11.14.2 Three Dimensional Geometry and Topology, Computational Geometry

CGAL: Computational Geometry Algorithms Library,
2016 Code, Computational Geometry.
WWW Link. 1611

Do Carmo, M.P.,
Differential Geometry of Curves and Surfaces,
Prentice-Hall1976. BibRef 7600

Posdamer, J.L.[Jeffrey L.],
A Vector Development of the Fundamentals of Computational Geometry,
CGIP(6), No. 4, August 1977, pp. 382-393.
Elsevier DOI 0501
From work of Forrest. BibRef

Franklin, W.R.[W. Randolph],
An exact hidden sphere algorithm that operates in linear time,
CGIP(15), No. 4, April 1981, pp. 364-379.
Elsevier DOI 0501
Hidden line algorithm, linear time. BibRef

Boehm, W.[Wolfgang],
On Cubics: a Survey,
CGIP(19), No. 3, July 1982, pp. 201-226.
Elsevier DOI Survey, Cubics. BibRef 8207

Rosenfeld, A.,
Three-Dimensional Digital Topology,
InfoControl(50), 1981, pp. 119-127. BibRef 8100
Earlier: UMD-TR-936, September 1980.
See also Digital Topology: Introduction and Survey. BibRef

Edelsbrunner, H., Overmars, M.H., Seidel, R.,
Some methods of computational geometry applied to computer graphics,
CVGIP(28), No. 1, October 1984, pp. 92-108.
Elsevier DOI 0501
Windowing 2D picture. BibRef

Fisher, R.B.[Robert B.], Orr, M.J.L.[Mark J.L.],
Solving Geometric Constraints in a Parallel Network,
IVC(6), No. 2, May 1988, pp. 100-106.
Elsevier DOI BibRef 8805 EdinburghSolving sets of inequalities. BibRef

Bribiesca, E.[Ernesto],
A Geometric Structure for Two-Dimensional Shapes and Three-Dimensional Surfaces,
PR(25), No. 5, May 1992, pp. 483-496.
Elsevier DOI Uses a representation called Slope Change notation (SCN) which is invariant to translation and rotation. (Angles between adjacent segments in the contour for 2D). BibRef 9205

Lee, C.N.[Chung-Nim], Rosenfeld, A.[Azriel],
Simple Connectivity Is not Locally Computable for Connected 3D Images,
CVGIP(51), No. 1, July 1990, pp. 87-95.
Elsevier DOI simply connected and contractible are locally computable in 2D, but not 3D. BibRef 9007

Kovalevsky, V.A.[Vladimir A.],
Finite Topology as Applied to Image Analysis,
CVGIP(46), No. 2, May 1989, pp. 141-161.
Elsevier DOI BibRef 8905

Kovalevsky, V.A.[Vladimir A.],
Axiomatic Digital Topology,
JMIV(26), No. 1-2, November 2006, pp. 41-58.
Springer DOI 0701
BibRef
Earlier:
Algorithms in Digital Geometry Based on Cellular Topology,
IWCIA04(366-393).
Springer DOI 0505

See also New Concept for Digital Geometry, A. BibRef

Koenderink, J.J., van Doorn, A.J.,
Two-Plus-One-Dimensional Differential Geometry,
PRL(15), No. 5, May 1994, pp. 439-443. Differential Geometry. Multi-scale ridge detection. BibRef 9405

Saha, P.K., Chaudhuri, B.B., Chanda, B., Majumder, D.D.[D. Dutta],
Topology Preservation in 3D Digital Space,
PR(27), No. 2, February 1994, pp. 295-300.
Elsevier DOI 3D topology operations. BibRef 9402

Kong, T.Y., Rosenfeld, A.,
Special Issue on Topology and Geometry in Computer Vision,
JMIV(6), No. 2-3, June 1996, pp. 107-107. 9608
BibRef

Rothwell, C.A.[Charlie A.], Mundy, J.L.[Joe L.], Hoffman, W.[William],
Representing Objects Using Topology,
ORCV96(79) 9611
BibRef

Hall, R.W., Hu, C.Y.,
Time-Efficient Computation of 3D Topological Functions,
PRL(17), No. 9, August 1 1996, pp. 1017-1033. 9609
BibRef

Bezdek, J.C.[James C.], Pal, N.R.[Nikhil R.],
An Index of Topological Preservation for Feature-Extraction,
PR(28), No. 3, March 1995, pp. 381-391.
Elsevier DOI PCA, Sammon and Kohonen self-organizing feature map and preserving order. BibRef 9503

Verri, A.[Alessandro], Uras, C.[Claudio],
Metric-Topological Approach to Shape Representation and Recognition,
IVC(14), No. 3, April 1996, pp. 189-207.
Elsevier DOI 9607
Theory of Size functions. BibRef

Uras, C.[Claudio], Verri, A.[Alessandro],
Computing Size Functions From Edge Maps,
IJCV(23), No. 2, June 1997, pp. 169-183.
DOI Link 9708
BibRef
Earlier:
Studying Shape Through Size Functions,
MDSG94(81). BibRef

Toussaint, G.T.,
Special Issue on Computational Geometry,
PIEEE(80), No. 9, September 1992, pp. 1347-1517. BibRef 9209
And: PRL(14), No. 9, September 1993, pp. 697-748. Editor. BibRef

Dobkin, D.P.,
Computational Geometry and Computer Graphics,
PIEEE(80), No. 9, September 1992, pp. 1400-1411. BibRef 9209

Chiang, Y.J., Tamassia, R.,
Dynamic Algorithms in Computational Geometry,
PIEEE(80), No. 9, September 1992, pp. 1412-1434. BibRef 9209

Atallah, M.J.,
Parallel Techniques For Computational Geometry,
PIEEE(80), No. 9, September 1992, pp. 1435-1448. BibRef 9209

