7.2.3 Digital Geometry

Chapter Contents (Back)
Discrete Topology. Digital Geometry.
See also General Spatial Reasoning and Geometric Reasoning Issues, Visual Relations.

Pavlidis, T.[Theo],
Filling Algorithms for Raster Graphics,
CGIP(10), No. 2, June 1979, pp. 126-141.
Elsevier DOI Filling irregular polygons. BibRef 7906

Davis, L.S.[Larry S.], Benedikt, M.L.[Michael L.],
Computational Models of Space: Isovists and Isovist Fields,
CGIP(11), No. 1, September 1979, pp. 49-72.
Elsevier DOI BibRef 7909

Kim, C.E.,
Digital Disks,
PAMI(6), No. 3, May, 1984, pp. 372-374. BibRef 8405

Bennett, J.R., MacDonald, J.S.,
On the Measurement of Curvature in a Quantized Environment,
TC(24), 1975, pp. 803-820. BibRef 7500

Eccles, M.J., McQueen, M.P.C., Rosen, D.,
Analysis of the Digitized Boundaries of Planar Objects,
PR(9), No. 1, January 1977, pp. 31-41.
Elsevier DOI points, or directions, or curvatures for boundary. BibRef 7701

Jagoe, R.[Roger], Paton, K.[Keith],
Generalized Counting in digital Pictures,
CGIP(7), No. 1, February 1978, pp. 52-66.
Elsevier DOI Evaluate chest x ray anaysis. BibRef 7802

Wiejak, J.S.,
Region Digitization and Boundary Estimation,
IVC(1), No. 2, May 1983, pp. 99-102.
Elsevier DOI BibRef 8305

Melter, R.A.[Robert A.], Tomescu, I.[Ioan],
Metric Bases in Digital Geometry,
CVGIP(25), No. 1, January 1984, pp. 113-121.
Elsevier DOI BibRef 8401

Harary, F., Melter, R.A., Tomescu, I.,
Digital Metrics: A Graph-Theoretical Approach,
PRL(2), 1984, pp. 159-163. BibRef 8400

Medek, V.,
Culling Hidden Edges of Rectangular Parallelpipeds,
CVGIP(28), No. 2, November 1984, pp. 263-268.
Elsevier DOI BibRef 8411

Kanatani, K.I.[Ken-Ichi],
Constraints on Length and Angle,
CVGIP(41), No. 1, January 1988, pp. 28-42.
Elsevier DOI Perspective projection of line segments on image plane. BibRef 8801

Sarnak, N., Tarjan, R.E.,
Planar Point Location Using Persistent Search Trees,
CACM(29), No. 7, July 1986, pp. 669-679. BibRef 8607

Toussaint, G.T.[Godfried T.],
The Relative Neighbourhood Graph of a Finite Planar Set,
PR(12), No. 4, 1980, pp. 261-268.
Elsevier DOI 0309
Graph for structure. related to MST. BibRef

Houle, M.E., Toussaint, G.T.,
Computing the Width of a Set,
PAMI(10), No. 5, September 1988, pp. 761-765.
IEEE DOI BibRef 8809

Bogomolny, A.,
Digital Geometry May Not Be Discrete,
CVGIP(43), No. 2, August 1988, pp. 205-220. image part number.
Elsevier DOI BibRef 8808

Wolfson, E., Schwartz, E.L.,
Computing Minimal Distance on Polyhedral Surfaces,
PAMI(11), No. 9, September 1989, pp. 1001-1005.
IEEE DOI BibRef 8909

Schwartz, E.L., Shaw, A., Wolfson, E.,
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces,
PAMI(11), No. 9, September 1989, pp. 1005-1008.
IEEE DOI BibRef 8909

Ansari, N.[Nirwan], Delp, E.J.[Edward J.],
On the Distribution of a Deforming Triangle,
PR(23), No. 12, 1990, pp. 1333-1341.
Elsevier DOI Sphericity. Similarity between triangles. BibRef 9000

Nakamura, A.,
Continuous-Functions on Fuzzy Digital Pictures,
PRL(17), No. 5, May 1 1996, pp. 557-563. 9606
BibRef

Zunic, J.,
A Representation of Digital Hyperbolas Y=1/X Alpha+Beta,
PRL(17), No. 9, August 1 1996, pp. 975-983. 9609
BibRef

Rosenfeld, A., Haber, S.,
The Perimeter of a Fuzzy Set,
PR(18), No. 2, 1985, pp. 125-130.
Elsevier DOI BibRef 8500
Earlier: summary: PR(17), No. 6, 1984, pp. Page 678.
Elsevier DOI Set is not crisp, what is really the boundary? BibRef

