Frequency-based representation of 3D point-based surfaces using spherical harmonics
Authors: 
M. Mousa, R. Chaine, S. AkkoucheAuthors Info & Claims
Abstract
In this paper, we propose a precise frequency-based representation for oriented point-based surfaces using spherical harmonics. The representation can be useful in many applications, such as filtering, progressive transmission and coding of 3D surfaces. The basic computation in our approach is the spherical harmonics transform of local spherical radial functions induced by a set of points. An important feature of our approach is that the calculations are performed directly on local 2D triangulations of the point-based surface without any prior space voxelization. This property ensures that the complexity of our computation of the spherical harmonics transform is linear in the number of triangles in the local patch. We present some experimental results which demonstrate our technique.
References
[1]
1992 {1} Hoppe H., DeRose T., Duchamp T., McDonald J., Stuetzle W.: Surface reconstruction from unorganized points. In SIGGRAPH'92, 71-78.
[2]
2001 {2} Pauly M., Gross M.: Spectral processing of point-sampled geometry. In SIGGRAPH '01, 379-386.
[3]
2001 {3} Saupe D., Vranic D. V.: 3D model retrieval with spherical harmonics and moments. In DAGM'01, 392-397.
[4]
2001 {4} Vranic D., Saupe D.: 3D shape descriptor based on 3d fourier transform. In Digital Signal Processing for Multimedia Communications and Services, 271-274.
[5]
2001 {5} Zhang C., Chen T.: Efficient feature extraction for 2d/3d objects in mesh representation. In ICIP '01, 935-938.
[6]
2003 {6} Boissonnat J. D., Oudot S.: Provably good surface sampling and approximation. : In SGP'03 Eurographics Association, 9-18.
[7]
2003 {7} Funkhouser T., Min P., Kazhdan M., Chen J., Halderman A., Dobkin D., Jacobs D.: A search engine for 3d models. ACM Transactions on Graphics 22(1), 83-105.
[8]
2003 {8} Green R.: Spherical harmonic lighting: The gritty details. In Game Developers Conference.
[9]
2003 {9} Healy D., Rockmore D., Kostelec P., Moore S.: FFTs for the 2-sphere-improvements and variations. Fourier Analysis and Applications 9(4) 341-385.
[10]
2003 {10} Kazhdan M., Funkhonser T., Rusinkiewicz S.: Rotation invariant spherical harmonic representation of 3d shape descriptors. In SGP '03 156-164.
[11]
2003 {11} Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.-P.: Multi-level partition of unity implicits. ACM Trans. Graph. 22(3), 463-470.
[12]
2004 {12} Sorkine O., Cohen-Or D., Lipman Y., Alexa M., Rössl C., Seidel H.-P.: Laplacian surface editing. In SGP'04, 175-184.
[13]
2004 {13} Zhou K., Bao H., Shi J.: 3D surface filtering using spherical harmonics. Computer-Aided Design 36(4), 363-375.
[14]
2005 {14} Boubekeur T., Reuter P., Schlick C.: Visualization of point-based surfaces with locally reconstructed subdivision surfaces. In SMI'05, 23-32.
[15]
2005 {15} Kazhdan M.: Reconstruction of solid models from oriented point sets. In SGP'05, 73-82.
[16]
2006 {16} Křivánek J., Konttinen J., Bouatouch K., Pattanaik S., Žára J.: Fast approximation to spherical harmonic rotation. In SCCG'06, ACM Press.
[17]
2006 {17} Mousa M., Chaine R., Akkouche S.: Direct spherical harmonic transform of a triangulated mesh. JGT 11(2), 17-26.
[18]
2006 {18} Mousa M., Chaine R., Akkouche S.: Frequency-based representation of 3d models using spherical harmonics. In WSCG'06, 193-200.
[19]
2006 {19} Tosic I., Frossard P.: FST-based reconstruction of 3d-models from non-uniformly sampled datasets on the sphere. In Picture Coding Symposium.
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- Frequency-based representation of 3D point-based surfaces using spherical harmonics
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Polish Academy of Sciences
Poland
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Published: 01 January 2006
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