11.14.2 Three Dimensional Geometry and Topology, Computational Geometry

DoCarmo, 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.
WWW Version. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 0701Topological distortions from digitization. Use overlapping balls rather than cubes. BibRef

Stelldinger, P.[Peer],
Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples,
IWCIA08(xx-yy).
WWW Version. 0804 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.
WWW Version. 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. 0804Shape; 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. 0505Reconstruct 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 may work or IEEE-CS DOI may work. 0709 BibRef
Earlier: A2, A1:
Topology Preserving Digitization with FCC and BCC Grids,
IWCIA06(226-240).
WWW Version. 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).
WWW Version. 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 may work or IEEE-CS DOI may work. 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.
WWW Version. 0804 BibRef
Earlier:
Equivalence Between Regular n-G-Maps and n-Surfaces,
IWCIA04(122-136).
WWW Version. 0505n-G-Maps from geometric modeling and computational geometry. n-Surfaces from discrete imagery. 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. IEEE Top Reference. 0207The 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 may work or IEEE-CS DOI may work.
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. IEEE Top Reference. 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. IEEE Top Reference. 0310 BibRef
Earlier:
Bending Invariant Representations for Surfaces,
CVPR01(I:168-174).
IEEE Abstract. IEEE Top Reference. 0110Description 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 may work or IEEE-CS DOI may work. 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. 0505Discrete surface; (26, 6)-Adjacency; Strongly separating; Continuous analogue BibRef

Melin, E.[Erik],
Digital Surfaces and Boundaries in Khalimsky Spaces,
JMIV(28), No. 2, June 2007, pp. 169-177.
WWW Version. 0710 BibRef
Earlier:
How to Find a Khalimsky-Continuous Approximation of a Real-Valued Function,
IWCIA04(351-365).
WWW Version. 0505 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).
WWW Version. 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).
WWW Version. 0512 BibRef

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

Bayro-Corrochano, E.[Eduardo], Machucho-Cadena, R.[Ruben],
Object Manipulation using Fuzzy Logic and Geometric Algebra,
ICPR06(I: 1120-1123).
WWW Version. 0609 BibRef

Ĺström, K.,
Geometrical Computer Vision from Chasles to Today,
SCIA05(182-183).
WWW Version. 0506From projective geometry and photogrammetry to algebraic geometry. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work.
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 9800

Pennec, X.[Xavier], Ayache, N.J.[Nicholas J.],
Randomness and Geometric Figures in Computer Vision,
CVPR96(484-491).
IEEE Abstract. IEEE Top Reference.
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.,
Topological Investigations of Object Models,
ICPR96(I: 110-114).
IEEE DOI may work or IEEE-CS DOI may work. 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 .