7.3.3 Medial Axis Transform, MAT, Skeletons in Three Dimensions

Bertrand, G., Malandain, G.,
A Note on Building Skeleton Models Via 3-D Medial Surface Axis Thinning Algorithms,
GMIP(57), No. 6, November 1995, pp. 537-538. BibRef 9511

Turkiyyah, G.M., Storti, D.W., Ganter, M., Chen, H., Vimawala, M.,
An Accelerated Triangulation Method for Computing the Skeletons of Free-Form Solid Models,
CAD(29), No. 1, January 1997, pp. 5-19. 9702
BibRef

Pudney, C.,
Distance-Ordered Homotopic Thinning: A Skeletonization Algorithm for 3D Digital Images,
CVIU(72), No. 3, December 1998, pp. 404-413.
WWW Version. BibRef 9812

Borgefors, G.[Gunilla], Nyström, I.[Ingela], Sanniti di Baja, G.[Gabriella],
Computing skeletons in three dimensions,
PR(32), No. 7, July 1999, pp. 1225-1236.
WWW Version. BibRef 9907

Sanniti di Baja, G.[Gabriella], Nyström, I.[Ingela], Borgefors, G.[Gunilla],
Discrete 3D Tools Applied to 2D Grey-Level Images,
CIAP05(229-236).
Springer DOI Link 0509
BibRef

Svensson, S.[Stina], Borgefors, G.[Gunilla], Nyström, I.[Ingela],
On Reversible Skeletonization Using Anchor-Points from Distance Transforms,
JVCIR(10), No. 4, December 1999, pp. 379-397. 0010
BibRef

Svensson, S.[Stina], Nyström, I.[Ingela], Borgefors, G.[Gunilla],
Fully Reversible Skeletonization for Volume Images Based on Anchor-Points from the D^26 Distance Transform,
SCIA99(Image Analysis). BibRef 9900

Svensson, S.[Stina], Borgefors, G.[Gunilla],
Digital Distance Transforms in 3D Images Using Information from Neighbourhoods up to 5×5×5,
CVIU(88), No. 1, October 2002, pp. 24-53.
WWW Version. 0301
BibRef
Earlier: A2, A1:
Fuzzy border distance transforms and their use in 2d skeletonization,
ICPR02(I: 180-183).
IEEE DOI Link 0211
BibRef

Ma, C.M.[Cherng-Min], Wan, S.Y.[Shu-Yen],
A medial-surface oriented 3-d two-subfield thinning algorithm,
PRL(22), No. 13, November 2001, pp. 1439-1446.
Elsevier DOI Link 0108
BibRef

Chatzis, V., Pitas, I.,
Interpolation of 3-D binary images based on morphological skeletonization,
MedImg(19), No. 7, July 2000, pp. 699-710.
IEEE Top Reference. 0110
BibRef

Lee, T.Y.[Tong-Yee], Wang, W.H.[Wen-Hsiu],
Morphology-based three-dimensional interpolation,
MedImg(19), No. 7, July 2000, pp. 711-721.
IEEE Top Reference. 0110
BibRef

Jonker, P.P.[Pieter P.],
Skeletons in N dimensions using shape primitives,
PRL(23), No. 6, April 2002, pp. 677-686.
Elsevier DOI Link 0202
BibRef

Ma, C.M.[Cherng-Min], Wan, S.Y.[Shu-Yen], Chang, H.K.[Her-Kun],
Extracting medial curves on 3D images,
PRL(23), No. 8, June 2002, pp. 895-904.
Elsevier DOI Link 0204
BibRef

Giblin, P.J.[Peter J.], Kimia, B.B.[Benjamin B.],
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks,
IJCV(54), No. 1-3, August 2003, pp. 143-157.
WWW Version. 0306
BibRef
Earlier: ICCV99(385-391).
IEEE DOI Link BibRef

Giblin, P.J.[Peter J.], Kimia, B.B.[Benjamin B.],
A Formal Classification of 3D Medial Axis Points and their Local Geometry,
PAMI(26), No. 2, February 2004, pp. 238-251.
IEEE Abstract. 0402
BibRef
Earlier: CVPR00(I: 566-573).
IEEE Abstract.
IEEE DOI Link 0005
BibRef

Pollitt, A.[Anthony], Giblin, P.J.[Peter J.], Kimia, B.B.[Benjamin B.],
Consistency Conditions on the Medial Axis,
ECCV04(Vol II: 530-541).
WWW Version. 0405
BibRef

Giblin, P.J.[Peter J.], Kimia, B.B.[Benjamin B.],
On the Intrinsic Reconstruction of Shape from its Symmetries,
PAMI(25), No. 7, July 2003, pp. 895-911.
IEEE Abstract. 0307
BibRef
Earlier: CVPR99(II: 79-84).
IEEE Abstract.
IEEE DOI Link BibRef

