3D Recognition Using Affine Invariants

Abstract

The size of 3D data stored around the web has become bigger. Therefore the development of recognition applications and retrieval systems of 3D models is important. This paper deals with invariants for 3D models recognition. Thus under general affine transform we propose in a first time determinants of three points to realize invariance under affinity. To solve starting point problem we needs Fourier Series (FS) to extract affine invariant descriptors, called Fourier Series Descriptor (FSD). The difference between first and second approaches: in first approach determinants are computed on cartesian coordinates directly while in the second one determinants are computed from FS coefficients to eliminate dependency on starting point. The FS are also applied on 2D slices to generate affine invariants for 3D volume. FS can be computed based on hole points of volume, but this technique. The principal advantages of proposed approaches is the possibility to handle affine transform and 3D volume. Two types of 3D objects are used in the experimentations: mesh and volume, the Princeton Shape Benchmarek (PSB) is also used to test our descriptor based on FSD.

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A. El Oirrak, M. Elhachloufi, E. Ait Lmaati, M. Sadgal and M. Najib Kaddioui, "3D Recognition Using Affine Invariants," Journal of Signal and Information Processing, Vol. 3 No. 2, 2012, pp. 179-184. doi: 10.4236/jsip.2012.32024.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] T. F. Ansary, M. Daoudi and J. P. Vandeborre, “A Bayesian 3D Search Engine Using Adaptive Views Clustering,” IEEE Transaction on Multimedia, Vol. 9, 2007, pp. 78-88. doi:10.1109/TMM.2006.886359
[2] E. A. Lmaati, A. El Oirrak and M. N. Kaddioui, “3D Model Retrieval Based on 3D Discrete Cosine Transform,” International Arab Journal of Information Technology, Vol. 7, No. 3, 2010, pp. 264-271.
[3] E. A. Lmaati, A. El Oirrak and M. N. Kaddioui, “A 3D Search Engine Based on 3d Curve Analysis,” Signal, Image and Video Processing, Vol. 4, No. 1, 2009, pp. 89-98.
[4] MPEG-7 Video Group, “Information Technology Multimedia Content Description Interface,” Part 3: Visual, ISO/ IEC FCD, 15938:3/N4062, MPEG-7, 2001.
[5] R. Osada, T. Funkhouser, B. Chazelle and D. Dobkin, “Matching 3D Models with Shape Distributions,” Proceedings of the International Conference on Shape Modeling & Applications, Genova, 2001, pp. 154-166.
[6] E. Paquet and M. Rioux, “A Query by Content Software for Three-Dimensional Models Databases Management,” Conference on Recent Advances 3-D Digital Imaging and Modeling, Ottawa, 12-15 May 1999, pp. 345-352.
[7] D. Y. Chen, M. Ouhyoung, X. P. Tian and Y. T. Shen, “On Visual Similarity Based 3D Model Retrieval,” Eurographics, Vol. 22, No. 3, 2003, pp. 223-232.
[8] D. V. Vranic and D. Saupe, “3D Model Retrieval with Spherical Harmonics and Moments,” B. Radig and S. Florczyk, Eds., Proceedings of the 23rd DAGM-Symposium on Pattern Recognition, Munich, 2001, pp. 392-397.
[9] D. V. Vranic and D. Saupe, “Description of 3D Shape Using a Complex Function on the Sphere,” IEEE International Conference on Multimedia ICME, Vol. 1, 2002, pp. 177-180.
[10] D. V. Vranic, “An Improvement of Rotation Invariant 3D-Shape Descriptor Based on Functions on Concentric Spheres,” IEEE International Conference on Image Processing, 14-17 September 2003, pp. 757-760.
[11] J.-L. Dugelay, A. Baskurt and M. Daoudi, “3D Object processing: Indexing Compression and Watermarking,” John Wiley Sons Inc., New York, 2008.
[12] A. Eloirrak, M. Daoudi and D. Aboutajdine, “Affine Invariant Descriptors Using Fourier Series,” Pattern Recognition Letters, Vol. 23, No. 10, 2002, pp. 1109-1118. doi:10.1016/S0167-8655(02)00027-2
[13] A. Eloirrak, M. Daoudi and D. Aboutajdine, “Affine Invariant Descriptors for Color Images Using Fourier Series,” Pattern Recognition Letters, Vol. 24, No. 9, 2003, pp. 1339-1348. doi:10.1016/S0167-8655(02)00375-6
[14] Udeepta, D. Bordoloi and H.-W. Shen, “Space Efficient Fast Isosurface Extension for Large Datasets,” IEEE Visualization, Washington DC, 19-24 October 2003, pp. 201-208.
[15] P. Shilane, M. Kazhdan, P. Min and T. Funkhouser, “The Princeton Shape Benchmark,” Shape Modeling International, 2004, pp. 345-352.
[16] M. Garland and P. Heckbert, “Surface Simplification Using Quadric Error Metrics,” Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, 3-8 August 1997.
[17] M. Novotni and R. Klein, “3D Zernike Descriptors for Content Based Shape Retrieval,” Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications, Seattle, 16-20 June 2003, pp. 216-225. doi:10.1145/781606.781639
[18] M. Heczko, D. A. Keim, Saupe and D. Vranic, “Verfahren zur Ahnlichkeitssuche auf 3D Objekten (Methods for Similarity Search on 3D Databases),” Datenbank-Spektrum, Vol. 2, No. 2, 2002, pp. 54-63.

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