Solid shape
Determination of the orientation of 3D objects using spherical harmonics
Graphical Models and Image Processing
Stop minding your p's and q's: a simplified O(n) planar embedding algorithm
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The Complex EGI: A New Representation for 3-D Pose Determination
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D zernike descriptors for content based shape retrieval
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Surface Classification Using Conformal Structures
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
A Survey of Content Based 3D Shape Retrieval Methods
SMI '04 Proceedings of the Shape Modeling International 2004
Rotation Estimation from Spherical Images
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Conformal Method for Quantitative Shape Extraction: Performance Evaluation
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Directional histogram model for three-dimensional shape similarity
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Discrete conformal shape representation and reconstruction of 3d mesh objects
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
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The 2D Fourier Descriptor is an elegant and powerful technique for 2D shape analysis. This paper intends to extend such technique to 3D. Though conceptually natural, such an extension is not trivial in that two critical problems, the spherical parametrization and invariants construction, must be solved. By using a newly developed surface parametrization method–the discrete conformal mapping (DCM)—we propose a 3D Fourier Descriptor (3D-FD) for representing and recognizing arbitrarily-complex genus-zero mesh objects. A new DCM algorithm is suggested which solves the first problem efficiently. We also derive a method to construct a truly complete set of Spherical Harmonic invariants. The 3D-FD descriptors have been tested on different complex mesh objects. Experiment results for shape representation are satisfactory.