11.5.4.3 General Three-Dimensional Symmetries, 3-D Symmetry

Arcelli, C., and Levialdi, S.,
Parallel Shrinking in Three Dimensions,
CGIP(1), No. 1, April 1972, pp. 21-30.
Elsevier DOI superposition of 2-D shrinking algorithms. BibRef 7204

Lobregt, S., Verbeek, P.W., and Groen, F.C.A.,
Three-Dimensional Skeletonization: Principle and Algorithm,
PAMI(2), No. 1, January 1980, pp. 75-77. BibRef 8001

Kanade, T.[Takeo],
Recovery of the Three-Dimensional Shape of and Object from a Single View,
AI(17), No. 1-3, August 1981, pp. 409-460.
Elsevier DOI BibRef 8108
And: CMU-CS-TR-79-153, CMU CS Dept., October 1979. Skew Symmetry. Perceptual Grouping. Parallel lines in a drawing are parallel lines in space. Skewed symmetry in a drawing is a bilateral symmetry in space. Thus skew symmetric figures are excluded from recognition. BibRef

Nackman, L.R., and Pizer, S.M.,
Three-Dimensional Shape Description Using the Symmetric Axis Transform,
PAMI(7), No. 2, March 1985, pp. 187-202. BibRef 8503
And: A1 only: Ph.D.Thesis, Univ. of NC, 1982.
See also Hierarchical Shape Description Via the Multiresolution Symmetric Axis Transform. BibRef

Nackman, L.R.[Lee R.],
Curvature Relations in Three-Dimensional Symmetric Axes,
CGIP(20), No. 1, September 1982, pp. 43-57.
Elsevier DOI Radius curvature and boundary curvature. BibRef 8209

Hafford, K.J.[Kimberly Jyl], Preston, Jr., K.[Kendall],
Three-Dimensional Skeletonization of Elongated Solids,
CVGIP(27), No. 1, July 1984, pp. 78-91.
Elsevier DOI Tetradecahedral neighborhood. BibRef 8407

Wolter, J.D., Woo, T.C., Volz, R.A.,
Optimal Algorithms for Symmetry Detection in Two and Three Dimensions,
VC(1), 1985, pp. 37-48. BibRef 8500

Fukushima, S., Okumura, T.,
Modeling a Three-Dimensional Shape from a Silhouette by Detecting Symmetry,
IEICE(J74-D-II), No. 12, 1991, pp. 1697-1705. BibRef 9100
And: English version: SCJ(24), No. 3, 1993, pp. 59-69. BibRef

Saint-Marc, P., Rom, H., and Medioni, G.G.,
B-Spline Contour Representation and Symmetry Detection,
PAMI(15), No. 11, November 1993, pp. 1191-1197.
IEEE DOI Eariler with A1, A3 only: BibRef 9311
B-Spline Contour Representations and Symmetry Detection,
ECCV90(604-606).
Springer DOI Detect Symmetries for shape from contour. BibRef

Manninen, A.T.,
Statistical Calculations of 3D-Orientation Parameters of Flat Symmetrical Polyhedrons,
PRL(14), 1993, pp. 207-211. BibRef 9300

Cham, T.J.[Tat-Jen], Cipolla, R.[Roberto],
Symmetry Detection Through Local Skewed Symmetries,
IVC(13), No. 5, June 1995, pp. 439-450.
Elsevier DOI BibRef 9506
And: Cambridge UniversityTechnical Report CUED/F-INFENG/TR183, November 1994. BibRef
Earlier:
Skewed Symmetry Detection Through Local Skewed Symmetries,
BMVC94(xx-yy).
PDF File. 9409
BibRef
And:
A Local Approach To Recovering Global Skewed Symmetry,
ICPR94(A:222-226).
IEEE DOI Hough Transform. Detect global symmetry prior to segmentation. BibRef

Sherbrooke, E.C., Patrikalakis, N.M., Brisson, E.,
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids,
VCG(2), No. 1, March 1996, pp. 44-61. BibRef 9603