Skiena, S.S.,
Interactive Reconstruction via Geometric Probing,
PIEEE(80), 1992, pp. 1364-1383. BibRef 9200

Goh, S.C., Lee, C.N.,
Counting Minimal 18-Paths in 3D Digital Space,
PRL(14), 1993, pp. 39-52. BibRef 9300

Biswas, S.S., Ray, A.,
Region Merging in 3-D Images Using Morphological Operators,
PRL(14), 1993, pp. 23-30. BibRef 9300

Goh, S.C., Lee, C.N.,
Counting Minimal Paths in 3D Digital Geometry,
PRL(13), 1992, pp. 765-771. BibRef 9200

Chaudhuri, B.B.,
Some Shape Definitions in Fuzzy Geometry of Space,
PRL(12), 1991, pp. 531-535. BibRef 9100

Lee, D.T., Preparata, F.P.,
Computational Geometry: A Survey,
TC(33), 1984, pp. 1072-1101. Survey, Computational Geometry. BibRef 8400

Tang, Y.Y., Suen, C.Y.,
New Algorithms for Fixed and Elastic Geometric Transformation Models,
IP(3), No. 4, July 1994, pp. 355-366.
IEEE DOI BibRef 9407

Latecki, L.J.[Longin Jan],
Discrete Representation of Spatial Objects in Computer Vision,
KluwerJanuary 1998, ISBN 0-7923-4912-1.
WWW Link. BibRef 9801

Latecki, L.J.,
3D Well-Composed Pictures,
GMIP(59), No. 3, May 1997, pp. 164-172. 9708

See also Well-Composed Sets. BibRef

Stelldinger, P.[Peer], Latecki, L.J.[Longin Jan], Siqueira, M.[Marcelo],
Topological Equivalence between a 3D Object and the Reconstruction of Its Digital Image,
PAMI(29), No. 1, January 2007, pp. 126-140.
IEEE DOI 0701
Topological distortions from digitization. Use overlapping balls rather than cubes. BibRef

Stelldinger, P.[Peer], Tcherniavski, L.[Leonid],
Provably correct reconstruction of surfaces from sparse noisy samples,
PR(42), No. 8, August 2009, pp. 1650-1659.
Elsevier DOI 0904
BibRef
Earlier: A1, Only:
Topologically correct surface reconstruction using alpha shapes and relations to ball-pivoting,
ICPR08(1-4).
IEEE DOI 0812
BibRef
And: A1, Only:
Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples,
IWCIA08(xx-yy).
Springer DOI 0804
Surface reconstruction; Topology preservation; Alpha-shapes; Delaunay triangulation BibRef

Stelldinger, P.[Peer], Tcherniavski, L.[Leonid],
Contour Reconstruction for Multiple 2D Regions Based on Adaptive Boundary Samples,
IWCIA09(266-279).
Springer DOI 0911
BibRef

Tcherniavski, L.[Leonid], Bähnisch, C.[Christian], Meine, H.[Hans], Stelldinger, P.[Peer],
How to define a locally adaptive sampling criterion for topologically correct reconstruction of multiple regions,
PRL(33), No. 11, 1 August 2012, pp. 1451-1459.
Elsevier DOI 1206
Nonmanifold surface reconstruction; Topology preservation; Sampling criteria; Point set decimation BibRef

Siqueira, M.[Marcelo], Latecki, L.J.[Longin Jan], Tustison, N.J.[Nicholas J.], Gallier, J.[Jean], Gee, J.C.[James C.],
Topological Repairing of 3D Digital Images,
JMIV(30), No. 3, March 2008, pp. 249-274.
Springer DOI 0802
BibRef

Tustison, N.J., Avants, B.B., Siqueira, M., Gee, J.C.,
Topological Well-Composedness and Glamorous Glue: A Digital Gluing Algorithm for Topologically Constrained Front Propagation,
IP(20), No. 6, June 2011, pp. 1756-1761.
IEEE DOI 1106
BibRef

Stelldinger, P.[Peer], Terzic, K.[Kasim],
Digitization of non-regular shapes in arbitrary dimensions,
IVC(26), No. 10, 1 October 2008, pp. 1338-1346.
Elsevier DOI 0804
Shape; Digitization; Repairing; Topology; Reconstruction; Irregular grid BibRef

Stelldinger, P.[Peer], Latecki, L.J.[Longin Jan],
3D Object Digitization: Majority Interpolation and Marching Cube,
ICPR06(I: 71-74).
IEEE DOI 0609
BibRef
And:
3D Object Digitization: Majority Interpolation and Marching Cubes,
ICPR06(II: 1173-1176).
IEEE DOI 0609
BibRef
And:
3D Object Digitization: Topology Preserving Reconstruction,
ICPR06(III: 693-696).
IEEE DOI 0609
BibRef

Hartley, R.I.[Richard I.], and Zisserman, A.[Andrew],
Multiple View Geometry in Computer Vision,
Cambridge University PressJune 2004. ISBN: 978-0521540518. Second Edition.
HTML Version. Camera Calibration. Epipolar geometry, trifocal tensors. Projective geometry. Single view, 3 view. Buy this book: Multiple View Geometry in Computer Vision BibRef 0406

Stelldinger, P.[Peer], Köthe, U.[Ullrich],
Towards a general sampling theory for shape preservation,
IVC(23), No. 2, 1 February 2004, pp. 237-248.
Elsevier DOI 0412
BibRef
Earlier:
Shape Preservation during Digitization: Tight Bounds Based on the Morphing Distance,
DAGM03(108-115).
Springer DOI 0310
Shape similarity related to human perception, sampling for arbitrary dimensional spaces. BibRef

