pairs of pixels in two-valued digital images. 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.
Elsevier DOI 0307
Analysis of connectivity. 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.
Elsevier DOI 0309
Verify parallel thinning. 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).
Springer DOI 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.
Elsevier DOI 0402
Topoloical 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

Damiand, G.[Guillaume], Coeurjolly, D.[David],
A Generic and Parallel Algorithm for 2D Image Discrete Contour Reconstruction,
ISVC08(II: 792-801).
Springer DOI 0812
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.
Elsevier DOI 0709
Digital planes; Arithmetic planes; Local configurations; Functionality of discrete planes BibRef

Berthé, V.[Valérie],
Arithmetic Discrete Planes Are Quasicrystals,
DGCI09(1-12).
Springer DOI 0909
BibRef

Domenjoud, E.[Eric], Jamet, D.[Damien], Toutant, J.L.[Jean-Luc],
On the Connecting Thickness of Arithmetical Discrete Planes,
DGCI09(362-372).
Springer DOI 0909
BibRef

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

Godoy, F.[Francisco], Rodríguez, A.[Andrea],
Defining and Comparing Content Measures of Topological Relations,
GeoInfo(8), No. 4, December 2004, pp. 347-371.
DOI Link 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.
Elsevier DOI 0711
Euler 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.
Elsevier DOI 0704
Shape 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).
IEEE DOI 0409
BibRef

Corriveau, D.[David], Allili, M.[Madjid],
Computing Homology: A Global Reduction Approach,
DGCI09(313-324).
Springer DOI 0909
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.
Springer DOI 0712
Qualitative topological analysis. Klein bottle topology. BibRef

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

Perea, J.A.[Jose A.], Carlsson, G.[Gunnar],
A Klein-Bottle-Based Dictionary for Texture Representation,
IJCV(107), No. 1, March 2014, pp. 75-97.
Springer DOI 1403
patch based, probability of patches. See also On the Local Behavior of Spaces of Natural Images. 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.
Springer DOI 0804
BibRef

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

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.],
Advances in combinatorial image analysis,
PR(42), No. 8, August 2009, pp. 1623-1625.
Elsevier DOI 0904
BibRef

Brimkov, V.E.[Valentin E.],
Parallel Algorithms for Combinatorial Pattern Matching,
IWCIA14(8-16).
Springer DOI 1405
BibRef

Brimkov, V.E.[Valentin E.],
Complexity and Approximability Issues in Combinatorial Image Analysis,
IWCIA11(5-8).
Springer DOI 1105
BibRef

Barneva, R.P.[Reneta P.], Brimkov, V.E.[Valentin E.],
Guest editorial: Contemporary challenges in combinatorial image analysis,
IJIST(19), No. 2, June 2009, pp. 37-38.
DOI Link 0905
Special issue introduction. BibRef

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.],
Digital Stars and Visibility of Digital Objects,
CompIMAGE10(11-23).
Springer DOI 1006
See also Object Discretizations in Higher Dimensions. BibRef

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.],
Linear Time Constant-Working Space Algorithm for Computing the Genus of a Digital Object,
ISVC08(I: 669-677).
Springer DOI 0812
BibRef

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.], Brimkov, B.[Boris], de Vieilleville, F.[François],
Offset Approach to Defining 3D Digital Lines,
ISVC08(I: 678-687).
Springer DOI 0812
BibRef

Pulcini, G.[Gabriele],
Computing surfaces via pq-permutations,
IJIST(19), No. 2, June 2009, pp. 132-139.
DOI Link 0905
BibRef

Nempont, O.[Olivier], Atif, J.[Jamal], Angelini, E.[Elsa], Bloch, I.[Isabelle],
A New Fuzzy Connectivity Measure for Fuzzy Sets: And Associated Fuzzy Attribute Openings,
JMIV(34), No. 2, June 2009, pp. xx-yy.
Springer DOI 0906
BibRef
Earlier:
A New Fuzzy Connectivity Class Application to Structural Recognition in Images,
DGCI08(xx-yy).
Springer DOI 0804
BibRef

Bloch, I.[Isabelle], Atif, J.[Jamal],
Hausdorff Distances Between Distributions Using Optimal Transport and Mathematical Morphology,
ISMM15(522-534).
Springer DOI 1506
BibRef

Groisser, D.[David], Tagare, H.D.[Hemant D.],
On the Topology and Geometry of Spaces of Affine Shapes,
JMIV(34), No. 2, June 2009, pp. xx-yy.
Springer DOI 0906
BibRef