Giblin, P.J.[Peter J.], Kimia, B.B.[Benjamin B.], Pollitt, A.J.[Anthony J.],
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations,
PAMI(31), No. 5, May 2009, pp. 900-918.
IEEE DOI Link 0903
BibRef
Earlier: A1, A2, Only: ECCV02(II: 718 ff.).
HTML Version. 0205
Minimal information to generate closed, non-intersecting boundaries. BibRef

Diatta, A.[André], Giblin, P.J.[Peter J.],
Geometry of Isophote Curves,
ScaleSpace05(50-61).
WWW Version. 0505
BibRef

Attali, D., Montanvert, A.,
Computing and Simplifying 2D and 3D Continuous Skeletons,
CVIU(67), No. 3, September 1997, pp. 261-273.
WWW Version. 9710
BibRef
Earlier:
Modeling noise for a better simplification of skeletons,
ICIP96(III: 13-16).
IEEE DOI Link 9610
BibRef

Attali, D., Bertolino, P., Montanvert, A.,
Using Polyballs to Approximate Shapes and Skeletons,
ICPR94(A:626-628).
IEEE DOI Link BibRef 9400

Bonnassie, A., Peyrin, F., Attali, D.,
A new method for analyzing local shape in three-dimensional images based on medial axis transformation,
SMC-B(33), No. 4, August 2003, pp. 700-705.
IEEE Abstract. 0308
BibRef
Earlier:
Shape Description of Three-dimensional Images Based on Medial Axis,
ICIP01(III: 931-934).
IEEE Abstract. 0108
BibRef

Attali, D., Lachaud, J.O.[Jacques-Olivier],
Constructing iso-surfaces satisfying the Delaunay constraint. Application to the skeleton computation,
CIAP99(382-387).
IEEE DOI Link 9909
BibRef

Fadili, M.J., Melkemi, M., El Moataz, A.,
Non-convex onion-peeling using a shape hull algorithm,
PRL(25), No. 14, 15 October 2004, pp. 1577-1585.
WWW Version. 0410
BibRef

Shah, J.[Jayant],
Gray skeletons and segmentation of shapes,
CVIU(99), No. 1, July 2005, pp. 96-109.
WWW Version. 0506
BibRef

Shah, J.[Jayant],
Skeletons of 3D Shapes,
ScaleSpace05(339-350).
WWW Version. 0505
BibRef

Strand, R.[Robin], Borgefors, G.[Gunilla],
Distance transforms for three-dimensional grids with non-cubic voxels,
CVIU(100), No. 3, December 2005, pp. 294-311.
WWW Version. 0512
BibRef

Strand, R.[Robin],
Sampling and Ideal Reconstruction on the 3D Diamond Grid,
ICPR10(4609-4612).
IEEE DOI Link 1008
BibRef

Strand, R.[Robin],
Using the Hexagonal Grid for Three-Dimensional Images: Direct Fourier Method Reconstruction and Weighted Distance Transform,
ICPR06(II: 1169-1172).
IEEE DOI Link 0609
BibRef
Earlier:
The Euclidean Distance Transform Applied to the FCC and BCC Grids,
IbPRIA05(I:243).
Springer DOI Link 0509
BibRef
Earlier:
Surface skeletons in grids with non-cubic voxels,
ICPR04(I: 548-551).
IEEE DOI Link 0409
BibRef

Strand, R.[Robin],
Weighted distances based on neighbourhood sequences,
PRL(28), No. 15, 1 November 2007, pp. 2029-2036.
WWW Version. 0711
BibRef
Earlier:
Weighted Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids,
SCIA07(452-461).
Springer DOI Link 0706
Digital geometry; Distance functions; Neighbourhood sequences; Weighted distance; Discrete geometry BibRef

Nagy, B.[Benedek], Strand, R.[Robin],
Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors,
IJIST(19), No. 2, June 2009, pp. 146-157.
WWW Version. 0905
BibRef
Earlier: A2, A2:
Weighted Neighborhood Sequences in Non-standard Three-Dimensional Grids: Parameter Optimization,
IWCIA08(xx-yy).
Springer DOI Link 0804
BibRef
And: A2, A2:
Weighted Neighbourhood Sequences in Non-Standard Three-Dimensional Grids: Metricity and Algorithms,
DGCI08(xx-yy).
Springer DOI Link 0804
BibRef
Earlier: A1, A2:
Approximating Euclidean Distance Using Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids,
IWCIA06(89-100).
Springer DOI Link 0606
See also Isoperimetrically Optimal Polygons in the Triangular Grid. BibRef

Nagy, B.[Benedek], Strand, R.[Robin],
Neighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids,
IWCIA09(96-108).
Springer DOI Link 0911
BibRef

