11.14.2 Three Dimensional Geometry and Topology, Computational Geometry

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 Version. 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 Version. 0501
BibRef

Boehm, W.,
On Cubics: a Survey,
CGIP(19), No. 3, July 1982, pp. 201-226.
WWW Version. 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 Version. 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 Version. 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 Version. 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 Version. BibRef 9007

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

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

Kovalevsky, V.A.,
Algorithms in Digital Geometry Based on Cellular Topology,
IWCIA04(366-393).
WWW Version. 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 Version. 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 Version. BibRef 9503

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

Uras, C.[Claudio], and Verri, A.[Alessandro],
Computing Size Functions From Edge Maps,
IJCV(23), No. 2, June 1997, pp. 169-183.
WWW Version. 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 Link BibRef 9407

Latecki, L.J.[Longin Jan],
Discrete Representation of Spatial Objects in Computer Vision,
KluwerJanuary 1998, ISBN 0-7923-4912-1.
WWW Version. 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 Link 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 Link
WWW Version. 0904
BibRef
Earlier: A1, Only:
Topologically correct surface reconstruction using alpha shapes and relations to ball-pivoting,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef
And: A1, Only:
Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples,
IWCIA08(xx-yy).
Springer DOI Link 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 Link 0911
BibRef

Siqueira, M.[Marcelo], Latecki, L.J.[Longin Jan], Tustison, N.[Nicholas], Gallier, J.[Jean], Gee, J.[James],
Topological Repairing of 3D Digital Images,
JMIV(30), No. 3, March 2008, pp. 249-274.
Springer DOI Link 0802
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 Version. 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).
WWW Version. 0609
BibRef
And:
3D Object Digitization: Majority Interpolation and Marching Cubes,
ICPR06(II: 1173-1176).
WWW Version. 0609
BibRef
And:
3D Object Digitization: Topology Preserving Reconstruction,
ICPR06(III: 693-696).
WWW Version. 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 Version. 0412
BibRef
Earlier:
Shape Preservation during Digitization: Tight Bounds Based on the Morphing Distance,
DAGM03(108-115).
HTML Version. 0310
BibRef

Stelldinger, P.[Peer],
Shape Preserving Sampling and Reconstruction of Grayscale Images,
IWCIA04(522-533).
WWW Version. 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 Link 0709
BibRef
Earlier: A2, A1:
Topology Preserving Digitization with FCC and BCC Grids,
IWCIA06(226-240).
Springer DOI Link 0606
BibRef

Jonas, A., Kiryati, N.,
Digital Representation Schemes for 3D Curves,
PR(30), No. 11, November 1997, pp. 1803-1816.
WWW Version.
WWW Version. 9801
BibRef

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

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

Bertrand, G.[Gilles], Malgouyres, R.[Rémy],
Some Topological Properties of Surfaces in Z3,
JMIV(11), No. 3, December 1999, pp. 207-221.
WWW Version. 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 Link 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. 0008

WWW Version. 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 Version. 0110
BibRef

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

WWW Version. 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 Version. 0005
BibRef
Earlier: UMD--TR3877, February 1998.
WWW Version.
WWW Version. 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 Link 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 Link 0804
BibRef
Earlier:
Equivalence Between Regular n-G-Maps and n-Surfaces,
IWCIA04(122-136).
WWW Version. 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 Link 0909
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: 551-555).
HTML Version. 0009
BibRef

Klette, R.[Reinhard], Yip, B.[Ben],
Evaluation of Curve Length Measurements,
ICPR00(Vol I: 610-613).
IEEE DOI Link
HTML Version. 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 Abstract. 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 Link 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 Version. BibRef 0001

Boissonnat, J.D., Teillaud, M., (Eds.),
Effective Computational Geometry for Curves and Surfaces,
Springer2006, ISBN 978-3-540-33258-9.
WWW Version. 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 Version. 0709
BibRef
Earlier:
A Maximum Set of (26,6)-Connected Digital Surfaces,
IWCIA04(291-306).
WWW Version. 0505
Discrete surface; (26, 6)-Adjacency; Strongly separating; Continuous analogue BibRef

Ciria, J.C., Domínguez, E., Francés, A.R., Quintero, A.,
Universal Spaces for (k,kbar)-Surfaces,
DGCI09(385-396).
Springer DOI Link 0909
BibRef

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

Melin, E.[Erik],
Digital Khalimsky Manifolds,
JMIV(33), No. 3, March 2009, pp. xx-yy.
Springer DOI Link 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.
WWW Version. 0803
BibRef
Earlier:
Curves, Hypersurfaces, and Good Pairs of Adjacency Relations,
IWCIA04(276-290).
WWW Version. 0505
BibRef

Brimkov, V.E.[Valentin E.], Maimone, A.[Angelo], Nordo, G.[Giorgio],
Counting Gaps in Binary Pictures,
IWCIA06(16-24).
Springer DOI Link 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 Link 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 Link 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 Version. 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 Link
WWW Version. 1001
Surface area; Surface area measure; Anisotropy; 3D binary image; Configuration; Gauss digitization; Local method; Rose of normal directions BibRef

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

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

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

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

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

Mercat, C.[Christian],
Discrete Complex Structure on Surfel Surfaces,
DGCI08(xx-yy).
Springer DOI Link 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 Link 0607
Surface representation. BibRef

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

Brunet, F.[Florent], Bartoli, A.E.[Adrien E.], Navab, N.[Nassir], Malgouyres, R.[Rémy],
Nurbs Warps,
BMVC09(xx-yy).
PDF Version. 0909
BibRef

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

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

Yang, L.[Li],
Tetrahedron mapping of points from n-space to three-space,
ICPR02(IV: 343-346).
IEEE DOI Link 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.).
HTML Version. 0209
BibRef

Kolcun, A.,
NonConformity Problem in 3D Grid Decompositions,
WSCG02(249).
Postscript Version.
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).
PDF Version.
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 Link
HTML Version. 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 Abstract.
WWW Version. 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 Link 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 .