H. L. Zou
ABSTRACT
Mirror symmetry is an important constraint in 3D reconstruction of an object from a 2D sketch and the subsequent beautification of the 3D model. This paper proposes a new method to detect symmetry planes from a sketch by exploiting the topological connections of the edges it contains. Experiments show that the method can detect all the symmetry planes and the corresponding symmetric vertex pairs, edge pairs and face pairs as well.
- Darga P. T., Liffiton M. H., Sakallah K. A., and Markov I. L. 2004. Exploiting Structure in Symmetry Detection for CNF. Design Automation Conference (DAC), IEEE/ACM, San Diego, CA; 530--534. Google Scholar
Digital Library
- Gibbson A. 1985. Algorithmic Graph Theory. Cambridge University Press.Google Scholar
- Gould R. 1988. Graph Theory. Redwood City, CA: Addison-Wesley.Google Scholar
- Jiang X. Y. and Bunke H. 1992. A Simple and Efficient Algorithm for Determining the Symmetries of Polyhedra. Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing; 54(1): 91--95. Google ScholarDigital Library
- Kanade T. 1981. Recovery of the Three-dimensional Shape of an Object from a Single View. Artificial Intelligence; 17: 409 -- 460.Google Scholar
- Leclerc Y. G. and Fiscler M. A. 1992. An Optimization Based Approach to the Interpretation of Single Line Drawings as 3D Wire Frame. Computer Vision: 9(2): 113--136. Google ScholarDigital Library
- Lipson H. and Shpitalni M. 1996. Optimization- based reconstruction of a 3D object from a single freehand line drawing. Computer Aided Design; 28(8): 651--663.Google Scholar
- Liu J. Z. and Lee Y. T. 2001. A Graph-based method for Face Identification from a Single 2D Line Drawing. IEEE Transaction on Pattern Analysis and Machine Intelligence; 23(10): 1089--1106. Google ScholarDigital Library
- Liu J. Z., Lee Y. T. and Cham W. K. 2002. Identifying Faces in a 2D Line Drawing Representing a Manifold Object. IEEE Transaction on Pattern Analysis and Machine Intelligence; 24(12): 1579--1593. Google ScholarDigital Library
- O'Mara D. T. J. 2002. Automated facial metrology. Ph.D. thesis. University of Western Australia.Google Scholar
- Marola G. 1989. On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Image. IEEE Transactions on Pattern Analysis and Machine Intelligence; 11(1): 104--108. Google ScholarDigital Library
- McKay B. D. 1981. Practical Graph Isomorphism. Congressus Numerantium, 30: 45--87.Google Scholar
- McKay B. D., 1990. Nauty User's Guide (version 1.5), Technical report TR-CS-90-02, Computer Science Department, Australian National University.Google Scholar
- Nalwa V. S. 1989. Line-Drawing Interpretation: Bilateral Symmetry. IEEE Transactions on Pattern Analysis and Machine Intelligence; 11(10): 1117--1120. Google ScholarDigital Library
- Oh W. G., Asada M. and Tsuji S. 1988. Model-Based Matching Using Skewed Symmetry Information. Proc. Int'l Conf. Pattern Recognition, pp. 1043--1045.Google Scholar
- Parui S. K. and Majumder D. D. 1983. Symmetry analysis by computer. Pattern Recognition, 16(1): 63--67.Google ScholarCross Ref
- Rich E., Knight K. 1991. Artificial Intelligence. New York: McGraw-Hill Inc. Google ScholarDigital Library
- Shpitalni M. and Lipson H. 1996. Identification of Faces in a 2D Line Drawing Projection of a Wire frame Object. IEEE Transactions on Pattern Analysis and Machine Intelligence; 18(10): 1000--1012. Google ScholarDigital Library
- Shen D. G., Ip H. H. S. and Teoh E. K. 2001. Robust Detection of Skewed Symmetries by Combining Local and Semi-Local Affine Invariants. Pattern Recognition; 34: 1417--1428.Google Scholar
- Skiena S. 1990. Implementing Discrete Mathematics: Combinatorics and Graph Theory With Mathematica. Redwood City, CA :Addison-Wesley. Google ScholarDigital Library
- Sugimoto K. and Tomita F. 1994. Detection of Skewed-Symmetrical Shape. Proceedings of the International Conference on Image Processing. Austin, Texas, USA,; 1: 696--700.Google Scholar
- Sun C. and Si D. 1999. Fast Reflectional Symmetry Detection Using Orientation Histograms. Real-Time Imaging; 5 (1): 63--74. Google ScholarDigital Library
- Weinberg L. 1996. A simple and efficient algorithm for determining isomorphisms of planar triply connected graphs. IEEE Transactions on Circuit Theory; 13(2): 142--148.Google ScholarCross Ref
- Yip R. K. K., Tam P. K. S. and Leung D. N. K. 1994. Application of elliptic Fourier descriptors to symmetry detection under parallel projection. IEEE Transactions on Pattern Analysis and Machine Intelligence; 16(3): 277--286. Google ScholarDigital Library
- Yip R. Hough. 2000. A transform technique for the detection of reflectional symmetry and skew-symmetry. Pattern Recognition Letters; 21: 117--130. Google ScholarDigital Library
- Zabrodsky H. 1993. Computational Aspects of Pattern Characterization - Continuous Symmetry. PhD thesis, Hebrew University, Jerusalem. Israel.Google Scholar
- Zabrodsky H., Peleg S., and Avnir D. 1992. Hierarchical Symmetry. Proc. Int'l Conf. Pattern Recognition, Aug. 30-Sept.3, The Hague, The Netherlands; 9--11.Google Scholar
- Zabrodsky H., Peleg S. and Avnir D. 1995. Symmetry as a Continuous Feature. IEEE Transactions on Pattern Analysis and Machine Intelligence; 17(12):1154--1166. Google ScholarDigital Library
- Zabrodsky H. and Weinshall D. 3D symmetry from 2D data. 1994. Proc. European Conf. Computer Vision, Stockholm, Sweden.Google Scholar
Recommendations
Detecting mirror symmetry in single-view wireframe sketches of polyhedral shapes
As part of a strategy for creating 3D models of engineering objects from a sketched input, we attempt to identify mirror symmetry planes early in the process. Our input is a 2D line-drawing derived from a single view sketch of a polyhedral shape, and ...
Dominant Symmetry Plane Detection for Point-Based 3D Models
In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element’s area as the initial weight, a ...
Skewed Rotation Symmetry Group Detection
We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation ...
Comments