Rosenfeld, A.[Azriel], Klette, R.[Reinhard],
Degree of Adjacency or Surroundedness,
PR(18), No. 2, 1985, pp. 169-177.
Elsevier DOI BibRef 8500
Earlier: Abstract: PR(17), No. 6, 1984, pp. 678.
Elsevier DOI How adjacent are 2 regions? BibRef

Ching, Y.T., Lee, D.T.,
Finding the Diameter of a Set of Lines,
PR(18), No. 3-4, 1985, pp. 249-255.
Elsevier DOI n straight lines. O(n log n) for diameter. BibRef 8500

Rosenfeld, A.,
Fuzzy Plane Geometry: Triangles,
PRL(15), 1994, pp. 1261-1264. BibRef 9400

Kulkarni, S.R., Mitter, S.K., Richardson, T.J., Tsitsiklis, J.N.,
Local Versus Nonlocal Computation of Length of Digitized-Curves,
PAMI(16), No. 7, July 1994, pp. 711-718.
IEEE DOI BibRef 9407

Maio, D., Maltoni, D., Razzi, S.,
Topological Clustering of Maps Using a Genetic Algorithm,
PRL(16), 1995, pp. 89-96. BibRef 9500

Rosenfeld, A.,
Geometric Properties of Sets of Lines,
PRL(16), 1995, pp. 549-556. BibRef 9500

Veelaert, P.[Peter],
Periodic Differences of Digitized Curves,
PRL(14), 1993, pp. 169-172. BibRef 9300

Veelaert, P.[Peter],
Selecting Appropriate Difference Operators for Digital Images by Local Feature Detection,
JEI(6), No. 4, October 1997, pp. 415-425. 9807
BibRef

Veelaert, P.[Peter], Teelen, K.[Kristof],
Adaptive and optimal difference operators in image processing,
PR(42), No. 10, October 2009, pp. 2317-2326.
Elsevier DOI 0906
BibRef
Earlier:
Optimal Difference Operator Selection,
DGCI08(xx-yy).
Springer DOI 0804
Difference operator; Grobner basis; Local feature detector; Tangent; Laplacian BibRef

Cimikowski, R.J.,
Properties of Some Euclidean Proximity Graphs,
PRL(13), 1992, pp. 417-423. BibRef 9200

Rhodes, F.,
Discrete Euclidean Metrics,
PRL(13), 1992, pp. 623-628. BibRef 9200

Parui, S.K.,
Some Geometric Operations on Binary Pictures and Their Shape Preserving Properties,
PRL(11), 1990, pp. 355-361. BibRef 9000
Earlier:
Shape preserving properties of some operations on binary pictures,
ICPR88(II: 773-775).
IEEE DOI 8811
BibRef

van Vliet, L.J., Verwer, B.J.H.,
A Contour Processing Method for Fast Binary Neighbourhood Operations,
PRL(7), 1988, pp. 27-36. BibRef 8800

Rosenfeld, A.,
'Continuous' Functions on Digital Pictures,
PRL(4), 1986, pp. 177-184. BibRef 8600

Melter, R.A.,
You Can (Sometimes) Tell an Image by Its Cover,
PRL(3), 1985, pp. 59-64. BibRef 8500

Rosenfeld, A.,
The Fuzzy Geometry Of Image Subsets,
PRL(2), 1984, pp. 311-317. BibRef 8400

Dyer, C.R.[Charles R.], Rosenfeld, A.,
Parallel Image Processing by Memory-Augmented Cellular Automata,
PAMI(3), No. 1, January 1981, pp. 29-41. Cellular Automata. BibRef 8101

Dyer, C.R.[Charles R.], Rosenfeld, A.,
Triangle Cellular Automata,
InfoControl(48), No. 1, January 1981, pp. 54-69. BibRef 8101

Latecki, L.J.[Longin Jan], Eckhardt, U., Rosenfeld, A.,
Well-Composed Sets,
CVIU(61), No. 1, January 1995, pp. 70-83.
DOI Link
See also 3D Well-Composed Pictures. BibRef 9501

Latecki, L.J.[Longin Jan], Prokop, F.,
Semi-Proximity Continuous-Functions in Digital Images,
PRL(16), No. 11, November 1995, pp. 1175-1187. BibRef 9511

Latecki, L.J.[Longin Jan], Rosenfeld, A.[Azriel],
Supportedness and Tameness Differentialless Geometry of Plane-Curves,
PR(31), No. 5, May 1998, pp. 607-622.
Elsevier DOI 9805
Planar arcs to describe parts of boundaries. BibRef

Giraldo, A.[Antonio], Gross, A.D.[Ari D.], Latecki, L.J.[Longin Jan],
Digitizations preserving shape,
PR(32), No. 3, March 1999, pp. 365-376.
Elsevier DOI BibRef 9903

