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.
WWW Link. 0501
BibRef

Dyer, C.R.,
Computing the Euler Number of an Image from its Quadtree,
CGIP(13), No. 3, July 1980, pp. 270-276.
WWW Link. 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 Link. 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 Link. BibRef 8404

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

Kawai, S.,
Topology Quasi-Preservation by Local Parallel Operations,
CVGIP(23), No. 3, September 1983, pp. 353-365.
WWW Link. 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.
WWW Link. 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 Link. 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 Link. 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., and Rosenfeld, A.,
Digital Topology: Introduction and Survey,
CVGIP(48), No. 3, December 1989, pp. 357-393.
WWW Link. 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.
WWW Link. (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 Link. (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 Link. 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 Link. BibRef 9512

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

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. 9609
Digital 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 Link. 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.,
A Simplified Fold Number Detector for Shapes with Monotonic Radii,
PR(29), No. 6, June 1996, pp. 997-1005.
WWW Link. 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.,
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.
WWW Link. 0005
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 application for hole detection,
PR(34), No. 11, November 2001, pp. 2253-2258.
WWW Link. 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 Link. 0304
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.
WWW Link. 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 Link. 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 Link. 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).
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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
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.
WWW Link. 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.
WWW Link. 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], 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
BibRef

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


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 11, 2017 at 13:31:57