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.
DOI Link 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.
Elsevier DOI 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 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.
DOI Link 0301
BibRef
Earlier: A2, A1:
Fuzzy border distance transforms and their use in 2d skeletonization,
ICPR02(I: 180-183).
IEEE DOI 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 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 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 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.
DOI Link 0306
BibRef
Earlier: ICCV99(385-391).
IEEE DOI 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 DOI 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).
Springer DOI 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 DOI 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 0903
BibRef
Earlier: A1, A2, Only: ECCV02(II: 718 ff.).
Springer DOI 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).
Springer DOI 0505
BibRef

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

Attali, D., Bertolino, P., Montanvert, A.,
Using Polyballs to Approximate Shapes and Skeletons,
ICPR94(A:626-628).
IEEE DOI 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 DOI 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 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.
Elsevier DOI 0410
sequence of onvex polygons. BibRef

Shah, J.[Jayant],
Gray skeletons and segmentation of shapes,
CVIU(99), No. 1, July 2005, pp. 96-109.
Elsevier DOI 0506
BibRef
And:
Skeletons of 3D Shapes,
ScaleSpace05(339-350).
Springer DOI 0505
No presmoothing required. Pruned skeleton. 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.
Elsevier DOI 0512
BibRef

Strand, R.[Robin],
Sampling and Ideal Reconstruction on the 3D Diamond Grid,
ICPR10(4609-4612).
IEEE DOI 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 0609
BibRef
Earlier:
The Euclidean Distance Transform Applied to the FCC and BCC Grids,
IbPRIA05(I:243).
Springer DOI 0509
BibRef
Earlier:
Surface skeletons in grids with non-cubic voxels,
ICPR04(I: 548-551).
IEEE DOI 0409
BibRef

Strand, R.[Robin],
Weighted distances based on neighbourhood sequences,
PRL(28), No. 15, 1 November 2007, pp. 2029-2036.
Elsevier DOI 0711
BibRef
Earlier:
Weighted Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids,
SCIA07(452-461).
Springer DOI 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.
DOI Link 0905
BibRef
Earlier: A2, A2:
Weighted Neighborhood Sequences in Non-standard Three-Dimensional Grids: Parameter Optimization,
IWCIA08(xx-yy).
Springer DOI 0804
BibRef
And: A2, A2:
Weighted Neighbourhood Sequences in Non-Standard Three-Dimensional Grids: Metricity and Algorithms,
DGCI08(xx-yy).
Springer DOI 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 0606

See also Isoperimetrically Optimal Polygons in the Triangular Grid. BibRef

Nagy, B.[Benedek], Strand, R.[Robin], Normand, N.[Nicolas],
A Weight Sequence Distance Function,
ISMM13(292-301).
Springer DOI 1305
BibRef

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

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

See also Distances with neighbourhood sequences in cubic and triangular grids. BibRef

Nagy, B.[Benedek], Strand, R.[Robin],
Neighborhood Sequences in the Diamond Grid: Algorithms with Four Neighbors,
IWCIA09(109-121).
Springer DOI 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 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 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 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 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 0802
BibRef
And:
Fast and precise kinematic skeleton extraction of 3D dynamic meshes,
ICPR08(1-4).
IEEE DOI 0812
BibRef
Earlier:
Invariant High Level Reeb Graphs of 3D Polygonal Meshes,
3DPVT06(105-112).
IEEE DOI 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 0904
BibRef
Earlier:
From 3D Discrete Surface Skeletons to Curve Skeletons,
ICIAR08(xx-yy).
Springer DOI 0806
3D Object; Surface skeleton; Distance transform; Topology preservation; Reversibility BibRef

Serino, L.[Luca], Sanniti di Baja, G.[Gabriella],
Pruning the 3D Curve Skeleton,
ICPR14(2269-2274)
IEEE DOI 1412
Context BibRef

Serino, L.[Luca], Arcelli, C.[Carlo], Sanniti di Baja, G.[Gabriella],
Decomposing and Sketching 3D Objects by Curve Skeleton Processing,
CIARP13(I:25-32).
Springer DOI 1311
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 1103
BibRef
Earlier:
The (3,4,5) Curvilinear Skeleton,
DGCI09(409-420).
Springer DOI 0909
BibRef
Earlier:
A New Set of Topology Preserving Removal Operations in the 3D Space,
ICPR06(III: 1055-1058).
IEEE DOI 0609
Compute surface and curve skeletons. Use the 3,4,5 weighted distance, anchor points. Skeletons centered within object.
See also Approximating the Skeleton for Fine-to-Coarse Shape Representation. 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 1101
(3, 4, 5) weighted distance transform; Anchor point; Simple point; Skeletonization BibRef

Serino, L.[Luca], Arcelli, C.[Carlo], Sanniti di Baja, G.[Gabriella],
From skeleton branches to object parts,
CVIU(129), No. 1, 2014, pp. 42-51.
Elsevier DOI 1411
BibRef
Earlier: A3, A1, A2:
From Linear Representations to Object Parts,
MCPR12(1-12).
Springer DOI 1208
BibRef
Earlier: A1, A3, A2:
Using the Skeleton for 3D Object Decomposition,
SCIA11(447-456).
Springer DOI 1105
3D object decomposition BibRef

Serino, L.[Luca], Sanniti di Baja, G.[Gabriella],
A new strategy for skeleton pruning,
PRL(76), No. 1, 2016, pp. 41-48.
Elsevier DOI 1605
2D Skeleton BibRef