Rieger, J.H.,
Topographical Properties of Generic Images,
IJCV(23), No. 1, May 1997, pp. 79-92.
DOI Link 9708
BibRef

Kenmochi, Y.[Yukiko], Imiya, A.[Atsushi], Ichikawa, A.[Akira],
Discrete Combinatorial Geometry,
PR(30), No. 10, October 1997, pp. 1719-1728.
Elsevier DOI 9712
BibRef

Daragon, X.[Xavier], Couprie, M.[Michel], Bertrand, G.[Gilles],
Discrete Surfaces and Frontier Orders,
JMIV(23), No. 3, November 2005, pp. 379-399.
Springer DOI 0510
BibRef

Couprie, M.[Michel], Bertrand, G.[Gilles], Kenmochi, Y.[Yukiko],
Discretization in 2D and 3D orders,
GM(65), No. 1-3, May 2003, pp. 77-91.
Elsevier DOI 0309
BibRef

Bertrand, G.[Gilles],
Completions and Simple Homotopy,
DGCI14(63-74).
Springer DOI 1410
BibRef
Earlier:
New Structures Based on Completions,
DGCI13(83-94).
Springer DOI 1304
BibRef
Earlier:
Completions and Simplicial Complexes,
DGCI11(129-140).
Springer DOI 1104

See also On Topological Watersheds. BibRef

Kenmochi, Y.[Yukiko], Imiya, A.[Atsushi],
Combinatorial boundary of a 3D lattice point set,
JVCIR(17), No. 4, August 2006, pp. 738-766.
Elsevier DOI 0711
Boundary extraction; Combinatorial surface; Polyhedral complex BibRef

Kenmochi, Y.[Yukiko], Nomura, Y.[Yusuke],
Local configurations in discrete combinatorial surfaces,
IVC(25), No. 10, 1 October 2007, pp. 1657-1670.
Elsevier DOI 0709
Discrete surface; Local configurations; Polyhedral complex BibRef

Thibault, Y.[Yohan], Sugimoto, A.[Akihiro], Kenmochi, Y.[Yukiko],
Hinge Angles for 3D Discrete Rotations,
IWCIA09(122-134).
Springer DOI 0911
BibRef

Mecke, J.,
On the relationship between the 0-cell and the typical cell of a stationary random tessellation,
PR(32), No. 9, September 1999, pp. 1645-1648.
Elsevier DOI the O-cell is larger than average -- analysis. BibRef 9909

Worboys, M.[Michael],
Imprecision in Finite Resolution Spatial Data,
GeoInfo(2), No. 3, October 1998, pp. 257-279.
DOI Link BibRef 9810

Holbling, W.[Werner], Kuhn, W.[Werner], Frank, A.U.[Andrew U.],
Finite-Resolution Simplicial Complexes,
GeoInfo(2), No. 3, October 1998, pp. 281-298.
DOI Link BibRef 9810

Bykov, A.I.[Alexander I.], Zerkalov, L.G.[Leonid G.], Pineda, M.A.R.[Mario A. Rodríguez],
Index of a point of 3-D digital binary image and algorithm for computing its Euler characteristic,
PR(32), No. 5, May 1999, pp. 845-850.
Elsevier DOI Characterization of simple points in 3D BibRef 9905

van Lieshout, M.N.M.,
Size-biased random closed sets,
PR(32), No. 9, September 1999, pp. 1631-1644.
Elsevier DOI Analysis of random sets. BibRef 9909

Brass, P.[Peter],
On strongly normal tesselations,
PRL(20), No. 8, August 1999, pp. 957-960. BibRef 9908

Kendall, W.S.[Wilfrid S.], Thoennes, E.[Elke],
Perfect simulation in stochastic geometry,
PR(32), No. 9, September 1999, pp. 1569-1586.
Elsevier DOI Simulation. Kinds of samples. BibRef 9909

Rosenfeld, A.[Azriel], Saha, P.K.[Punam K.], Nakamura, A.[Akira],
Interchangeable pairs of pixels in two-valued digital images,
PR(34), No. 9, September 2001, pp. 1853-1865.
Elsevier DOI 0108
reversing adjacent values preserves topology. Prove one exists in simply connected sets. BibRef

Kong, T.Y.[T. Yung], Saha, P.K.[Punam Kumar], Rosenfeld, A.[Azriel],
Strongly normal sets of contractible tiles in N dimensions,
PR(40), No. 2, February 2007, pp. 530-543.
Elsevier DOI 0611
Strongly normal; n-Dimensional; Contractible; Shared subset BibRef

Saha, P.K.[Punam K.], Kong, T.Y.[T. Yung], Rosenfeld, A.[Azriel],
Strongly Normal Sets of Tiles in N Dimensions,
UMD--TR4242, April 2001.
WWW Link. Tiles, generalizations of pixels. BibRef 0104