Stelldinger, P.[Peer],
Shape Preserving Sampling and Reconstruction of Grayscale Images,
IWCIA04(522-533).
Springer DOI 0505
Reconstruct the true image after various samplings. BibRef

Strand, R.[Robin], Stelldinger, P.[Peer],
Topology Preserving Marching Cubes-like Algorithms on the Face-Centered Cubic Grid,
CIAP07(781-788).
IEEE DOI 0709
BibRef
Earlier: A2, A1:
Topology Preserving Digitization with FCC and BCC Grids,
IWCIA06(226-240).
Springer DOI 0606
BibRef

Jonas, A.[Amnon], Kiryati, N.[Nahum],
Digital Representation Schemes for 3D Curves,
PR(30), No. 11, November 1997, pp. 1803-1816.
Elsevier DOI 9801
Compare various descriptions. BibRef

Jonas, A.[Amnon], Kiryati, N.[Nahum],
Length Estimation in 3-D Using Cube Quantization,
JMIV(8), No. 3, May 1998, pp. 215-238.
DOI Link 9804
BibRef

Mohr, R.[Roger], Wu, C.K.[Cheng-Ke],
Geometry Based Computer Vision,
IVC(16), No. 1, January 30 1998, pp. 1-2.
Elsevier DOI 9803
Intro to special issue. BibRef

Boufama, B.S.[Boubakeur S.], Mohr, R.[Roger], Morin, L.[Luce],
Using Geometric-Properties For Automatic Object Positioning,
IVC(16), No. 1, January 30 1998, pp. 27-33.
Elsevier DOI 9803
Position relative to another, e.g. a tool. BibRef

Bertrand, G.[Gilles], Malgouyres, R.[Rémy],
Some Topological Properties of Surfaces in Z3,
JMIV(11), No. 3, December 1999, pp. 207-221.
DOI Link BibRef 9912

Malgouyres, R.[Rémy], Francés, A.R.[Angel R.],
Determining Whether a Simplicial 3-Complex Collapses to a 1-Complex Is NP-Complete,
DGCI08(xx-yy).
Springer DOI 0804
BibRef

Adán, A.[Antonio], Cerrada, C.[Carlos], Feliu, V.[Vicente],
Modeling Wave Set: Definition and Application of a New Topological Organization for 3D Object Modeling,
CVIU(79), No. 2, August 2000, pp. 281-307.
DOI Link 0008
BibRef

Adán, A.[Antonio], Cerrada, C.[Carlos], Feliu, V.[Vicente],
Automatic pose determination of 3D shapes based on modeling wave sets: a new data structure for object modeling,
IVC(19), No. 12, October 2001, pp. 867-890.
Elsevier DOI 0110
Shperical data structure. BibRef

González, E.[Elizabeth], Adán, A.[Antonio], Feliú, V.[Vicente],
2D shape representation and similarity measurement for 3D recognition problems: An experimental analysis,
PRL(33), No. 2, 15 January 2012, pp. 199-217.
Elsevier DOI 1112
3D object recognition; Shape representation; Similarity measures; Shape recognition
See also Active object recognition based on Fourier descriptors clustering.
See also Global shape invariants: a solution for 3D free-form object discrimination/identification problem. BibRef

Fielding, G.[Gabriel], Kam, M.[Moshe],
Computing the Cost of Occlusion,
CVIU(79), No. 2, August 2000, pp. 324-329.
DOI Link 0008
BibRef

Saha, P.K.[Punam K.], Rosenfeld, A.[Azriel],
Determining Simplicity and Computing Topological Change in Strongly Normal Partial Tilings of R^2 or R^3,
PR(33), No. 1, January 2000, pp. 105-118.
Elsevier DOI 0005
BibRef
Earlier: UMD--TR3877, February 1998.
WWW Link. BibRef

Lachaud, J.O.[Jacques-Olivier], Montanvert, A.[Annick],
Continuous Analogs of Digital Boundaries: A Topological Approach to Iso-Surfaces,
GM(62), No. 3, May 2000, pp. 129-164. 0005
BibRef
Earlier:
Digital surfaces as a basis for building isosurfaces,
ICIP98(II: 977-981).
IEEE DOI 9810
BibRef

Alayrangues, S.[Sylvie], Daragon, X.[Xavier], Lachaud, J.O.[Jacques-Olivier], Lienhardt, P.[Pascal],
Equivalence between Closed Connected n-G-Maps without Multi-Incidence and n-Surfaces,
JMIV(32), No. 1, September 2008, pp. xx-yy.
Springer DOI 0804
BibRef
Earlier:
Equivalence Between Regular n-G-Maps and n-Surfaces,
IWCIA04(122-136).
Springer DOI 0505
n-G-Maps from geometric modeling and computational geometry. n-Surfaces from discrete imagery. BibRef

Alayrangues, S.[Sylvie], Peltier, S.[Samuel], Damiand, G.[Guillaume], Lienhardt, P.[Pascal],
Border Operator for Generalized Maps,
DGCI09(300-312).
Springer DOI 0909

See also Removal Operations in nD Generalized Maps for Efficient Homology Computation. BibRef

Peternell, M.[Martin],
Geometric Properties of Bisector Surfaces,
GM(62), No. 3, May 2000, pp. 202-236. 0005
BibRef

Zhu, Q.M.[Qiu-Ming],
On the Geometries of Conic Section Representation of Noisy Object Boundaries,
JVCIR(10), No. 2, June 1999, pp. 130-154. 0010
BibRef

Sommer, G.,
Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics,
Springer-Verlag2001. ISBN 3-540-41198-4. Clifford or Geometric algebra. BibRef 0100

Bülow, T.[Thomas], Klette, R.[Reinhard],
Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm,
PAMI(24), No. 7, July 2002, pp. 962-970.
IEEE Abstract. 0207
The curve is a set of cubes in 3 space, what is the shortest polygonal curve BibRef