Bandeira, L.[Lourenço], Pina, P.[Pedro], Saraiva, J.[José],
A multi-layer approach for the analysis of neighbourhood relations of polygons in remotely acquired images,
PRL(31), No. 10, 15 July 2010, pp. 1175-1183.
Elsevier DOI 1008
BibRef
Earlier:
A New Approach to Analyse Neighbourhood Relations in 2D Polygonal Networks,
CIARP08(397-404).
Springer DOI 0809
Polygonal networks; Mathematical morphology; Topology; Mars BibRef

Tøssebro, E.[Erlend], Nygård, M.[Mads],
Representing topological relationships for spatiotemporal objects,
GeoInfo(15), No. 4, October 2011, pp. 633-661.
WWW Link. 1110
BibRef

Chun, J.[Jinhee], Kaothanthong, N.[Natsuda], Kasai, R.[Ryosei], Korman, M.[Matias], Nöllenburg, M.[Martin], Tokuyama, T.[Takeshi],
Algorithms for computing the maximum weight region decomposable into elementary shapes,
CVIU(116), No. 7, July 2012, pp. 803-814.
Elsevier DOI 1202
Combinatorial optimization; Image segmentation; Computational geometry Decompose into Union of basic shapes. BibRef

Gonzalez-Diaz, R.[Rocio], Real Jurado, P.[Pedro],
Computational Topology in Image Context,
PRL(33), No. 11, 1 August 2012, pp. 1435.
Elsevier DOI 1206
BibRef

Bendich, P.[Paul], Cabello, S.[Sergio], Edelsbrunner, H.[Herbert],
A point calculus for interlevel set homology,
PRL(33), No. 11, 1 August 2012, pp. 1436-1444.
Elsevier DOI 1206
Continuous functions; Interlevel sets; Homology; Vector spaces; Persistence diagrams; Exact sequences BibRef

Mazo, L.[Loïc], Passat, N.[Nicolas], Couprie, M.[Michel], Ronse, C.[Christian],
Topology on Digital Label Images,
JMIV(44), No. 3, November 2012, pp. 254-281.
WWW Link. 1209
BibRef

Mazo, L.[Loïc], Passat, N.[Nicolas], Couprie, M.[Michel], Ronse, C.[Christian],
Digital Imaging: A Unified Topological Framework,
JMIV(44), No. 1, September 2012, pp. 19-37.
WWW Link. 1206
BibRef
Earlier:
A Unified Topological Framework for Digital Imaging,
DGCI11(163-174).
Springer DOI 1104
See also Topological Properties of Thinning in 2-D Pseudomanifolds. BibRef

Mazo, L.[Loïc],
A Framework for Label Images,
CTIC12(1-10).
Springer DOI 1206
BibRef

Ngo, P.[Phuc], Passat, N.[Nicolas], Kenmochi, Y.[Yukiko], Talbot, H.[Hugues],
Topology-Preserving Rigid Transformation of 2D Digital Images,
IP(23), No. 2, February 2014, pp. 885-897.
IEEE DOI 1402
image registration BibRef

Ngo, P.[Phuc], Kenmochi, Y.[Yukiko], Debled-Rennesson, I.[Isabelle], Passat, N.[Nicolas],
Convexity-Preserving Rigid Motions of 2D Digital Objects,
DGCI17(69-81).
Springer DOI 1711
BibRef

Ngo, P.[Phuc], Kenmochi, Y.[Yukiko], Passat, N.[Nicolas], Talbot, H.[Hugues],
Topology-Preserving Conditions for 2D Digital Images Under Rigid Transformations,
JMIV(49), No. 2, June 2014, pp. 418-433.
Springer DOI 1405
BibRef
Earlier:
Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations,
DGCI13(155-168).
Springer DOI 1304
BibRef

Kenmochi, Y.[Yukiko], Ngo, P.[Phuc], Talbot, H.[Hugues], Passat, N.[Nicolas],
Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search,
DGCI14(99-110).
Springer DOI 1410
BibRef

Ngo, P.[Phuc], Sugimoto, A.[Akihiro], Kenmochi, Y.[Yukiko], Passat, N.[Nicolas], Talbot, H.[Hugues],
Discrete Rigid Transformation Graph Search for 2D Image Registration,
PSIVTWS13(228-239).
Springer DOI 1402
BibRef

Peters, J.F.[James F.],
Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces,