Rosenfeld, A.[Azriel], Saha, P.K.[Punam K.],
Interchangeable Pairs of Pixels in Digital Images,
UMD--TR4057, September 1999.
WWW Link. Topology of binary images (2 valued) where pixel values are interchanged. BibRef 9909

Klette, R.[Reinhard],
Digital Geometry: The Birth of a New Discipline,
FIU01(Chapter 2). BibRef 0100

Ronse, C.[Christian], Tajine, M.[Mohamed],
Discretization in Hausdorff Space,
JMIV(12), No. 3, June 2000, pp. 219-242.
DOI Link 0003
BibRef

Ronse, C.[Christian], Tajine, M.[Mohamed],
Hausdorff Discretization for Cellular Distances and Its Relation to Cover and Supercover Discretizations,
JVCIR(12), No. 2, June 2001, pp. 169-200.
DOI Link 0201
BibRef

Tajine, M.[Mohamed],
Digital Segments and Hausdorff Discretization,
IWCIA08(xx-yy).
Springer DOI 0804
BibRef

Mercer, R.E., Barron, J.L., Bruen, A.A., Cheng, D.,
Fuzzy points: algebra and application,
PR(35), No. 5, May 2002, pp. 1153-1166.
Elsevier DOI 0202
BibRef

Udupa, J.K.[Jayaram K.], Grevera, G.J.[George J.],
Go digital, go fuzzy,
PRL(23), No. 6, April 2002, pp. 743-754.
Elsevier DOI 0202
BibRef

Borgefors, G.[Gunilla], Nyström, I.[Ingela], Sanniti di Baja, G.[Gabriella],
Special Issue: Discrete Geometry for Computer Imagery,
PRL(23), No. 6, April 2002, pp. 621.
Elsevier DOI 0202
BibRef

Nyström, I.[Ingela], Sanniti di Baja, G.[Gabriella], Svensson, S.[Stina],
Discrete Geometry for Computer Imagery Introduction,
IVC(23), No. 2, 1 February 2004, pp. 87-88.
Elsevier DOI 0412
Intro. BibRef

Grossmann, R.[Ruth], Kiryati, N.[Nahum], Kimmel, R.[Ron],
Computational Surface Flattening: A Voxel-Based Approach,
PAMI(24), No. 4, April 2002, pp. 433-441.
IEEE DOI 0204
BibRef
Earlier: VF01(196-204).
Springer DOI Turning a voxel surface into 2-D. Use to map 2-D textures onto the surface. Also related cortex analysis papers.
See also Estimating Shortest Paths and Minimal Distances on Digitized Three-Dimensional Surfaces.
See also Length Estimation in 3-D Using Cube Quantization. BibRef

Hajdu, A.[András],
Geometry of neighbourhood sequences,
PRL(24), No. 15, November 2003, pp. 2597-2606.
Elsevier DOI 0308
Generalize results of (
See also Octagonal Distances For Digital Pictures. ) about geometric properties of two-dimensional periodic neighbourhood sequences. BibRef

Fazekas, A.[Attila], Hajdu, A.[András], Hajdu, L.[Lajos],
Metrical neighborhood sequences in Zn,
PRL(26), No. 13, 1 October 2005, pp. 2022-2032.
Elsevier DOI 0509
BibRef

Hajdu, A., Nagy, B., Zorgo, Z.,
Indexing and segmenting colour images using neighbourhood sequences,
ICIP03(I: 957-960).
IEEE DOI 0312
BibRef

Fazekas, A., Hajdu, A., Sánta, I., Tóth, T.,
Neighborhood Sequences and Their Applications in the Digital Image Processing,
CAIP05(766).
Springer DOI 0509

See also Skeletonization Based on Metrical Neighborhood Sequences. BibRef

Hajdu, A.[Andras], Toth, T.[Tamas],
Approximating non-metrical Minkowski distances in 2D,
PRL(29), No. 6, 15 April 2008, pp. 813-821.
Elsevier DOI 0803
Minkowski distance; Discrete approximation; Neighborhood sequence; Chamfering; Geometry BibRef

Lachaud, J.O.[Jacques-Olivier], Vialard, A.[Anne],
10th International Conference on Discrete Geometry for Computer Imagery: Discrete topology and geometry for image and object representation,
GM(65), No. 1-3, May 2003, pp. Page 1.
Elsevier DOI 0309
Overview of issue. BibRef

Coeurjolly, D.[David], Miguet, S., Tougne, L.,
2D and 3D Visibility in Discrete Geometry: An Application to Discrete Geodesic Paths,
PRL(25), No. 5, 5 April 2004, pp. 561-570.
Elsevier DOI 0403
Visibility definintion. BibRef

Ricard, J., Coeurjolly, D., Baskurt, A.[Atilla],
Generalization of angular radial transform,
ICIP04(IV: 2211-2214).
IEEE DOI 0505
BibRef