Bülow, T.[Thomas], Klette, R.[Reihnard],
Rubber Band Algorithm for Estimating the Length of Digitized Space-curves,
ICPR00(Vol III: 547-551).
IEEE DOI 0009
BibRef

Klette, R.[Reinhard], Yip, B.[Ben],
Evaluation of Curve Length Measurements,
ICPR00(Vol I: 610-613).
IEEE DOI 0009
BibRef

Park, I.K.[In Kyu], Lee, K.M.[Kyoung Mu], Lee, S.U.[Sang Uk],
Models and algorithms for efficient multiresolution topology estimation of measured 3-D range data,
SMC-B(33), No. 4, August 2003, pp. 706-711.
IEEE Abstract. 0308
BibRef

Elad, A.[Asi], Kimmel, R.[Ron],
On bending invariant signatures for surfaces,
PAMI(25), No. 10, October 2003, pp. 1285-1295.
IEEE Abstract. 0310
BibRef
Earlier:
Bending Invariant Representations for Surfaces,
CVPR01(I:168-174).
IEEE DOI 0110
Description invariant to bending. Iosmetric surfaces. Deform the object by bending. BibRef

Sun, M.M., Yang, J.,
Topology Description for Data Distributions Using a Topology Graph With Divide-and-Combine Learning Strategy,
SMC-B(36), No. 6, December 2006, pp. 1296-1305.
IEEE DOI 0701
BibRef

de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.,
Computational Geometry: Algorithms and Applications,
Springer-VerlagBerlin and Heidelberg GmbH & Co., January 2000. ISBN: 3540656200.
WWW Link. BibRef 0001

Boissonnat, J.D., Teillaud, M., (Eds.),
Effective Computational Geometry for Curves and Surfaces,
Springer2006, ISBN 978-3-540-33258-9.
WWW Link. Voronoi surfaces, meshing, triangulation. Differential geometry on surfaces. BibRef 0600

Ciria, J.C., de Miguel, A., Domínguez, E., Francés, A.R., Quintero, A.,
Local characterization of a maximum set of digital (26, 6)-surfaces,
IVC(25), No. 10, 1 October 2007, pp. 1685-1697.
Elsevier DOI 0709
BibRef
Earlier:
A Maximum Set of (26,6)-Connected Digital Surfaces,
IWCIA04(291-306).
Springer DOI 0505
Discrete surface; (26, 6)-Adjacency; Strongly separating; Continuous analogue BibRef

Ciria, J.C., Domínguez, E., Francés, A.R., Quintero, A.,
A plate-based definition of discrete surfaces,
PRL(33), No. 11, 1 August 2012, pp. 1485-1494.
Elsevier DOI 1206
BibRef
Earlier:
Universal Spaces for (k,kbar)-Surfaces,
DGCI09(385-396).
Springer DOI 0909
Digital Topology; Discrete surface; Combinatorial surface; Continuous analogue; Strong separation BibRef

Ciria, J.C., Domínguez, E., Francés, A.R., Quintero, A.,
Generalized Simple Surface Points,
DGCI13(59-70).
Springer DOI 1304
Discrete and Combinatorial Topology BibRef

Melin, E.[Erik],
Digital Surfaces and Boundaries in Khalimsky Spaces,
JMIV(28), No. 2, June 2007, pp. 169-177.
Springer DOI 0710
BibRef
Earlier:
How to Find a Khalimsky-Continuous Approximation of a Real-Valued Function,
IWCIA04(351-365).
Springer DOI 0505
BibRef

Melin, E.[Erik],
Digital Khalimsky Manifolds,
JMIV(33), No. 3, March 2009, pp. xx-yy.
Springer DOI 0903
BibRef

Brimkov, V.E.[Valentin E.], Klette, R.[Reinhard],
Border and Surface Tracing: Theoretical Foundations,
PAMI(30), No. 4, April 2008, pp. 577-590.
IEEE DOI 0803
BibRef
Earlier:
Curves, Hypersurfaces, and Good Pairs of Adjacency Relations,
IWCIA04(276-290).
Springer DOI 0505
BibRef

Brimkov, V.E.[Valentin E.], Maimone, A.[Angelo], Nordo, G.[Giorgio],
Counting Gaps in Binary Pictures,
IWCIA06(16-24).
Springer DOI 0606
BibRef

Brimkov, V.E.[Valentin E.], Maimone, A.[Angelo], Nordo, G.[Giorgio], Barneva, R.P.[Reneta P.], Klette, R.[Reinhard],
The Number of Gaps in Binary Pictures,
ISVC05(35-42).
Springer DOI 0512
BibRef

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.], Brimkov, B.[Boris],
Minimal Offsets That Guarantee Maximal or Minimal Connectivity of Digital Curves in nD,
DGCI09(337-349).
Springer DOI 0909
BibRef

Heyden, A.[Anders], and Pollefeys, M.[Marc],
Multiple View Geometry,
ETCV04(Chapter 3). Survey, Projective Geometry. BibRef 0400

Inselberg, A.[Alfred],
Parallel Coordinates: Visual Multidimensional Geometry and Its Applications,
Springer2009, ISBN: 978-0-387-21507-5
WWW Link. Visualization. Buy this book: Parallel Coordinates: Visual Multidimensional Geometry and Its Applications 0911
BibRef

Ziegel, J.[Johanna], Kiderlen, M.[Markus],
Estimation of surface area and surface area measure of three-dimensional sets from digitizations,
IVC(28), No. 1, Januray 2010, pp. 64-77.
Elsevier DOI 1001
Surface area; Surface area measure; Anisotropy; 3D binary image; Configuration; Gauss digitization; Local method; Rose of normal directions BibRef

