Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
A simple and efficient algorithm for determining the symmetries of polyhedra
CVGIP: Graphical Models and Image Processing
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry Identification of a 3-D Object Represented by Octree
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Reflective Symmetry Descriptor
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Determination of the Symmetries of Polyhedra and an Application to Object Recognition
CG '91 Proceedings of the International Workshop on Computational Geometry - Methods, Algorithms and Applications
Polyhedral Model Retrieval Using Weighted Point Sets
SMI '03 Proceedings of the Shape Modeling International 2003
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Matching 3D Models with Shape Distributions
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Testing congruence and symmetry for general 3-dimensional objects
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
Feature Combination and Relevance Feedback for 3D Model Retrieval
MMM '05 Proceedings of the 11th International Multimedia Modelling Conference
Symmetry descriptors and 3D shape matching
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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Recent advancements in 3D scanning technologies have inspired the development of effective methods for matching and retrieving 3D objects. A common pre-processing stage of these retrieval methods is to normalize the position, size, and orientation of the objects based on PCA. It aligns an object's orientation based on PCA eigenvectors, and normalizes its size uniformly in all 3 spatial dimensions based on the variance of the object points. However, orientation alignment by PCA is not robust, and objects with similar shape can be misaligned. Uniform scaling of the objects is not ideal because it does not take into account the differences in the objects' 3D aspect ratios, resulting in misalignment that can exaggerate the shape difference between the objects. This paper presents a method for computing 3D objects' bilateral symmetry planes (BSPs) and BSP axes and extents, and a method for normalizing 3D objects based on BSP axes and extents. Compared to normalization methods based on PCA and minimum volume bounding box, our BSP-based method can normalize and align similar objects in the same category in a semantically more meaningful manner, such as aligning the objects' heads, bodies, legs, etc.