Nagy, B.[Benedek], Strand, R.[Robin],
A Connection between Z n and Generalized Triangular Grids,
ISVC08(II: 1157-1166).
Springer DOI Link 0812
BibRef

Nagy, B.[Benedek], Strand, R.[Robin],
Neighborhood Sequences in the Diamond Grid: Algorithms with Four Neighbors,
IWCIA09(109-121).
Springer DOI Link 0911
BibRef

Cornea, N.D.[Nicu D.], Silver, D.[Deborah], Yuan, X.S.[Xiao-Song], Balasubramanian, R.[Raman],
Computing hierarchical curve-skeletons of 3D objects,
VC(21), No. 11, October 2005, pp. 945-955.
Springer DOI Link 0511
BibRef

Biasotti, S.[Silvia], Attali, D.[Dominique], Boissonnat, J.D.[Jean-Daniel], Edelsbrunner, H.[Herbert], Elber, G.[Gershon], Mortara, M.[Michela], Sanniti di Baja, G.[Gabriella], Spagnuolo, M.[Michela], Tanase, M.[Mirela], Veltkamp, R.C.[Remco C.],
Skeletal Structures,
ShapeAnalysis08(5). 0802
BibRef

Huang, A., Liu, H.M., Lee, C.W., Yang, C.Y., Tsang, Y.M.,
On Concise 3-D Simple Point Characterizations: A Marching Cubes Paradigm,
MedImg(28), No. 1, January 2009, pp. 43-51.
IEEE DOI Link 0901
Skeletonization, center line extraction BibRef

Saude, A.V.[Andre V.], Couprie, M.[Michel], Lotufo, R.A.[Roberto A.],
Discrete 2D and 3D euclidean medial axis in higher resolution,
IVC(27), No. 4, 3 March 2009, pp. 354-363.
Elsevier DOI Link
WWW Version. 0804
Medial axis; Skeleton; Euclidean distance See also Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels. BibRef

Couprie, M.[Michel],
Hierarchic Euclidean Skeletons in Cubical Complexes,
DGCI11(141-152).
Springer DOI Link 1104
BibRef

Tierny, J.[Julien], Vandeborre, J.P.[Jean-Philippe], Daoudi, M.[Mohamed],
Enhancing 3D mesh topological skeletons with discrete contour constrictions,
VC(24), No. 3, March 2008, pp. 155-172.
Springer DOI Link 0802
BibRef
And:
Fast and precise kinematic skeleton extraction of 3D dynamic meshes,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef
Earlier:
Invariant High Level Reeb Graphs of 3D Polygonal Meshes,
3DPVT06(105-112).
IEEE DOI Link 0606
BibRef

Arcelli, C.[Carlo], Sanniti di Baja, G.[Gabriella], Serino, L.[Luca],
A parallel algorithm to skeletonize the distance transform of 3D objects,
IVC(27), No. 6, 4 May 2009, pp. 666-672.
Elsevier DOI Link
WWW Version. 0904
BibRef
Earlier:
From 3D Discrete Surface Skeletons to Curve Skeletons,
ICIAR08(xx-yy).
Springer DOI Link 0806
3D Object; Surface skeleton; Distance transform; Topology preservation; Reversibility BibRef

Arcelli, C.[Carlo], Sanniti di Baja, G.[Gabriella], Serino, L.[Luca],
Distance-Driven Skeletonization in Voxel Images,
PAMI(33), No. 4, April 2011, pp. 709-720.
IEEE DOI Link 1103
BibRef
Earlier:
The (3,4,5) Curvilinear Skeleton,
DGCI09(409-420).
Springer DOI Link 0909
BibRef
Earlier:
A New Set of Topology Preserving Removal Operations in the 3D Space,
ICPR06(III: 1055-1058).
IEEE DOI Link 0609
Compute surface and curve skeletons. Use the 3,4,5 weighted distance, anchor points. Skeletons centered within object. BibRef

Serino, L.[Luca], Arcelli, C.[Carlo], Sanniti di Baja, G.[Gabriella],
On the computation of the (3, 4, 5) curve skeleton of 3D objects,
PRL(32), No. 9, 1 July 2011, pp. 1406-1414.
Elsevier DOI Link
WWW Version. 1101
(3, 4, 5) weighted distance transform; Anchor point; Simple point; Skeletonization BibRef

Serino, L.[Luca], Sanniti di Baja, G.[Gabriella],
Selecting Anchor Points for 2D Skeletonization,
ICIAR11(I: 344-353).
Springer DOI Link 1106
BibRef

Serino, L.[Luca], Sanniti di Baja, G.[Gabriella], Arcelli, C.[Carlo],
Using the Skeleton for 3D Object Decomposition,
SCIA11(447-456).
Springer DOI Link 1105
BibRef