Brlek, S.[Srecko], Provencal, X.[Xavier],
Discrete geometry for computer imagery,
PRL(32), No. 9, 1 July 2011, pp. 1355.
Elsevier DOI 1101
Section introduction. BibRef

Gonzalez-Diaz, R.[Rocio], José Jiménez, M.[María], Medrano, B.[Belén], Real Jurado, P.[Pedro],
A tool for integer homology computation: lambda-AT-model,
IVC(27), No. 7, 4 June 2009, pp. 837-845.
Elsevier DOI 0904
BibRef
Earlier:
Extending the Notion of AT-Model for Integer Homology Computation,
GbRPR07(330-339).
Springer DOI 0706
BibRef
And:
A Graph-with-Loop Structure for a Topological Representation of 3D Objects,
CAIP07(506-513).
Springer DOI 0708
Algebraic topological model; nD digital image; Integer homology; Chain complex BibRef

Boutry, N.[Nicolas], Gonzalez-Diaz, R.[Rocio], Jimenez, M.J.[Maria-Jose],
One More Step Towards Well-Composedness of Cell Complexes over nD Pictures,
DGCI19(101-114).
Springer DOI 1905
BibRef

Gonzalez-Diaz, R.[Rocio], Ion, A.[Adrian], Jose Jimenez, M.[Maria], Poyatos, R.[Regina],
Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology,
CAIP11(I: 286-293).
Springer DOI 1109
BibRef

Gonzalez-Diaz, R.[Rocio], Jose Jimenez, M.[Maria], Medrano, B.[Belen],
Cubical Cohomology Ring of 3D Photographs,
IJIST(21), No. 1, 2011, pp. 76-85.
DOI Link cohomology ring, cubical complexes, 3D digital images BibRef 1100

Gonzalez-Diaz, R.[Rocio], Jimenez, M.J.[Maria-Jose], Medrano, B.[Belen],
Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images,
JMIV(59), No. 1, September 2017, pp. 106-122.
Springer DOI 1708
BibRef
Earlier:
Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images,
DGCI16(268-281).
WWW Link. 1606
BibRef

Gonzalez-Diaz, R.[Rocio], Jose Jimenez, M.[Maria], Medrano, B.[Belen], Molina-Abril, H.[Helena], Real Jurado, P.[Pedro],
Integral Operators for Computing Homology Generators at Any Dimension,
CIARP08(356-363).
Springer DOI 0809
BibRef

Gonzalez-Diaz, R.[Rocio], Ion, A.[Adrian], Iglesias-Ham, M.[Mabel], Kropatsch, W.G.[Walter G.],
Invariant Representative Cocycles of Cohomology Generators Using Irregular Graph Pyramids,
CVIU(115), No. 7, July 2011, pp. 1011-1022.
Elsevier DOI 1106
BibRef
Earlier:
Irregular Graph Pyramids and Representative Cocycles of Cohomology Generators,
GbRPR09(263-272).
Springer DOI 0905
Graph pyramids; Representative cocycles of cohomology generators
See also Directly computing the generators of image homology using graph pyramids. BibRef

Gonzalez-Diaz, R.[Rocio], Lamar, J.[Javier], Umble, R.[Ronald],
Cup Products on Polyhedral Approximations of 3D Digital Images,
IWCIA11(107-119).
Springer DOI 1105
BibRef

Gonzalez-Diaz, R.[Rocio], Jose Jimenez, M.[Maria], Medrano, B.[Belen],
Well-Composed Cell Complexes,
DGCI11(153-162).
Springer DOI 1104
transform the cubical complex of a 3D binary digital image into a cell complex that is homotopy equivalent to the first and whose boundary surface is composed by 2D manifolds. BibRef

Perriollat, M.[Mathieu], Hartley, R.I.[Richard I.], Bartoli, A.E.[Adrien E.],
Monocular Template-based Reconstruction of Inextensible Surfaces,
IJCV(95), No. 2, November 2011, pp. 124-137.
WWW Link. 1109
BibRef
Earlier: BMVC08(xx-yy).
PDF File. 0809
Use point correspondence between the image and deformed surface. BibRef

Malti, A.[Abed], Herzet, C.,
Elastic Shape-from-Template with Spatially Sparse Deforming Forces,
CVPR17(143-151)
IEEE DOI 1711
Force, Minimization, Shape, Strain, Transmission, line, matrix, methods BibRef

Malti, A.[Abed], Hartley, R.I.[Richard I.], Bartoli, A.E.[Adrien E.], Kim, J.H.[Jae-Hak],
Monocular Template-Based 3D Reconstruction of Extensible Surfaces with Local Linear Elasticity,
CVPR13(1522-1529)
IEEE DOI 1309
BibRef

Brunet, F.[Florent], Bartoli, A.E.[Adrien E.], Hartley, R.I.[Richard I.],
Monocular template-based 3D surface reconstruction: Convex inextensible and nonconvex isometric methods,
CVIU(125), No. 1, 2014, pp. 138-154.
Elsevier DOI 1406
3D reconstruction BibRef

Brunet, F.[Florent], Hartley, R.I.[Richard I.], Bartoli, A.E.[Adrien E.], Navab, N.[Nassir], Malgouyres, R.[Remy],
Monocular Template-Based Reconstruction of Smooth and Inextensible Surfaces,
ACCV10(III: 52-66).
Springer DOI 1011
BibRef

Abate, M., Tovena, F.,
Curves and Surfaces,
SpringerNew-York, 2012.