Sheehy, D.J., Armstrong, C.G., Robinson, D.J.,
Shape-Description by Medial Surface Construction,
VCG(2), No. 1, March 1996, pp. 62-72. BibRef 9603

Grupen, R.A., Henderson, T.C., Hansen, C.D.,
Apparent Symmetries in Range Data,
PRL(7), 1988, pp. 107-111. BibRef 8800

Sun, C.M.[Chang Ming], Sherrah, J.[Jamie],
3D Symmetry Detection Using the Extended Gaussian Image,
PAMI(19), No. 2, February 1997, pp. 164-168.
IEEE DOI 9703
Detect the symmetry by converting to a Gaussian Image, then convolve the GI. BibRef

Forsyth, D.A.,
Recognizing Algebraic Surfaces from Their Outlines,
IJCV(18), No. 1, April 1996, pp. 21-40.
Springer DOI 9605
BibRef
Earlier: ICCV93(476-480).
IEEE DOI Theory. BibRef

Zisserman, A.[Andrew], Mundy, J.L.[Joe L.], Forsyth, D.A.[David A.], Liu, J.[Jane], Pillow, N.[Nic], Rothwell, C.A.[Charlie A.], Utcke, S.[Sven],
Class-Based Grouping in Perspective Images,
ICCV95(183-188).
IEEE DOI Extract generalized cylinders using perspective, from the countours. BibRef 9500

Forsyth, D.A., Mundy, J.L., Zisserman, A., Rothwell, C.A.,
Recognizing Rotationally Symmetric Surfaces from Their Outlines,
ECCV92(639-647).
Springer DOI BibRef 9200

Shimshoni, I.[Ilan], Moses, Y.[Yael], Lindenbaum, M.[Michael],
Shape Reconstruction of 3D Bilaterally Symmetric Surfaces,
IJCV(39), No. 2, September 2000, pp. 97-110.
DOI Link 0008
BibRef
Earlier: CIAP99(76-81).
IEEE DOI 9909
BibRef

Prasad, V.S.N.[V. Shiv Naga], Yegnanarayana, B.,
Finding axes of symmetry from potential fields,
IP(13), No. 12, December 2004, pp. 1559-1566.
IEEE DOI 0412
BibRef

Robert-Inacio, F.[Frédérique],
Symmetry parameters for 3D pattern classification,
PRL(26), No. 11, August 2005, pp. 1732-1739.
Elsevier DOI 0506
Generalization of 2D symmetry to 3D. BibRef

Penman, D.W.[David W.], Alwesh, N.S.[Nawar S.],
3D Pose estimation of symmetrical objects of unknown shape,
IVC(24), No. 5, 1 May 2006, pp. 447-454.
Elsevier DOI 0606
Orientation; Pose estimation; Symmetry; Range data Given a plane of bilateral symmetry. BibRef

Penman, D.W.[David W.], Valkenburg, R.J., Alwesh, N.S.[Nawar S.],
Robust calibration of the position of reference targets for a six degrees of freedom pose sensor,
IVCNZ08(1-6).
IEEE DOI 0811
BibRef

Bucksch, A.[Alexander], Lindenbergh, R.[Roderik],
CAMPINO: A skeletonization method for point cloud processing,
PandRS(63), No. 1, January 2008, pp. 115-127.
Elsevier DOI 0711
Skeletonization; CAMPINO; Point cloud; Terrestrial laser scanning (C)ollapsing (A)nd (M)erging (P)rocedures (IN) (O)ctree-graphs. BibRef

Bucksch, A.[Alexander], Lindenbergh, R.[Roderik], Menenti, M.[Massimo],
SkelTre: Robust skeleton extraction from imperfect point clouds,
VC(26), No. 10, October 2010, pp. 1283-1300.
WWW Link. 1101
BibRef

Raviv, D.[Dan], Bronstein, A.M.[Alexander M.], Bronstein, M.M.[Michael M.], Kimmel, R.[Ron],
Full and Partial Symmetries of Non-rigid Shapes,
IJCV(89), No. 1, August 2010, pp. xx-yy.
Springer DOI 1004
BibRef
Earlier:
Symmetries of non-rigid shapes,
NRTL07(1-7).
IEEE DOI 0710

