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Efficient 3D geometric and Zernike moments computation from unstructured surface meshes
José María Pozo1, Maria-Cruz Villa-Uriol, Alejandro F Frangi
1Center for Computational Imaging & Simulation Technologies in Biomedicine, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain. jose.pozo@upf.edu
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 18, 2010
Summary
This study presents efficient algorithms for calculating 3D geometric moments and 3D Zernike moments from surface meshes. These methods offer significant computational speedups for homogeneous objects compared to existing techniques.
Area of Science:
- Computational geometry
- Computer graphics
- Image analysis
Background:
- Calculating 3D geometric moments is crucial for shape analysis and object recognition.
- Existing volumetric methods are computationally intensive.
- Surface-based methods offer potential for reduced complexity but have limitations.
Purpose of the Study:
- To introduce and evaluate fast exact and approximate algorithms for 3D geometric moments from surface meshes.
- To develop a rapid algorithm for 3D Zernike moments computation.
- To analyze the trade-offs between accuracy and computational cost.
Main Methods:
- Developed an exact algorithm reducing complexity from N(9) to N(6).
- Introduced a series approximation algorithm with complexity reduced to N(3).
- Created a fast algorithm for 3D Zernike moments with N(4) complexity.
Main Results:
- The proposed exact algorithm significantly improves computational efficiency for geometric moments.
- The approximate algorithm provides a tunable balance between accuracy and speed.
- The new Zernike moment algorithm is faster than previous N(6) methods.
Conclusions:
- Surface-based algorithms are efficient for computing moments of homogeneous objects.
- The developed algorithms offer substantial computational advantages for 3D shape analysis.
- The approximate method's accuracy depends on mesh quality and desired moment order.
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