Zunic, J.[Jovisa],
On the Number of Digital Discs,
JMIV(21), No. 3, November 2004, pp. 199-204.
DOI Link 0410
Disc is a set of N integer points inside a real disc. BibRef

Huxley, M.N.[Martin N.], Žunic, J.[Joviša],
The Number of N-Point Digital Discs,
PAMI(29), No. 1, January 2007, pp. 159-161.
IEEE DOI 0701
BibRef
Earlier:
On the Number of Digitizations of a Disc Depending on Its Position,
IWCIA04(219-231).
Springer DOI 0505
Refine the upper bound on the number. BibRef

Huxley, M.N.[Martin N.], Žunic, J.[Joviša],
The Number of Different Digital N-Discs,
JMIV(56), No. 3, November 2016, pp. 403-408.
WWW Link. 1609
BibRef

di Mambro, E.[Emmanuel], Haïdar, R.[Riad], Guérineau, N.[Nicolas], Primot, J.[Jérôme],
Sharpness limitations in the projection of thin lines by use of the Talbot experiment,
JOSA-A(21), No. 12, December 2004, pp. 2276-2282.
WWW Link. 0501
BibRef

Pavlidis, T.[Theo],
Discrete geometry and Azriel Rosenfeld,
PRL(26), No. 3, February 2005, pp. 235-238.
Elsevier DOI 0501
Reflection on Azriel Rosenfeld's life work. BibRef

Xu, D., Do, M.N.,
On the Number of Rectangular Tilings,
IP(15), No. 10, October 2006, pp. 3225-3230.
IEEE DOI 0609
BibRef

Li, F.J.[Fa-Jie], Klette, R.[Reinhard],
Analysis of the rubberband algorithm,
IVC(25), No. 10, 1 October 2007, pp. 1588-1598.
Elsevier DOI 0709
BibRef
And:
Euclidean Shortest Paths in Simple Cube Curves at a Glance,
CAIP07(661-668).
Springer DOI 0708
BibRef
Earlier:
Finding the Shortest Path Between Two Points in a Simple Polygon by Applying a Rubberband Algorithm,
PSIVT06(280-291).
Springer DOI 0612
BibRef
Earlier:
Shortest Paths in a Cuboidal World,
IWCIA06(415-429).
Springer DOI 0606
Digital geometry; Shortest Euclidean path; Cube-curves; Minimum-length polygonal curve
See also Decomposing a Simple Polygon into Trapezoids. BibRef

Li, F.J.[Fa-Jie], Klette, R.[Reinhard],
Approximate Shortest Paths in Simple Polyhedra,
DGCI11(513-524).
Springer DOI 1104
BibRef
Earlier:
An Approximate Algorithm for Solving the Watchman Route Problem,
RobVis08(189-206).
Springer DOI 0802
BibRef

Li, F.J.[Fa-Jie], Klette, R.[Reinhard],
Calculating the Number of Tunnels,
CIARP08(421-428).
Springer DOI 0809
BibRef

Li, F.J.[Fa-Jie], Klette, R.[Reinhard], Fu, X.[Xue],
Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm,
PSIVT07(236-247).
Springer DOI 0712
Euclidean shortest path. BibRef

Deng, M.[Min], Cheng, T.[Tao], Chen, X.Y.[Xiao-Yong], Li, Z.L.[Zhi-Lin],
Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants,
GeoInfo(11), No. 2, June 2007, pp. 239-267.
Springer DOI 0709
BibRef

Deng, M.[Min], Li, Z.L.[Zhi-Lin],
A Statistical Model for Directional Relations Between Spatial Objects,
GeoInfo(12), No. 2, June 2008, pp. xx-yy.
Springer DOI 0804
BibRef

Suhadolnik, A.[Alojz], Petrisic, J.[Joze], Kosel, F.[Franc],
Numerical calculation of digital curve length by using anchored discrete convolution,
IVC(26), No. 7, 2 July 2008, pp. 990-999.
Elsevier DOI 0804
Digital curve; Curve length; Anchored discrete convolution; Digital image BibRef

Skala, V.[Vaclav],
Length, Area And Volume Computation In Homogeneous Coordinates,
IJIG(6), No. 4, October 2006, pp. 625-639. 0610
BibRef

Skala, V.[Vaclav],
Intersection Computation In Projective Space Using Homogeneous Coordinates,
IJIG(8), No. 4, October 2008, pp. 615-628. 0804
BibRef

Balasubramanian, M.[Mukund], Polimeni, J.R.[Jonathan R.], Schwartz, E.L.[Eric L.],
Exact Geodesics and Shortest Paths on Polyhedral Surfaces,
PAMI(31), No. 6, June 2009, pp. 1006-1016.
IEEE DOI 0904
Computing distances along convex and non-convex polyhedral surfaces. Either exact minimal-geodesic paths or shortest paths. Runtime is Cubic or less. Apply to mesh generation for brain data. BibRef