Springer2014. ISBN 978-3-642-53844-5.
WWW Link. 1404
BibRef

Birtea, P.[Petre], Comanescu, D.[Dan], Popa, C.A.[Calin-Adrian],
Averaging on Manifolds by Embedding Algorithm,
JMIV(49), No. 2, June 2014, pp. 454-466.
Springer DOI 1405
finding critical points of cost functions defined on a differential manifold BibRef

Azuela, J.H.S.[J.H. Sossa], Espino, E.R., Santiago, R., López, A., Ayala, A.P., Jimenez, E.V.C.,
Alternative formulations to compute the binary shape Euler number,
IET-CV(8), No. 3, June 2014, pp. 171-181.
DOI Link 1407
BibRef

Richardson, E.[Eitan], Werman, M.[Michael],
Efficient classification using the Euler characteristic,
PRL(49), No. 1, 2014, pp. 99-106.
Elsevier DOI 1410
Euler BibRef

Richardson, E.[Eitan], Peleg, S.[Shmuel], Werman, M.[Michael],
Scene geometry from moving objects,
AVSS14(13-18)
IEEE DOI 1411
Cameras BibRef

Climent, J.[Juan], Oliveira, L.S.[Luiz S.],
A new algorithm for number of holes attribute filtering of grey-level images,
PRL(53), No. 1, 2015, pp. 24-30.
Elsevier DOI 1502
Attribute filtering BibRef

Schrack, G., Stocco, L.,
Generation of Spatial Orders and Space-Filling Curves,
IP(24), No. 6, June 2015, pp. 1791-1800.
IEEE DOI 1504
Cryptography BibRef

Haarmann, J.[Jason], Murphy, M.P.[Meg P.], Peters, C.S.[Casey S.], Staecker, P.C.[P. Christopher],
Homotopy Equivalence in Finite Digital Images,
JMIV(53), No. 3, November 2015, pp. 288-302.
Springer DOI 1511
BibRef

Boxer, L.[Laurence], Staecker, P.C.[P. Christopher],
Connectivity Preserving Multivalued Functions in Digital Topology,
JMIV(55), No. 3, July 2016, pp. 370-377.
WWW Link. 1604
BibRef

Zou, B.[Beiji], Liu, Q.[Qing], Chen, Z.L.[Zai-Liang], Fu, H.P.[Hong-Pu], Zhu, C.Z.[Cheng-Zhang],
Surroundedness based multiscale saliency detection,
JVCIR(33), No. 1, 2015, pp. 378-388.
Elsevier DOI 1512
Saliency detection BibRef

Kuijpers, B.[Bart], Moelans, B.[Bart],
Algebraic and Geometric Characterizations of Double-Cross Matrices of Polylines,
IJGI(5), No. 9, 2016, pp. 152.
DOI Link 1610
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Díaz-del-Río, F.[Fernando], Real, P.[Pedro], Onchis, D.M.[Darian M.],
A parallel Homological Spanning Forest framework for 2D topological image analysis,
PRL(83, Part 1), No. 1, 2016, pp. 49-58.
Elsevier DOI 1609
Computational algebraic topology BibRef

Díaz-del-Río, F.[Fernando], Real, P.[Pedro], Onchis, D.M.[Darian M.],
Labeling Color 2D Digital Images in Theoretical Near Logarithmic Time,
CAIP17(II: 391-402).
Springer DOI 1708
BibRef

Romero, A.[Ana], Rubio, J.[Julio], Sergeraert, F.[Francis],
Effective homology of filtered digital images,
PRL(83, Part 1), No. 1, 2016, pp. 23-31.
Elsevier DOI 1609
Effective homology BibRef

Bermudez-Cameo, J.[Jesus],
New contributions on line-projections in omnidirectional vision,
ELCVIA(15), No. 2, 2016, pp. 24-26.
DOI Link 1611
Geometry of line projections in omnidirectional images. BibRef

Zhou, Z.[Zhen], Huang, Y.Z.[Yong-Zhen], Wang, L.[Liang], Tan, T.N.[Tie-Niu],
Exploring generalized shape analysis by topological representations,
PRL(87), No. 1, 2017, pp. 177-185.
Elsevier DOI 1703
Topology BibRef

Shen, J.W.[Jing-Wei], Zhou, T.[Tinggang], Chen, M.[Min],
A 27-Intersection Model for Representing Detailed Topological Relations between Spatial Objects in Two-Dimensional Space,
IJGI(6), No. 2, 2017, pp. xx-yy.
DOI Link 1703
BibRef

Kuijpers, B.[Bart], Revesz, P.Z.[Peter Z.],
A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number,
IJGI(6), No. 3, 2017, pp. xx-yy.
DOI Link 1704
BibRef