See also Partial Similarity of Objects, or How to Compare a Centaur to a Horse. BibRef

Aflalo, Y.[Yonathan], Kimmel, R.[Ron], Raviv, D.[Dan],
Scale Invariant Geometry for Nonrigid Shapes,
SIIMS(6), No. 3, 2013, pp. 1579-1597.
DOI Link 1310
BibRef

Raviv, D.[Dan], Bayro-Corrochano, E.[Eduardo], Raskar, R.[Ramesh],
LRA: Local Rigid Averaging of Stretchable Non-rigid Shapes,
IJCV(124), No. 2, September 2017, pp. 132-144.
Springer DOI 1708
the mean structure of non-rigid stretchable shapes. BibRef

Raviv, D.[Dan], Dubrovina, A.[Anastasia], Kimmel, R.[Ron],
Hierarchical Matching of Non-rigid Shapes,
SSVM11(604-615).
Springer DOI 1201
BibRef

Aflalo, Y.[Yonathan], Brezis, H.[Haim], Kimmel, R.[Ron],
On the Optimality of Shape and Data Representation in the Spectral Domain,
SIIMS(8), No. 2, 2015, pp. 1141-1160.
DOI Link 1507
representing smooth functions on surfaces. BibRef

Aflalo, Y.[Yonathan], Kimmel, R.[Ron],
Spectral multidimensional scaling,
NAS(110), No. 45, 2013, pp. 18,052-18,057.
DOI Link 1608
BibRef

Aflalo, Y.[Yonathan], Bronstein, A.M.[Alexander M.], Kimmel, R.[Ron],
On convex relaxation of graph isomorphism,
NAS(112), No. 10, 2015, pp. 2942-2947.
DOI Link 1608
BibRef

Aflalo, Y.[Yonathan], Dubrovina, A.[Anastasia], Kimmel, R.[Ron],
Spectral Generalized Multi-dimensional Scaling,
IJCV(118), No. 3, July 2016, pp. 380-392.
Springer DOI 1608
Embed a given set of points into a simple domain. BibRef

Raviv, D.[Dan], Raskar, R.[Ramesh],
Scale Invariant Metrics of Volumetric Datasets,
SIIMS(8), No. 1, 2015, pp. 403-425.
DOI Link 1503
BibRef

Raviv, D.[Dan], Kimmel, R.[Ron],
Affine Invariant Geometry for Non-rigid Shapes,
IJCV(111), No. 1, January 2015, pp. 1-11.
WWW Link. 1502
BibRef

Raviv, D.[Dan], Bronstein, A.M.[Alexander M.], Bronstein, M.M.[Michael M.], Kimmel, R.[Ron], Sapiro, G.[Guillermo],
Diffusion symmetries of non-rigid shapes.,
3DPVT10(xx-yy).
WWW Link. 1005
BibRef

Raviv, D.[Dan], Bronstein, A.M.[Alexander M.], Bronstein, M.M.[Michael M.], Waisman, D.[Dan], Sochen, N.A.[Nir A.], Kimmel, R.[Ron],
Equi-affine Invariant Geometry for Shape Analysis,
JMIV(50), No. 1-2, September 2014, pp. 144-16.
Springer DOI 1408
BibRef
Earlier: A1, A2, A3, A6, A5, Only:
Equi-Affine Invariant Geometries of Articulated Objects,
WTFCV11(177-190).
Springer DOI 1210
BibRef
And: A1, A3, A2, A6, A5, Only:
Affine-invariant diffusion geometry for the analysis of deformable 3D shapes,
CVPR11(2361-2367).
IEEE DOI 1106
BibRef

Rosman, G.[Guy], Bronstein, A.M.[Alex M.], Bronstein, M.M.[Michael M.], Tai, X.C.[Xue-Cheng], Kimmel, R.[Ron],
Group-Valued Regularization for Analysis of Articulated Motion,
NORDIA12(I: 52-62).
Springer DOI 1210
BibRef