Wu, C.J.[Chih-Jen], Tsai, W.H.[Wen-Hsiang],
A Space-Mapping Method for Object Location Estimation Adaptive to Camera Setup Changes for Vision-Based Automation Applications,
CirSysVideo(22), No. 1, January 2012, pp. 157-162.
IEEE DOI 1201
Map object locations based on camera changes. BibRef

Micheli, M.[Mario], Michor, P.W.[Peter W.], Mumford, D.[David],
Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks,
SIIMS(5), No. 1 2012, pp. 394.
DOI Link 1203
BibRef

Micheli, M.[Mario],
Effects of curvature on the analysis of landmark shape manifolds,
ICIP08(1164-1167).
IEEE DOI 0810
BibRef

Baerentzen, J.A., Gravesen, J., Anton, F., Aanaes, H.,
Guide to Computational Geometry Processing: Foundations, Algorithms, and Methods,
Springer2012. ISBN 978-1-4471-4074-0

Wagner, H.[Hubert], Dlotko, P.[Pawel],
Towards topological analysis of high-dimensional feature spaces,
CVIU(121), No. 1, 2014, pp. 21-26.
Elsevier DOI 1404
Computational topology BibRef

Gutierrez, A.[Antonio], Jimenez, M.J.[Maria Jose], Monaghan, D.[David], O'Connor, N.E.[Noel E.],
Topological evaluation of volume reconstructions by voxel carving,
CVIU(121), No. 1, 2014, pp. 27-35.
Elsevier DOI 1404
Voxel carving BibRef

Cabalar, P.[Pedro], Santos, P.E.[Paulo E.],
A qualitative spatial representation of string loops as holes,
AI(238), No. 1, 2016, pp. 1-10.
Elsevier DOI 1608
Spatial representation BibRef

Comic, L.[Lidija], Nagy, B.[Benedek],
A topological 4-coordinate system for the face centered cubic grid,
PRL(83, Part 1), No. 1, 2016, pp. 67-74.
Elsevier DOI 1609
Topological coordinate system BibRef

Kurlin, V.[Vitaliy],
A fast persistence-based segmentation of noisy 2D clouds with provable guarantees,
PRL(83, Part 1), No. 1, 2016, pp. 3-12.
Elsevier DOI 1609
BibRef
Earlier:
A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images,
CAIP15(I:606-617).
Springer DOI 1511
BibRef
Earlier:
A Fast and Robust Algorithm to Count Topologically Persistent Holes in Noisy Clouds,
CVPR14(1458-1463)
IEEE DOI 1409
Delaunay triangulation BibRef

Zeppelzauer, M.[Matthias], Zielinski, B.[Bartosz], Juda, M.[Mateusz], Seidl, M.[Markus],
A study on topological descriptors for the analysis of 3D surface texture,
CVIU(167), 2018, pp. 74-88.
Elsevier DOI 1804
BibRef
Earlier:
Topological Descriptors for 3D Surface Analysis,
CTIC16(77-87).
Springer DOI 1608
Surface texture analysis, 3D surface classification, Surface topology analysis, Surface representation, Persistence image BibRef

Gonzalez-Lorenzo, A.[Aldo], Juda, M.[Mateusz], Bac, A.[Alexandra], Mari, J.L.[Jean-Luc], Real, P.[Pedro],
Fast, Simple and Separable Computation of Betti Numbers on Three-Dimensional Cubical Complexes,
CTIC16(130-139).
Springer DOI 1608
Betti Numbers: count the number of holes of each dimension in a space BibRef

Gonzalez-Lorenzo, A.[Aldo], Bac, A.[Alexandra], Mari, J.L.[Jean-Luc], Real, P.[Pedro],
Two Measures for the Homology Groups of Binary Volumes,
DGCI16(154-165).
WWW Link. 1606
Topology. BibRef

Alderson, T.[Troy], Mahdavi-Amiri, A.[Ali], Samavati, F.F.[Faramarz F.],
Offsetting spherical curves in vector and raster form,
VC(34), No. 6-8, June 2018, pp. 973-984.
Springer DOI 1806
inside/outside testing for vectors. BibRef

Molina-Abril, H.[Helena], Real, P.[Pedro], Díaz-del-Río, F.[Fernando],
Generating (co)homological information using boundary scale,
PRL(133), 2020, pp. 240-246.
Elsevier DOI 2005
Geometric cell complex, Algebraic-topological model, Scale-space model, Homology groups, Hierarchical graph BibRef

Real, P.[Pedro], Molina-Abril, H.[Helena], Díaz del Río, F.[Fernando], Onchis, D.M.[Darian M.],
Generating Second Order (Co)homological Information within AT-Model Context,
CTIC19(68-81).
Springer DOI 1901
Algebraic Topological Model. BibRef

Zheng, P.F.[Peng-Fei], Liu, Q.[Qing], Lou, J.J.[Jing-Jing], Lian, C.J.[Cheng-Jie], Lin, D.J.[Da-Jun],
A free-form surface flattening algorithm that minimizes geometric deformation energy,
IET-IPR(16), No. 9, 2022, pp. 2544-2556.
DOI Link 2206
Surface flatening -- more commone in mechanical, manufacturing engineering areas. BibRef

Nagy, B.[Benedek], Saadat, M.R.[Mohammad-Reza],
Digital geometry on a cubic stair-case mesh,
PRL(164), 2022, pp. 140-147.
Elsevier DOI 2212
Cubic mesh, Semi-regular grids, Nontraditional grids, Digital distance, Rhombille tessellation, Path-based distance, Pixel geometry BibRef

Reani, Y.[Yohai], Bobrowski, O.[Omer],
Cycle Registration in Persistent Homology With Applications in Topological Bootstrap,
PAMI(45), No. 5, May 2023, pp. 5579-5593.
IEEE DOI 2304
Measurement, Point cloud compression, Shape, Kernel, Machine learning, Data analysis, Viterbi algorithm, wasserstein distance. BibRef