Abeysinghe, S.S.[Sasakthi S.], Ju, T.[Tao],
Interactive skeletonization of intensity volumes,
VC(25), No. 5-7, May 2009, pp. xx-yy.
Springer DOI Link 0905
BibRef

Ju, T.[Tao], Baker, M.L.[Matthew L.], Chiu, W.[Wah],
Computing a Family of Skeletons of Volumetric Models for Shape Description,
GMP06(235-247).
Springer DOI Link 0607
BibRef

Saude, A.V.[Andre Vital],
New reduced discrete Euclidean nD medial axis with optimal algorithm,
PRL(31), No. 1, January 2010, pp. 91-99.
Elsevier DOI Link
WWW Version. 1011
Medial axis; Skeleton; Euclidean distance; Shape representation BibRef

Lin, S.Y.[Shih-Ying], Horng, S.J.[Shi-Jinn], Kao, T.W.[Tzong-Wann], Fahn, C.S.[Chin-Shyurng], Fan, P.Z.[Ping-Zhi], Chen, Y.H.[Yuan-Hsin], Khan, M.K.[Muhammad Khurram], Bourgeois, A.[Anu], Terano, T.[Takao],
3D block-based medial axis transform and chessboard distance transform based on dominance,
IVC(29), No. 4, March 2011, pp. 272-285.
Elsevier DOI Link
WWW Version. 1102
Parallel algorithm; Image processing; CREW; PRAM model; Block-based medial axis transform; Chessboard distance transform; Euclidean distance transform BibRef

Ma, J.[Jaehwan], Bae, S.W.[Sang Won], Choi, S.[Sunghee],
3D medial axis point approximation using nearest neighbors and the normal field,
VC(28), No. 1, January 2012, pp. 7-19.
WWW Version. 1201
BibRef

Szilágyi, L.[László], Szilágyi, S.M.[Sándor Miklós], Iclanzan, D.[David], Szabó, L.[Lehel],
Efficient 3D Curve Skeleton Extraction from Large Objects,
CIARP11(133-140).
Springer DOI Link 1111
BibRef

Khromov, D.[Denis],
Curve-Skeletons Based on the Fat Graph Approximation,
ACIVS11(239-248).
Springer DOI Link 1108
BibRef

Antunez, E.[Emilio], Guibas, L.J.[Leonidas J.],
Robust extraction of 1D skeletons from grayscale 3D images,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef

Rizvandi, N.B.[Nikzad Babaii], Pižurica, A.[Aleksandra], Philips, W.[Wilfried],
Machine vision detection of isolated and overlapped nematode worms using skeleton analysis,
ICIP08(2972-2975).
IEEE DOI Link 0810
BibRef
And:
Automatic Individual Detection and Separation of Multiple Overlapped Nematode Worms Using Skeleton Analysis,
ICIAR08(xx-yy).
Springer DOI Link 0806
BibRef

Wattuya, P.[Pakaket], Jiang, X.Y.[Xiao-Yi],
A Class of Generalized Median Contour Problem with Exact Solution,
SSPR06(109-117).
Springer DOI Link 0608
Finding average set of contours. BibRef

Ferchichi, S.[Seifeddine], Wang, S.R.[Sheng-Rui], Grira, S.[Sofiane],
New Algorithm to Extract Centerline of 2D Objects Based on Clustering,
ICIAR07(364-374).
Springer DOI Link 0708
BibRef
Earlier: A1, A2, Only:
A Clustering-based Algorithm for Extracting the Centerlines of 2D and 3D Objects,
ICPR06(II: 296-299).
IEEE DOI Link 0609
BibRef

Styner, M.[Martin], Gerig, G.[Guido],
Three-Dimensional Medial Shape Representation Incorporating Object Variability,
CVPR01(II:651-656).
IEEE Abstract. 0110
BibRef

Stolpner, S.[Svetlana], Siddiqi, K.[Kaleem],
Revealing Significant Medial Structure in Polyhedral Meshes,
3DPVT06(365-372).
IEEE DOI Link 0606
BibRef

Bouix, S., Siddiqi, K.,
Divergence-Based Medial Surfaces,
ECCV00(I: 603-618).
WWW Version. 0003
BibRef

Giannitrapani, R.[Riccardo], Murino, V.[Vittorio],
Three-Dimensional Skeleton Extraction by Point Set Contraction,
ICIP99(I:565-569).
IEEE Abstract. BibRef 9900

Borgefors, G., Sanniti di Baja, G.,
Multiresolution Skeletonization in Binary Pyramids,
ICPR96(IV: 570-574).
IEEE DOI Link 9608
(Univ. of Agricultural Sciences, S) BibRef

Vaillant, M., Davatzikos, C., Brya, R.,
Finding 3D Parametric Representation of the Deep Cortical Folds,
MMBIA96(MEDIAL AXES) BibRef 9600

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Processing of Skeletons for Descriptions .