11.14.2 Three Dimensional Geometry and Topology, Computational Geometry

Chapter Contents (Back)
Topology. Geometry. See also Digital Topology.

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.
WWW Link. 0501
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.
WWW Link. 0501
BibRef

Boehm, W.,
On Cubics: a Survey,
CGIP(19), No. 3, July 1982, pp. 201-226.
WWW Link. 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.
WWW Link. 0501
BibRef

Fisher, R.B., Orr, M.J.L.,
Solving Geometric Constraints in a Parallel Network,
IVC(6), No. 2, May 1988, pp. 100-106.
WWW Link. BibRef 8805 Edinburgh BibRef

Bribiesca, E.,
A Geometric Structure for Two-Dimensional Shapes and Three-Dimensional Surfaces,
PR(25), No. 5, May 1992, pp. 483-496.
WWW Link. 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., Rosenfeld, A.,
Simple Connectivity Is not Locally Computable for Connected 3D Images,
CVGIP(51), No. 1, July 1990, pp. 87-95.
WWW Link. BibRef 9007

Kovalevsky, V.A.,
Finite Topology as Applied to Image Analysis,
CVGIP(46), No. 2, May 1989, pp. 141-161.
WWW Link. BibRef 8905

Kovalevsky, V.A.[Vladimir A.],
Axiomatic Digital Topology,
JMIV(26), No. 1-2, November 2006, pp. 41-58.
Springer DOI 0701
See also New Concept for Digital Geometry, A. BibRef

Kovalevsky, V.A.,
Algorithms in Digital Geometry Based on Cellular Topology,
IWCIA04(366-393).
Springer DOI 0505
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

Majumder, D.D.,
Topology Preservation in 3D Digital Space,
PR(27), No. 2, February 1994, pp. 295-300.
WWW Link. 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.,
An Index of Topological Preservation for Feature-Extraction,
PR(28), No. 3, March 1995, pp. 381-391.
WWW Link. BibRef 9503

Verri, A., Uras, C.,
Metric-Topological Approach to Shape Representation and Recognition,
IVC(14), No. 3, April 1996, pp. 189-207.
WWW Link. 9607
BibRef

Uras, C.[Claudio], and 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.
WWW Link. 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

Stelldinger, P.[Peer], Köthe, U.[Ullrich],
Towards a general sampling theory for shape preservation,
IVC(23), No. 2, 1 February 2004, pp. 237-248.
WWW Link. 0412
BibRef
Earlier:
Shape Preservation during Digitization: Tight Bounds Based on the Morphing Distance,
DAGM03(108-115).
Springer DOI 0310
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., Kiryati, N.,
Digital Representation Schemes for 3D Curves,
PR(30), No. 11, November 1997, pp. 1803-1816.
WWW Link. 9801
BibRef

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

Mohr, R., Wu, C.K.,
Geometry Based Computer Vision,
IVC(16), No. 1, January 30 1998, pp. 1-2.
WWW Link. 9803
BibRef

Boufama, B.S., Mohr, R., Morin, L.,
Using Geometric-Properties For Automatic Object Positioning,
IVC(16), No. 1, January 30 1998, pp. 27-33.
WWW Link. 9803
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.
WWW Link. 0110
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.
WWW Link. 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.
WWW Link. 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

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], 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.

ISBN: 978-88-470-1940-9.
WWW Link. 1111
BibRef

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


WWW Link. 1208
BibRef

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


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

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

Zeppelzauer, M.[Matthias], Zielinski, B.[Bartosz], Juda, M.[Mateusz], Seidl, M.[Markus],
Topological Descriptors for 3D Surface Analysis,
CTIC16(77-87).
Springer DOI 1608
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

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

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, Morphing .


Last update:Nov 11, 2017 at 13:31:57