Abstract
Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N 4 log N) time for an N × N × N voxel grid, and computes a multiresolution approximation in O(N 3 log N) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Mitsumoto, H., Tamura, S., Okazaki, K., Kajimi, N., Fukui, Y.: Reconstruction using mirror images based on a plane symmetry recovery method (1992)
Zabrodsky, H., Peleg, S., Avnir, D.: Symmetry as a continuous feature. IEEE PAMI 17 (1995) 1154–1156
Liu, Y., Rothfus, W., Kanade, T.: Content-based 3d neuroradiologic image retrieval: Preliminary results (1998)
Leou, J., Tsai, W.: Automatic rotational symmetry determination for shape analysis. Pattern Recognition 20 (1987) 571–582
Wolfson, H., Reisfeld, D., Yeshurun, Y.: Robust facial feature detection using symmetry. Proceedings of the International Conference on Pattern Recognition (1992) 117–120
Atallah, M.J.: On symmetry detection. IEEE Trans. on Computers c-34 (1985) 663–666
Wolter, J.D., Woo, T.C., Volz, R.A.: Optimal algorithms for symmetry detection in two and three dimensions. The Visual Computer 1 (1985) 37–48
Marola, G.: On the detection of the axes of symmetry of symmetric and almost symmetric planar images. IEEE PAMI 11 (1989) 104–108
Shen, D., Ip, H., Cheung, K., Teoh, E.: Symmetry detection by generalized complex (gc) moments: A close-form solution. IEEE PAMI 21 (1999) 466–476
Sun, C., Si, D.: Fast reflectional symmetry detection using orientation histograms. Real-Time Imaging 5 (1999) 63–74
O’Mara, D., Owens, R.: Measuring bilateral symmetry in digital images. IEEE-TENCON-Digital Signal Processing Applications (1996)
Sun, C., Sherrah, J.: 3-d symmetry detection using the extended Gaussian image. IEEE PAMI 19 (1997)
Kovesi, P.: Symmetry and asymmetry from local phase. Tenth Australian Joint Converence on Artificial Intelligence (1997) 2–4
Elad, M., Tal, A., Ar, S.: Directed search in a 3d objects database using svm (2000)
Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Matching 3d models with shape distributions. Shape Matching International (2001)
Knuth, D., J.H. Morris, J., Pratt, V.: Fast pattern matching in strings. SIAM Journal of Computing 6 (1977) 323–350
Besl, P.J., Jain, R.C.: Three-dimensional object recognition. Computing Surveys 17 (1985) 75–145
Loncaric, S.: A survey of shape analysis techniques. Pattern Recognition 31 (1998) 983–1001
Pope, A.R.: Model-based object recognition: A survey of recent research. Technical Report TR-94-04, University of British Columbia (1994)
Veltkamp, R.C., Hagedoorn, M.: State-of-the-art in shape matching. Technical Report UU-CS-1999-27, Utrecht University, the Netherlands (1999)
Johnson, A., Hebert, M.: Efficient multiple model recognition in cluttered 3-d scenes. IEEE CVPR (1998) 671–677
Zhang, D., Hebert, M.: Harmonic maps and their applications in surface matching. IEEE CVPR 2 (1999)
Belongie, S., Malik, J.: Matching with shape contexts. IEEE Workshop on Content-based access of Image and Video-Libraries (2000)
Mori, G., Belongie, S., Malik, H.: Shape contexts enable efficient retrieval of similar shapes. CVPR 1 (2001) 723–730
B. Horn, B.: Extended gaussian images. PIEEE 72 (1984) 1656–1678
Fernández-Vidal, S., Bardinet, E., Malandain, G., Damas, S., de la Blanca Capilla, N.: Object representation and comparison inferred from its medial axis. ICPR 1 (2000) 712–715
Siddiqi, K., Shokoufandeh, A., Dickinson, S., Zucker, S.: Shock graphs and shape matching. IJCV 35 (1999) 13–32
Bloomenthal, J., Lim, C.: Skeletal methods of shape manipulation. Shape Modeling and Applications (1999) 44–47
Storti, D., Turkiyyah, G., Ganter, M., Lim, C., Stal, D.: Skeleton-based modeling operations on solids. Symposium on Solid Modeling and Applications (1997) 141–154
Serre, J.: Linear Representations of Finite Groups. Springer-Verlag, New York (1977)
Rubner, Y., Tomasi, C., Guibas, L.: A metric for distributions with applications to image databases. IEEE ICCV (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kazhdan, M., Chazelle, B., Dobkin, D., Finkelstein, A., Funkhouser, T. (2002). A Reflective Symmetry Descriptor. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_43
Download citation
DOI: https://doi.org/10.1007/3-540-47967-8_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43744-4
Online ISBN: 978-3-540-47967-3
eBook Packages: Springer Book Archive