Serino, L.[Luca], Sanniti di Baja, G.[Gabriella],
Selecting Anchor Points for 2D Skeletonization,
ICIAR11(I: 344-353).
Springer DOI 1106
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 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 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 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 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 Link. 1201
BibRef

Bucksch, A.[Alexander], Lindenbergh, R.C.[Roderik C.], Menenti, M.,
Skeltre: Fast Skeletonisation For Imperfect Point Cloud Data of Botanic Trees,
3DOR09(13-20)
PDF File.
DOI Link 1301
BibRef

Jalba, A.C.[Andrei C.], Kustra, J.[Jacek], Telea, A.C.[Alexandru C.],
Surface and Curve Skeletonization of Large 3D Models on the GPU,
PAMI(35), No. 6, June 2013, pp. 1495-1508.
IEEE DOI 1305
Shapes as meshes. BibRef

Vera, S.[Sergio], Gil, D.[Debora], Borràs, A.[Agnés], Linguraru, M.G.[Marius George], González Ballester, M.A.[Miguel Angel],
Geometric steerable medial maps,
MVA(24), No. 6, August 2013, pp. 1255-1266.
Springer DOI 1307
for volumes. BibRef

Sobiecki, A.[André], Jalba, A.[Andrei], Telea, A.[Alexandru],
Comparison of curve and surface skeletonization methods for voxel shapes,
PRL(47), No. 1, 2014, pp. 147-156.
Elsevier DOI 1408
Surface and curve skeletons BibRef

Martínez, J.[Jonàs], Pla, N.[Núria], Vigo, M.[Marc],
The three-dimensional cube and scale cube skeleton,
VC(31), No. 9, September 2015, pp. 1233-1252.
WWW Link. 1508
BibRef

Zhang, D.J.[De-Jia], Xie, N.[Ning], Liang, S.[Shuang], Jia, J.Y.[Jin-Yuan],
3D tree skeletonization from multiple images based on PyrLK optical flow,
PRL(76), No. 1, 2016, pp. 49-58.
Elsevier DOI 1605
Tree skeletonization BibRef

Ziamtsov, I.[Illia], Faizi, K.[Kian], Navlakha, S.[Saket],
Branch-Pipe: Improving Graph Skeletonization around Branch Points in 3D Point Clouds,
RS(13), No. 19, 2021, pp. xx-yy.
DOI Link 2110
BibRef

Matejek, B.[Brian], Franzmeyer, T.[Tim], Wei, D.L.[Dong-Lai], Wang, X.Y.[Xue-Ying], Zhao, J.L.[Jing-Lin], Palágyi, K.[Kálmán], Lichtman, J.W.[Jeff W.], Pfister, H.[Hanspeter],
Scalable Biologically-Aware Skeleton Generation for Connectomic Volumes,
MedImg(41), No. 9, September 2022, pp. 2360-2370.
IEEE DOI 2209
Skeleton, Neurons, Synapses, Biology, Soma, Neurites, Image segmentation, Skeleton generation, connectomics, biologically-constrained algorithms BibRef

Keller, M.[Marilyn], Zuffi, S.[Silvia], Black, M.J.[Michael J.], Pujades, S.[Sergi],
OSSO: Obtaining Skeletal Shape from Outside,
CVPR22(20460-20469)
IEEE DOI 2210
Biomechanics, Solid modeling, Shape, Stars, Bones, Face and gestures, 3D from single images, Biometrics, Medical, biological and cell microscopy BibRef

Lin, C.[Cheng], Li, C.J.[Chang-Jian], Liu, Y.[Yuan], Chen, N.[Nenglun], Choi, Y.K.[Yi-King], Wang, W.P.[Wen-Ping],
Point2Skeleton: Learning Skeletal Representations from Point Clouds,
CVPR21(4275-4284)
IEEE DOI 2111
Surface reconstruction, Shape, Semantics, Transforms, Skeleton BibRef

Zasinski, P., Kocinski, M., Materka, A.,
On extracting skeletons from binary 3D images,
WSSIP17(1-5)
IEEE DOI 1707
Algorithm design and analysis, Digital images, Image processing, Shape, Skeleton, Topology, 3D images, Binary images, Morphology, Skeletonization BibRef

Chaussard, J.[John], Noël, L.[Laurent], Biri, V.[Venceslas], Couprie, M.[Michel],
A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing,
DGCI13(119-130).
Springer DOI 1304
BibRef

Rossi, L.[Luca], Torsello, A.[Andrea],
An Adaptive Hierarchical Approach to the Extraction of High Resolution Medial Surfaces,
3DIMPVT12(371-378).
IEEE DOI 1212
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 1111
BibRef

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

Antunez, E.[Emilio], Guibas, L.J.[Leonidas J.],
Robust extraction of 1D skeletons from grayscale 3D images,
ICPR08(1-4).
IEEE DOI 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 0810
BibRef
And:
Automatic Individual Detection and Separation of Multiple Overlapped Nematode Worms Using Skeleton Analysis,
ICIAR08(xx-yy).
Springer DOI 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 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 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 0609
BibRef

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

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

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

Borgefors, G.[Gunilla], Sanniti di Baja, G.[Gabriella],
Multiresolution Skeletonization in Binary Pyramids,
ICPR96(IV: 570-574).
IEEE DOI 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 .