Rosman, G.[Guy], Bronstein, A.M.[Alexander M.], Bronstein, M.M.[Michael M.], Kimmel, R.[Ron],
Articulated Motion Segmentation Of Point Clouds by Group-Valued Regularization,
3DOR12(77-84)
DOI Link 1301
BibRef

Rosman, G.[Guy], Bronstein, M.M.[Michael M.], Bronstein, A.M.[Alexander M.], Wolf, A.[Alon], Kimmel, R.[Ron],
Group-Valued Regularization Framework for Motion Segmentation of Dynamic Non-rigid Shapes,
SSVM11(725-736).
Springer DOI 1201
BibRef

Devir, Y.S.[Yohai S.], Rosman, G.[Guy], Bronstein, A.M.[Alexander M.], Bronstein, M.M.[Michael M.], Kimmel, R.[Ron],
On reconstruction of non-rigid shapes with intrinsic regularization,
NORDIA09(272-279).
IEEE DOI 0910
BibRef

Bermanis, A.[Amit], Averbuch, A.[Amir], Keller, Y.[Yosi],
3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform,
IJCV(90), No. 2, November 2010, pp. 166-182.
WWW Link. 1011
BibRef

Han, D.J.[Dong-Jin], Hahn, H.S.[Hern-Soo],
Axis estimation and grouping of rotationally symmetric object segments,
PR(47), No. 1, 2014, pp. 296-312.
Elsevier DOI 1310
Axis estimation BibRef

Han, D.J.[Dong-Jin], Cooper, D.B.[David B.], Hahn, H.S.[Hern-Soo],
Fast axis estimation from a segment of rotationally symmetric object,
CVPR12(1154-1161).
IEEE DOI 1208
BibRef

Sawada, T., Li, Y.F.[Yun-Feng], Pizlo, Z.,
Detecting 3-D Mirror Symmetry in a 2-D Camera Image for 3-D Shape Recovery,
PIEEE(102), No. 10, October 2014, pp. 1588-1606.
IEEE DOI 1410
eye BibRef

Sfikas, K.[Konstantinos], Theoharis, T.[Theoharis], Pratikakis, I.E.[Ioannis E.],
Pose normalization of 3D models via reflective symmetry on panoramic views,
VC(30), No. 11, November 2014, pp. 1261-1274.
Springer DOI 1411
using symmetry plane. BibRef

Aguilar, W.[Wendy], Bribiesca, E.[Ernesto],
Symmetry detection in 3D chain coded discrete curves and trees,
PR(48), No. 4, 2015, pp. 1420-1439.
Elsevier DOI 1502
Shape-of-curve symmetry BibRef

Nagar, R., Raman, S.,
Revealing Hidden 3-D Reflection Symmetry,
SPLetters(23), No. 12, December 2016, pp. 1776-1780.
IEEE DOI 1612
computer vision BibRef

Esser, G.[Gregor], Becken, W.[Wolfgang], Altheimer, H.[Helmut], Muller, W.[Werner],
Generalization of the Minkwitz theorem to nonumbilical lines of symmetrical surfaces,
JOSA-A(34), No. 3, March 2017, pp. 441-448.
DOI Link 1703
Mathematical methods (general) BibRef

Brégier, R.[Romain], Devernay, F.[Frédéric], Leyrit, L.[Laetitia], Crowley, J.L.[James L.],
Defining the Pose of Any 3D Rigid Object and an Associated Distance,
IJCV(126), No. 6, June 2018, pp. 571-596.
Springer DOI 1804
BibRef
Earlier:
Symmetry Aware Evaluation of 3D Object Detection and Pose Estimation in Scenes of Many Parts in Bulk,
6DPose17(2209-2218)
IEEE DOI 1802
Cameras, Object detection, Performance evaluation, Pose estimation, Solid modeling, BibRef

Wen, C.[Cheng], Yu, B.[Baosheng], Tao, D.C.[Da-Cheng],
Learnable Skeleton-Aware 3D Point Cloud Sampling,
CVPR23(17671-17681)
IEEE DOI 2309
BibRef