Gerard, Y.[Yan], Coeurjolly, D.[David], Feschet, F.[Fabien],
Gift-Wrapping Based Preimage Computation Algorithm,
PR(42), No. 10, October 2009, pp. 2255-2264.
Elsevier DOI 0906
BibRef
Earlier: A1, A3, A2: DGCI08(xx-yy).
Springer DOI 0804
Digital geometry; Convex hull; Gift-wrapping; Visibility cone; Chords set BibRef

Gerard, Y.[Yan],
Reconstructing a Matrix with a Given List of Coefficients and Prescribed Row and Column Sums Is NP-Hard,
IWCIA08(xx-yy).
Springer DOI 0804
BibRef

Faure, A.[Alexandre], Buzer, L.[Lilian], Feschet, F.[Fabien],
Tangential Cover for Thick Digital Curves,
PR(42), No. 10, October 2009, pp. 2279-2287.
Elsevier DOI 0906
BibRef
Earlier: A1, A3, Only: DGCI08(xx-yy).
Springer DOI 0804
Digital geometry; Tangential cover; Digital segments; Alpha-thickness; Convex hull; Thick digital curves BibRef

Faure, A.[Alexandre], Feschet, F.[Fabien],
Linear Decomposition of Planar Shapes,
ICPR10(1096-1099).
IEEE DOI 1008
BibRef

Faure, A.[Alexandre], Feschet, F.[Fabien],
Multi-primitive Analysis of Digital Curves,
IWCIA09(30-42).
Springer DOI 0911
BibRef
Earlier:
Robust Decomposition of Thick Digital Shapes,
IWCIA08(xx-yy).
Springer DOI 0804
BibRef

Feschet, F.[Fabien],
Multiscale Analysis from 1D Parametric Geometric Decomposition of Shapes,
ICPR10(2102-2105).
IEEE DOI 1008
BibRef

Feschet, F.[Fabien],
The lattice width and quasi-straightness in digital spaces,
ICPR08(1-4).
IEEE DOI 0812
BibRef
Earlier:
The Exact Lattice Width of Planar Sets and Minimal Arithmetical Thickness,
IWCIA06(25-33).
Springer DOI 0606
BibRef

Chollet, A., Wallet, G., Fuchs, L., Largeteau-Skapin, G.[Gaëlle], Andres, É.[Éric],
Insight in discrete geometry and computational content of a discrete model of the continuum,
PR(42), No. 10, October 2009, pp. 2220-2228.
Elsevier DOI 0906
Discrete geometry; Nonstandard analysis; Arithmetization; Constructive mathematics BibRef

Suhadolnik, A.[Alojz], Petrišic, J.[Jože], Kosel, F.[Franc],
Digital Curve Length Calculation by Using B-spline,
JMIV(38), No. 2, October 2010, pp. 132-138.
WWW Link. 1011
BibRef

Srijuntongsiri, G.[Gun],
An iterative/subdivision hybrid algorithm for curve/curve intersection,
VC(27), No. 5, May 2011, pp. 365-371.
WWW Link. 1101
BibRef

Ahmad, O.S.[Ola Suleiman], Debayle, J.[Johan], Pinoli, J.C.[Jean-Charles],
A geometric-based method for recognizing overlapping polygonal-shaped and semi-transparent particles in gray tone images,
PRL(32), No. 15, 1 November 2011, pp. 2068-2079.
Elsevier DOI 1112
Salient corner detection; Contour detection; Clustering method; Overlapping particles recognition BibRef

Pinoli, J.C.[Jean-Charles], Debayle, J.[Johan],
General adaptive distance transforms on gray tone images: Application to image segmentation,
ICIP11(2845-2848).
IEEE DOI 1201
BibRef

Rivollier, S.[Séverine], Debayle, J.[Johan], Pinoli, J.C.[Jean-Charles],
Adaptive Shape Diagrams for Multiscale Morphometrical Image Analysis,
JMIV(49), No. 1, May 2014, pp. 51-68.
Springer DOI 1404
BibRef
Earlier:
Shape representation and analysis of 2D compact sets by shape diagrams,
IPTA10(411-416).
IEEE DOI 1007
BibRef

Presles, B.[Benoît], Debayle, J.[Johan], Pinoli, J.C.[Jean-Charles],
Shape recognition from shadows of 3-D convex geometrical objects,
ICIP12(509-512).
IEEE DOI 1302
BibRef