Hu, M.X.[Ming-Xiao], Zhou, Y.[Yan], Li, X.J.[Xu-Jie],
Robust and accurate computation of geometric distance for Lipschitz continuous implicit curves,
VC(33), No. 6-8, June 2017, pp. 937-947.
Springer DOI 1706
Distance between point and curve. BibRef

Xie, P.[Peng], Liu, Y.[Yaolin], He, Q.[Qingsong], Zhao, X.[Xiang], Yang, J.[Jun],
An Efficient Vector-Raster Overlay Algorithm for High-Accuracy and High-Efficiency Surface Area Calculations of Irregularly Shaped Land Use Patches,
IJGI(6), No. 6, 2017, pp. xx-yy.
DOI Link 1706
BibRef

Zrira, N.[Nabila], Bouyakhf, E.H.[El Houssine],
A novel incremental topological mapping using global visual features,
IJCVR(8), No. 1, 2018, pp. 18-31.
DOI Link 1804
BibRef

Assaf, R.[Rabih], Goupil, A.[Alban], Vrabie, V.[Valeriu], Boudier, T.[Thomas], Kacim, M.[Mohammad],
Persistent homology for object segmentation in multidimensional grayscale images,
PRL(112), 2018, pp. 277-284.
Elsevier DOI 1809
Algebraic topology, Object segmentation, Persistent homology BibRef


Boutry, N.[Nicolas], Géraud, T.[Thierry], Najman, L.[Laurent],
A Tutorial on Well-Composedness,
JMIV(60), No. 3, March 2018, pp. 443-478.
Springer DOI 1804
BibRef
Earlier: A1, A3, A2:
Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in Zn,
DGCI17(225-237).
Springer DOI 1711
BibRef

Mukherjee, S.[Sabyasachi], Bandyopadhyay, O.[Oishila], Biswas, A.[Arindam], Bhattacharya, B.B.[Bhargab B.],
Does Rotation Influence the Estimated Contour Length of a Digital Object?,
PReMI17(179-186).
Springer DOI 1711
BibRef

Chen, J.B.[Jian-Bin], Li, J.[Jun], Xu, Y.[Yang], Shen, G.T.[Guang-Tian], Gao, Y.J.[Yang-Jian],
A compact loop closure detection based on spatial partitioning,
ICIVC17(371-375)
IEEE DOI 1708
Image segmentation, Robots, Visualization, BoW, K-mean, Loop closure detection, Scene, segmentation BibRef

Šlapal, J.[Josef],
A Relational Generalization of the Khalimsky Topology,
IWCIA17(132-141).
Springer DOI 1706
BibRef

Sossa, H.[Humberto], Carreón, Á.[Ángel], Santiago, R.[Raúl],
Training a Multilayered Perceptron to Compute the Euler Number of a 2-D Binary Image,
MCPR16(44-53).
Springer DOI 1608
BibRef

Guihéneuf, P.A.[Pierre-Antoine],
Discretizations of Isometries,
DGCI16(71-92).
WWW Link. 1606
BibRef

Sossa, H.[Humberto],
On the number of holes of a 2-D binary object,
MVA15(299-302)
IEEE DOI 1507
Computers BibRef

Gérard, Y.[Yan], Vacavant, A.[Antoine],
About the Maximum Cardinality of the Digital Cover of a Curve with a Given Length,
DGCI14(13-24).
Springer DOI 1410
pixels in digitized curve. BibRef

Damiand, G.[Guillaume], Roussillon, T.[Tristan], Solnon, C.[Christine],
2D Topological Map Isomorphism for Multi-Label Simple Transformation Definition,
DGCI14(39-50).
Springer DOI 1410
BibRef

Castiglione, G.[Giusi], Massazza, P.[Paolo],
An Efficient Algorithm for the Generation of Z-Convex Polyominoes,
IWCIA14(51-61).
Springer DOI 1405
BibRef

Battaglino, D.[Daniela], Frosini, A.[Andrea], Guerrini, V.[Veronica], Rinaldi, S.[Simone], Socci, S.[Samanta],
Binary Pictures with Excluded Patterns,
DGCI14(25-38).
Springer DOI 1410
(polyomino). BibRef

Frosini, A.[Andrea], Picouleau, C.[Christophe], Rinaldi, S.[Simone],
On the Degree Sequences of Uniform Hypergraphs,
DGCI13(300-310).
Springer DOI 1304
BibRef