Aumentado-Armstrong, T.[Tristan], Tsogkas, S.[Stavros], Dickinson, S.J.[Sven J.], Jepson, A.D.[Allan D.],
Disentangling Geometric Deformation Spaces in Generative Latent Shape Models,
IJCV(131), No. 7, July 2023, pp. 1611-1641.
Springer DOI 2307
BibRef
Earlier: A1, A2, A4, A3:
Geometric Disentanglement for Generative Latent Shape Models,
ICCV19(8180-8189)
IEEE DOI 2004
computational geometry, image representation, neural nets, shape recognition, solid modelling, Geometry BibRef

Aumentado-Armstrong, T.[Tristan], Tsogkas, S.[Stavros], Dickinson, S.J.[Sven J.], Jepson, A.D.[Allan D.],
Representing 3D Shapes with Probabilistic Directed Distance Fields,
CVPR22(19321-19332)
IEEE DOI 2210
Surface reconstruction, Solid modeling, Shape, Scalability, Rendering (computer graphics), Probabilistic logic, Vision + graphics BibRef

Bhardwaj, K.[Kartikeya], Li, G.H.[Gui-Hong], Marculescu, R.[Radu],
How does topology influence gradient propagation and model performance of deep networks with DenseNet-type skip connections?,
CVPR21(13493-13502)
IEEE DOI 2111
Measurement, Training, Image coding, Artificial neural networks, Mathematical models, Topology BibRef

Pang, J.H.[Jia-Hao], Li, D.S.[Duan-Shun], Tian, D.[Dong],
TearingNet: Point Cloud Autoencoder to Learn Topology-Friendly Representations,
CVPR21(7449-7458)
IEEE DOI 2111
Deep learning, Surface reconstruction, Network topology, Shape, Topology, Pattern recognition, Proposals BibRef

Boutry, N.[Nicolas], Gonzalez-Diaz, R.[Rocio], Najman, L.[Laurent], Géraud, T.[Thierry],
A 4d Counter-example Showing that DWCNess Does Not Imply CWCness in nD,
IWCIA20(73-87).
Springer DOI 2009
Continuous Well-Composedness. Digital Well-Composedness BibRef

Chibane, J., Alldieck, T., Pons-Moll, G.,
Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion,
CVPR20(6968-6979)
IEEE DOI 2008
Shape, Image reconstruction, Topology, Feature extraction, Tensile stress BibRef

Haim, N., Segol, N., Ben-Hamu, H., Maron, H., Lipman, Y.,
Surface Networks via General Covers,
ICCV19(632-641)
IEEE DOI 2004
convolutional neural nets, image representation, learning (artificial intelligence), neural net architecture, Topology BibRef

Trager, M.[Matthew], Hebert, M.[Martial], Ponce, J.[Jean],
Coordinate-Free Carlsson-Weinshall Duality and Relative Multi-View Geometry,
CVPR19(225-233).
IEEE DOI 2002
BibRef

Biswas, R.[Ranita], Largeteau-Skapin, G.[Gaëlle], Zrour, R.[Rita], Andres, E.[Eric],
Rhombic Dodecahedron Grid: Coordinate System and 3D Digital Object Definitions,
DGCI19(27-37).
Springer DOI 1905
Non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. BibRef

Dey, T.K.[Tamal K.], Hou, T.[Tao], Mandal, S.[Sayan],
Persistent 1-Cycles: Definition, Computation, and Its Application,
CTIC19(123-136).
Springer DOI 1901
BibRef

Liao, Y., Donné, S., Geiger, A.[Andreas],
Deep Marching Cubes: Learning Explicit Surface Representations,
CVPR18(2916-2925)
IEEE DOI 1812
Shape, Surface reconstruction, Topology, Face, Surface treatment, Solid modeling BibRef

Thopalli, K.[Kowshik], Devi, S., Thiagarajan, J.J.[Jayaraman J.],
InterAug: A Tuning-Free Augmentation Policy for Data-Efficient and Robust Object Detection,
VIPriors23(253-261)
IEEE DOI Code:
WWW Link. 2401
BibRef

Som, A.[Anirudh], Thopalli, K.[Kowshik], Ramamurthy, K.N.[Karthikeyan Natesan], Venkataraman, V.[Vinay], Shukla, A.[Ankita], Turaga, P.[Pavan],
Perturbation Robust Representations of Topological Persistence Diagrams,
ECCV18(VII: 638-659).
Springer DOI 1810
BibRef

Ulm, M.[Michael], Brändle, N.[Norbert],
Learning tubes,
ICPR16(3655-3660)
IEEE DOI 1705
Clustering algorithms, Computational modeling, Electron tubes, Manifolds, Mathematical model, Noise level, Probes BibRef

Itoh, H.[Hayato], Imiya, A.[Atsushi], Sakai, T.[Tomoya],
Mathematical Aspects of Tensor Subspace Method,
SSSPR16(37-48).
Springer DOI 1611
BibRef

Yu, L.F., Duncan, N., Yeung, S.K.,
Fill and Transfer: A Simple Physics-Based Approach for Containability Reasoning,
ICCV15(711-719)
IEEE DOI 1602
liquid containability. From depth data. Cognition BibRef

Zulkifli, N.A., Rahman, A.A., van Oosterom, P.,
An Overview of 3D Topology for LADM-Based Objects,
GeoInfo15(71-73).
DOI Link 1602
BibRef

Boutry, N.[Nicolas], Geraud, T.[Thierry], Najman, L.[Laurent],
How to make nD images well-composed without interpolation,
ICIP15(2149-2153)
IEEE DOI 1512
Digital Topology; Mathematical Morphology; Well-Composed Sets; nD images BibRef

Stühmer, J.[Jan], Cremers, D.[Daniel],
A Fast Projection Method for Connectivity Constraints in Image Segmentation,
EMMCVPR15(183-196).
Springer DOI 1504
BibRef