Presles, B.[Benoît], Debayle, J.[Johan], Maillot, Y.[Yvan], Pinoli, J.C.[Jean-Charles],
Automatic Recognition of 2D Shapes from a Set of Points,
ICIAR11(I: 183-192).
Springer DOI 1106

See also Shape Reconstruction from an Unorganized Point Cloud with Outliers. BibRef

Lagarrigue, M.[Marthe], Debayle, J.[Johan], Jacquier, S.[Sandra], Gruy, F.[Frédéric], Pinoli, J.C.[Jean-Charles],
Geometrical Characterization of Various Shaped 3D-Aggregates of Primary Spherical Particules by Radial Distribution Functions,
ICIAR10(II: 434-443).
Springer DOI 1006
BibRef

Presles, B.[Benoit], Debayle, J.[Johan], Cameirao, A.[Ana], Fevotte, G.[Gilles], Pinoli, J.C.[Jean-Charles],
Volume estimation of 3D particles with known convex shapes from its projected areas,
IPTA10(399-404).
IEEE DOI 1007
BibRef

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Discretization of Parametrizable Signal Manifolds,
IP(20), No. 12, December 2011, pp. 3621-3633.
IEEE DOI 1112
BibRef
Earlier:
Curvature analysis of pattern transformation manifolds,
ICIP10(2689-2692).
IEEE DOI 1009
For transformation invariant analysis. One discretizzation for multiple patterns to minimize error distances. BibRef

Vural, E.[Elif], Frossard, P.[Pascal],
Learning Smooth Pattern Transformation Manifolds,
IP(22), No. 4, April 2013, pp. 1311-1325.
IEEE DOI 1303
BibRef
Earlier:
Learning pattern transformation manifolds for classification,
ICIP12(1165-1168).
IEEE DOI 1302
BibRef

Brimkov, V.E.[Valentin E.], Barneva, R.P.[Reneta P.], (Eds.)
Digital Geometry Algorithms,
Springer2012, ISBN: 978-94-007-4173-7

WWW Link. 1205
Survey, Digital Geometry. BibRef

Chen, L.M.[Li M.],
Digital Functions and Data Reconstruction: Digital-Discrete Methods,
Springer2013. ISBN: 978-1-4614-5637-7

WWW Link. 1212

See also Continuous Functions on Digital Pictures. Theory of digital functions and applications. 3D data reconstruction - Curve and surface fitting - Digital function - Digital geometry - Digital-discrete method - Gradually varied function - Image segmentation - Partial differential equation - Smooth function BibRef

Li, X.W.[Xiao-Wu], Xin, Q.[Qiao], Wu, Z.N.[Zhi-Nan], Zhang, M.S.[Ming-Sheng], Zhang, Q.[Qian],
A geometric strategy for computing intersections of two spatial parametric curves,
VC(29), No. 11, November 2013, pp. 1151-1158.
Springer DOI 1310
BibRef

Eisa, S.A.N.[Sameh Abdelwahab Nasr],
Numerical Curve Length Calculation Using Polynomial Interpolation,
JMIV(49), No. 2, June 2014, pp. 377-383.
WWW Link. 1405
BibRef

Edelsbrunner, H.[Herbert], Pausinger, F.[Florian],
Stable Length Estimates of Tube-Like Shapes,
JMIV(50), No. 1-2, September 2014, pp. 164-177.
WWW Link. 1408
BibRef

Fabbri, R.[Ricardo], Kimia, B.B.[Benjamin B.],
Multiview Differential Geometry of Curves,
IJCV(120), No. 3, December 2016, pp. 324-346.
Springer DOI 1609
BibRef
Earlier:
High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching,
EMMCVPR05(645-660).
Springer DOI 0601
BibRef

Usumezbas, A.[Anil], Fabbri, R.[Ricardo], Kimia, B.B.[Benjamin B.],
From Multiview Image Curves to 3D Drawings,
ECCV16(IV: 70-87).
Springer DOI 1611
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Soto Sánchez, J.E.[José Ezequiel], Medeiros e Sá, A.[Asla], de Figueiredo, L.H.[Luiz Henrique],
Acquiring periodic tilings of regular polygons from images,
VC(35), No. 6-8, June 2018, pp. 899-907.
Springer DOI 1906
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Boutry, N.[Nicolas], Géraud, T.[Thierry], Najman, L.[Laurent],
How to Make n-D Plain Maps Defined on Discrete Surfaces Alexandrov-Well-Composed in a Self-Dual Way,
JMIV(61), No. 6, July 2019, pp. 849-873.
Springer DOI 1907
BibRef
Earlier:
How to Make nD Functions Digitally Well-Composed in a Self-dual Way,
ISMM15(561-572).
Springer DOI 1506