Insafutdinov, E.[Eldar], Campbell, D.[Dylan], Henriques, J.F.[João F.], Vedaldi, A.[Andrea],
SNeS: Learning Probably Symmetric Neural Surfaces from Incomplete Data,
ECCV22(XXXII:367-383).
Springer DOI 2211
BibRef

Zhou, Y.[Yichao], Liu, S.[Shichen], Ma, Y.[Yi],
NeRD: Neural 3D Reflection Symmetry Detector,
CVPR21(15935-15944)
IEEE DOI 2111
Costs, Pose estimation, Detectors, Reflection, Pattern recognition BibRef

Jain, H.[Hardik], Hellwich, O.[Olaf],
GenIcoNet: Generative Icosahedral Mesh Convolutional Network,
3DV21(64-73)
IEEE DOI 2201
Convolutional codes, Training, Interpolation, Surface reconstruction, Systematics, Shape, Surface Mesh, Mesh Arithmetic BibRef

Jain, H.[Hardik], Wöllhaf, M., Hellwich, O.[Olaf],
Learning to Reconstruct Symmetric Shapes using Planar Parameterization of 3D Surface,
GMDL19(4133-4140)
IEEE DOI 2004
Code, Symmetry.
WWW Link. Gaussian processes, geometry, image reconstruction, image representation, iterative methods, ShapeNet BibRef

Ecins, A., Fermüller, C., Aloimonos, Y.,
Detecting Reflectional Symmetries in 3D Data Through Symmetrical Fitting,
Symmetry17(1779-1783)
IEEE DOI 1802
Measurement, Shape, Solid modeling, BibRef

Su, J.Y., Cheng, S.C., Hsieh, J.W., Hsu, T.H.,
Moment-based symmetry detection for scene modeling and recognition using RGB-D images,
ICPR16(3621-3626)
IEEE DOI 1705
Algorithm design and analysis, Classification algorithms, Computational modeling, Detectors, Feature extraction, Reflection, RGB-D images, moment-based symmetry detection, part-based scene modeling, symmetric patch detection, unsupervised, feature, representation BibRef

Mukhopadhyay, A., Bhandarkar, S.M., Porikli, F.M.[Fatih M.],
Detection and characterization of Intrinsic symmetry of 3D shapes,
ICPR16(1815-1820)
IEEE DOI 1705
Complexity theory, Geometry, Level measurement, Manifolds, Shape, Space vehicles, Three-dimensional, displays BibRef

Zhou, C.[Chen], Guney, F.[Fatma], Wang, Y.Z.[Yi-Zhou], Geiger, A.[Andreas],
Exploiting Object Similarity in 3D Reconstruction,
ICCV15(2201-2209)
IEEE DOI 1602
Buildings BibRef

Korman, S.[Simon], Ofek, E.[Eyal], Avidan, S.[Shai],
Peeking Template Matching for Depth Extension,
ICCV15(2174-2182)
IEEE DOI 1602
Extend depth image into unseen regions. Repeated structures. BibRef

Kakarala, R.[Ramakrishna], Kaliamoorthi, P.[Prabhu], Premachandran, V.[Vittal],
Three-Dimensional Bilateral Symmetry Plane Estimation in the Phase Domain,
CVPR13(249-256)
IEEE DOI 1309
phase; sampling; spherical harmonics; symmetry BibRef

Potapova, E.[Ekaterina], Zillich, M.[Michael], Vincze, M.[Markus],
Local 3D Symmetry for Visual Saliency in 2.5D Point Clouds,
ACCV12(I:434-445).
Springer DOI 1304
BibRef

Grushko, C.[Carmi], Raviv, D.[Dan], Kimmel, R.[Ron],
Intrinsic Local Symmetries: A Computational Framework,
3DOR12(33-38)
DOI Link 1301
BibRef

Sinha, S.N.[Sudipta N.], Ramnath, K.[Krishnan], Szeliski, R.S.[Richard S.],
Detecting and Reconstructing 3D Mirror Symmetric Objects,
ECCV12(II: 586-600).
Springer DOI 1210
BibRef