Frosini, A.[Andrea], Picouleau, C.[Christophe],
How to Decompose a Binary Matrix into Three hv-convex Polyominoes,
DGCI13(311-322).
Springer DOI 1304
BibRef

Cerri, A.[Andrea], Landi, C.[Claudia],
The Persistence Space in Multidimensional Persistent Homology,
DGCI13(180-191).
Springer DOI 1304
BibRef

Cerri, A.[Andrea], Ethier, M.[Marc], Frosini, P.[Patrizio],
The Coherent Matching Distance in 2D Persistent Homology,
CTIC16(216-227).
Springer DOI 1608
See also Comparing shapes through multi-scale approximations of the matching distance. BibRef

Cerri, A.[Andrea], Ethier, M.[Marc], Frosini, P.[Patrizio],
A Study of Monodromy in the Computation of Multidimensional Persistence,
DGCI13(192-202).
Springer DOI 1304
BibRef

Chassery, J.M.[Jean-Marc], Sivignon, I.[Isabelle],
Optimal Covering of a Straight Line Applied to Discrete Convexity,
DGCI13(1-10).
Springer DOI 1304
BibRef

Lalitha, D., Rangarajan, K., Thomas, D.G.[Durairaj Gnanaraj],
Rectangular Arrays and Petri Nets,
IWCIA12(166-180).
Springer DOI 1211
BibRef

Heras, J.[Jónathan], Dénès, M.[Maxime], Mata, G.[Gadea], Mörtberg, A.[Anders], Poza, M.[María], Siles, V.[Vincent],
Towards a Certified Computation of Homology Groups for Digital Images,
CTIC12(49-57).
Springer DOI 1206
BibRef

Brendel, P.[Piotr], Dlotko, P.[Pawel], Mrozek, M.[Marian], Zelazna, N.[Natalia],
Homology Computations via Acyclic Subspace,
CTIC12(117-127).
Springer DOI 1206
BibRef

Sagols, F.[Feliú], Marín, R.[Raúl],
The Inscribed Square Conjecture in the Digital Plane,
IWCIA09(411-424).
Springer DOI 0911
plane Jordan curve contains 4 points on a square. BibRef

Šlapal, J.[Josef],
Structuring Digital Spaces by Path-Partition Induced Closure Operators on Graphs,
CompIMAGE16(43-55).
Springer DOI 1704
BibRef
Earlier:
Adjacencies for Structuring the Digital Plane,
IWCIA12(115-127).
Springer DOI 1211
BibRef
And:
Convenient Closure Operators on Z2,
IWCIA09(425-436).
Springer DOI 0911
BibRef

Šlapal, J.[Josef],
A Jordan Curve Theorem in the Digital Plane,
IWCIA11(120-131).
Springer DOI 1105
BibRef
Earlier:
Jordan Curve Theorems with Respect to Certain Pretopologies on Z2,
DGCI09(252-262).
Springer DOI 0909
BibRef

Manocha, D.[Dinesh],
Digital Geometry Processing with Topological Guarantees,
DGCI08(xx-yy).
Springer DOI 0804
BibRef

Rodríguez, M.[Marc], Largeteau-Skapin, G.[Gaëlle], Andres, É.[Éric],
Local Non-planarity of Three Dimensional Surfaces for an Invertible Reconstruction: k-Cuspal Cells,
ISVC08(I: 925-934).
Springer DOI 0812
BibRef

Richard, A.[Aurélie], Wallet, G.[Guy], Fuchs, L.[Laurent], Andres, E.[Eric], Largeteau-Skapin, G.[Gaëlle],
Arithmetization of a Circular Arc,
DGCI09(350-361).
Springer DOI 0909
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).
Springer DOI 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 File. 0711
BibRef

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

Klette, G.[Gisela],
Simple Points in 2D and 3D Binary Images,
CAIP03(57-64).
Springer DOI 0311
A 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).
IEEE DOI 0311
BibRef

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

Klette, R.,
Topologies on the planar orthogonal grid,
ICPR02(II: 354-357).
IEEE DOI 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).
Springer DOI 0804
BibRef

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

Comic, L.[Lidija],
Morse Chain Complex from Forman Gradient in 3D with Z2 Coefficients,
CTIC16(42-52).
Springer DOI 1608
BibRef

Comic, L.[Lidija], de Floriani, L.[Leila],
Cancellation of Critical Points in 2D and 3D Morse and Morse-Smale Complexes,
DGCI08(xx-yy).
Springer DOI 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.).
Springer DOI 0209
BibRef

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

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

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

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

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


Last update:Nov 17, 2018 at 09:12:27