See also Well-Composed Sets. BibRef

Tosaka, K.[Kouki], Imiya, A.[Atsushi],
alpha-Pixels for Hierarchical Analysis of Digital Objects,
SSVM23(665-676).
Springer DOI 2307
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Fernique, T.[Thomas], Hashemi, A.[Amir], Sizova, O.[Olga],
Compact Packings of the Plane with Three Sizes of Discs,
DGCI19(420-431).
Springer DOI 1905
BibRef

Aveneau, L.[Lilian], Fuchs, L.[Laurent], Andres, E.[Eric],
Digital Geometry from a Geometric Algebra Perspective,
DGCI14(358-369).
Springer DOI 1410
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Li, F.J.[Fa-Jie], Pan, X.[Xiuxia],
An Approximation Algorithm for Computing Minimum-Length Polygons in 3D Images,
ACCV10(IV: 641-652).
Springer DOI 1011
Euclidean shortest path (ESP) to be calculated in a loop of face-connected grid cubes in the 3D orthogonal grid, which are defined by minimum-length polygonal (MLP) curves. How to compute the MLP
See also Analysis of the rubberband algorithm. BibRef

Chollet, A.[Agathe], Wallet, G.[Guy], Andres, E.[Eric], Fuchs, L.[Laurent], Largeteau-Skapin, G.[Gaëlle], Richard, A.[Aurélie],
Omega-Arithmetization of Ellipses,
CompIMAGE10(24-35).
Springer DOI 1006
BibRef

Chollet, A.[Agathe], Wallet, G.[Guy], Fuchs, L.[Laurent], Andres, E.[Eric], Largeteau-Skapin, G.[Gaëlle],
Omega-Arithmetization: A Discrete Multi-resolution Representation of Real Functions,
IWCIA09(316-329).
Springer DOI 0911
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Said, M.[Mouhammad], Lachaud, J.O.[Jacques-Olivier], Feschet, F.[Fabien],
Multiscale Analysis of Digital Segments by Intersection of 2D Digital Lines,
ICPR10(4097-4100).
IEEE DOI 1008
BibRef
Earlier:
Multiscale Discrete Geometry,
DGCI09(118-131).
Springer DOI 0909
BibRef

Kock, A.[Anders],
Affine Connections, and Midpoint Formation,
DGCI09(13-21).
Springer DOI 0909
Synthetic differential geometry. BibRef

Chen, L.[Li], Rong, Y.[Yongwu],
Linear time recognition algorithms for topological invariants in 3D,
ICPR08(1-4).
IEEE DOI 0812
BibRef

Guru, D.S., Prakash, H.N., Vikram, T.N.,
Spatial Topology of Equitemporal Points on Signatures for Retrieval,
PReMI07(128-135).
Springer DOI 0712
BibRef

Herley, C.,
Efficient inscribing of noisy rectangular objects in scanned images,
ICIP04(IV: 2399-2402).
IEEE DOI 0505
BibRef

Nouvel, B.[Bertrand],
Self-similar Discrete Rotation Configurations and Interlaced Sturmian Words,
DGCI08(xx-yy).
Springer DOI 0804
BibRef

Nouvel, B.[Bertrand], Rémila, É.[Éric],
Incremental and Transitive Discrete Rotations,
IWCIA06(199-213).
Springer DOI 0606
BibRef
Earlier:
Characterization of Bijective Discretized Rotations,
IWCIA04(248-259).
Springer DOI 0505
BibRef

Malandain, G.[Gregoire], Boissonnat, J.D.[Jean-Danie],
Computing the Diameter of a Point Set,
INRIARR-4233, July 2001.
HTML Version. 0211
BibRef

Chassery, J.M., Dupont, F., Sivignon, I., Vittone, J.,
Digital geometry fundaments: application to plane recognition,
CIAP01(622-636).
IEEE DOI 0210
BibRef

Klette, R.[Reinhard], Zunic, J.[Jovisa],
Multigrid Error Bounds for Moments of Arbitrary Order,
ICPR00(Vol III: 782-785).
IEEE DOI 0009
Errors for quantization errors in computing moments. BibRef

Khuller, S.[Samir], Rosenfeld, A.[Azriel], Wu, A.[Angela],
Centers of Pixels,
UMD--TR3866, January 1998.
WWW Link. BibRef 9801

Wagner, D.[Daniel],
Distance de Hausdorff et probleme discret-continu,
MastersThesis (in French), 1997. Universite Louis Pasteur.
PS File. BibRef 9700

Baratoff, G.[Gregory],
Distortions of stereoscopic visual space and quadratic Cremona transformations,
CAIP97(239-246).
Springer DOI 9709
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Leite, J.A.F.[José A. F.], Hancock, E.R.[Edwin R.],
A linear discriminator of width,
CIAP95(477-482).
Springer DOI 9509
BibRef

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Digital Geometry -- Lines, Curves and Contours .

Last update:Aug 31, 2023 at 09:37:21