Mitra, N.J.[Niloy J.], Bronstein, A.M.[Alex M.], Bronstein, M.M.[Michael M.],
Intrinsic Regularity Detection in 3D Geometry,
ECCV10(III: 398-410).
Springer DOI 1009
Symmetries, regularity, retpetitve structures. Reduce to 2D grid problem. BibRef

Kakarala, R.[Ramakrishna], Mao, D.S.[Dan-Sheng],
A theory of phase-sensitive rotation invariance with spherical harmonic and moment-based representations,
CVPR10(105-112).
IEEE DOI 1006
bispectrum for rotations and moments. Distinguish rotations from reflections. BibRef

Cailliere, D., Denis, F., Pele, D., Baskurt, A.,
3D mirror symmetry detection using Hough transform,
ICIP08(1772-1775).
IEEE DOI 0810
BibRef

Sawada, T.[Tadamasa], Pizlo, Z.[Zygmunt],
Detecting mirror-symmetry of a volumetric shape from its single 2D image,
Tensor08(1-8).
IEEE DOI 0806
BibRef

Fujimori, T.[Tomoyuki], Kobayashi, Y.[Yohei], Suzuki, H.[Hiromasa],
Separated Medial Surface Extraction from CT Data of Machine Parts,
GMP06(313-324).
Springer DOI 0607
BibRef

Pan, G.[Gang], Wang, Y.M.[Yue-Ming], Qi, Y.P.[Yi-Peng], Wu, Z.H.[Zhao-Hui],
Finding Symmetry Plane of 3D Face Shape,
ICPR06(III: 1143-1146).
IEEE DOI 0609
BibRef

Huynh, D.,
Affine Reconstruction from Monocular Vision in the Presence of a Symmetry Plane,
ICCV99(476-482).
IEEE DOI BibRef 9900

Imamura, H., Kitaoka, Y.[Yoshiyuki], Katsuma, Y., Kenmochi, Y., Kotani, K.,
Estimation of Stereo Image Pairs from Single Camera Views for a Roatating Spherical Object covered with Moving Texture,
ICIP99(IV:400-404).
IEEE DOI Smoothly Varying Surface BibRef 9900

Yiwu, L.[Lei], Cheong, W.[Wong],
A Novel Method for Detecting and Localising of Reflectional and Rotational Symmetry Under Weak Perspective Projection,
ICPR98(Vol I: 417-419).
IEEE DOI 9808
BibRef

Carlsson, S.,
Symmetry in perspective,
ECCV98(I: 249).
Springer DOI BibRef 9800

Nishimura, K., Tanaka, H.,
Active Shape Inferring Based on the Symmetry in Stable Poses: Shape from Function Approach,
ICPR96(I: 136-140).
IEEE DOI 9608
(Ritsumeikan Univ., J) BibRef

Tan, T.N.,
Monocular Reconstruction of 3-D Bilateral Symmetrical Objects,
BMVC96(Poster Session 1). 9608
BibRef
Earlier:
Structure, Pose and Motion of Bilateral Symmetric Objects,
BMVC95(xx-yy).
PDF File. 9509
University of Reading BibRef

Labonte, F., Shapira, Y., and Cohen, P.,
A Perceptually Plausible Model for Global Symmetry Detection,
ICCV93(258-263).
IEEE DOI BibRef 9300

Minovic, P., Ishikawa, S., Kato, K.,
Three-Dimensional Symmetry Measurement of Medical Entities,
ICPR92(I:457-460).
IEEE DOI BibRef 9200

Yuen, S.Y.K.[Shiu-Yin Kelvin],
Shape from Contour Using Symmetries,
ECCV90(437-453).
Springer DOI BibRef 9000

Brown, C.M.,
Symmetry Evaluators,
DARPA84(90-97). BibRef 8400

Kelley, R.B., Birk, J.R., Silva, R.,
Identification of Object Symmetry from Multiple Views,
PRIP78(327-330). BibRef 7800

Chapter on 3-D Object Description and Computation Techniques, Surfaces, Deformable, View Generation, Video Conferencing continues in
Generalized Cylinders -- Use .