Oswald, M.R.[Martin Ralf], Stühmer, J.[Jan], Cremers, D.[Daniel],
Generalized Connectivity Constraints for Spatio-temporal 3D Reconstruction,
ECCV14(IV: 32-46).
Springer DOI 1408
BibRef

Gueorguieva, S., Synave, R., Couture-Veschambre, C.,
Teaching Geometric Modeling Algorithms and Data Structures through Laser Scanner Acquisition Pipeline,
ISVC10(II: 416-428).
Springer DOI 1011
BibRef

Lenz, R.[Reiner], Mochizuki, R.[Rika], Chao, J.H.[Jin-Hui],
Iwasawa Decomposition and Computational Riemannian Geometry,
ICPR10(4472-4475).
IEEE DOI 1008
BibRef

Kafai, M.[Mehran], Miao, Y.[Yiyi], Okada, K.[Kazunori],
Directional mean shift and its application for topology classification of local 3D structures,
MMBIA10(170-177).
IEEE DOI 1006
Transform the 3D problem into 2D clustering problem. BibRef

Song, D.J.[Dong-Jin], Tao, D.C.[Da-Cheng],
Discrminative Geometry Preserving Projections,
ICIP09(2457-2460).
IEEE DOI 0911
BibRef

Berciano, A.[Ainhoa], Molina-Abril, H.[Helena], Pacheco, A.[Ana], Pilarczyk, P.[Pawel], Real Jurado, P.[Pedro],
Decomposing Cavities in Digital Volumes into Products of Cycles,
DGCI09(263-274).
Springer DOI 0909
BibRef

Amari, S.I.[Shun-Ichi],
Information Geometry and Its Applications: Convex Function and Dually Flat Manifold,
ETVC08(75-102).
Springer DOI 0811
BibRef

Matsuzoe, H.[Hiroshi],
Computational Geometry from the Viewpoint of Affine Differential Geometry,
ETVC08(103-123).
Springer DOI 0811
BibRef

Rémi, S.[Synave], Stefka, G.[Gueorguieva], Pascal, D.[Desbarats],
Constraint Shortest Path Computation on Polyhedral Surfaces,
ICCVGIP08(366-373).
IEEE DOI 0812
BibRef

Mercat, C.[Christian],
Discrete Complex Structure on Surfel Surfaces,
DGCI08(xx-yy).
Springer DOI 0804
BibRef

Cardoze, D.E.[David E.], Miller, G.L.[Gary L.], Phillips, T.[Todd],
Representing Topological Structures Using Cell-Chains,
GMP06(248-266).
Springer DOI 0607
Surface representation. BibRef

Åström, K.,
Geometrical Computer Vision from Chasles to Today,
SCIA05(182-183).
Springer DOI 0506
From projective geometry and photogrammetry to algebraic geometry. BibRef

Fourey, S.[Sébastien],
Simple Points and Generic Axiomatized Digital Surface-Structures,
IWCIA04(307-317).
Springer DOI 0505
BibRef

Kopperman, R.[Ralph], Pfaltz, J.L.[John L.],
Jordan Surfaces in Discrete Antimatroid Topologies,
IWCIA04(334-350).
Springer DOI 0505
BibRef

Yang, L.[Li],
Tetrahedron mapping of points from n-space to three-space,
ICPR02(IV: 343-346).
IEEE DOI 0211
BibRef

Kenmochi, Y.[Yukiko], Imiya, A.[Atsushi], Nomura, T.[Toshiaki], Kotani, K.[Kazunori],
Extraction of Topological Features from Sequential Volume Data,
VF01(333 ff.).
Springer DOI 0209
BibRef

Kolcun, A.,
NonConformity Problem in 3D Grid Decompositions,
WSCG02(249).
HTML Version. 0209
BibRef

Aguilera Ramírez, A.[Antonio], Pérez Aguila, R.[Ricardo],
A Method for Obtaining the Tesseract by Unraveling the 4D Hypercube,
WSCG02(1).
HTML Version. 0209
BibRef

Aloimonos, Y.,
Harmonic Computational Geometry: A new tool for visual correspondence,
BMVC02(Invited Talk). 0208
BibRef

Yui, S., Hara, K., Zha, H.B.[Hong-Bin], Hasegawa, T.,
A fast narrow band method and its application in topology-adaptive 3-D modeling,
ICPR02(IV: 122-125).
IEEE DOI 0211
BibRef

Chao, J.H.[Jin-Hui], Nakajima, M.[Masaki], Okada, S.[Shintaro],
A Hierarchical Invariant Representation of Spatial Topology of 3D Objects and Its Application to Object Recognition,
ICPR00(Vol I: 920-923).
IEEE DOI 0009
BibRef

Faugeras, O.D.,
From Geometry to Variational Calculus: Theory and Applications of Three-Dimensional Vision,
CVVRHC98(Merging CG and Real Images, Augmented Reality). BibRef 9808

Pennec, X.[Xavier], Ayache, N.J.[Nicholas J.],
Randomness and Geometric Figures in Computer Vision,
CVPR96(484-491).
IEEE DOI BibRef 9600

Choi, Y.[Young],
Vertex-Based Boundary Representations of Non-Manifold Geometric Models,
Ph.D.Dept of Mechanical Engineering, Carnegie Mellon University, August, 1989 BibRef 8908

Uray, P., Pinz, A.J.,
Topological Investigations of Object Models,
ICPR96(I: 110-114).
IEEE DOI 9608
(TU Graz, A) BibRef

Chapter on 3-D Object Description and Computation Techniques, Surfaces, Deformable, View Generation, Video Conferencing continues in
Virtual View Generation, View Synthesis, Image Based Rendering, IBR .