3D Objects Indexing Using Spherical Harmonic for Optimum Measurement Similarity
In this paper, we propose a method for three-dimensional
(3-D)-model indexing based on defining a new
descriptor, which we call new descriptor using spherical harmonics.
The purpose of the method is to minimize, the processing time on the
database of objects models and the searching time of similar objects
to request object.
Firstly we start by defining the new descriptor using a new
division of 3-D object in a sphere. Then we define a new distance
which will be used in the search for similar objects in the database.
[1] B.Cabral, N. Max and R. Springmeyer. Bidirectional Reflection
Functions from Surface Bump Maps SIGGRAPH 273-281, 1987
[2] Volker Schönefeld, Spherical Harmonics,1st July 2005
[3] Gerig, G. Styner, M. Jones, D., Weinberger, D. Lieberman, J., 2001.
Shape analysis of brain ventricles using spharm. In: MMBIA , pp. 171-
178.
[4] B.K.P Horn. Extended Gaussian Images. Proc. of the IEEE,
72(12):1671–1686, dec. 1984.
[5] http://scienceblogs.de/mathlog/2011/09/30/topologie-von-flachenclxxxvii/
[6] S.B. Kang and K. Ikeuchi. The complex EGI: a new representation for
3D pose determination. IEEE Trans. on Pattern Analysis and Machine
Intelligence, 16(3):249–258, March 1994.21, hal-00538470, version 1 -
22 Nov 2010
[7] Brecbuhler, Ch., Gerig, G., Kuhler, O., 1995. Parameterization of closed
surfaces for 3D shape description. Computer Image and Vision
Understanding 61 (2), 154-170.
[8] R. Ohbuchi, T.Minamitani, and T .Takei. Shape-similarity search of 3D
models by using enhanced shape functions. In Int. J. of Computer
Applications inTechnology (IJCAT), 23(3/4/5):70-85, 2005.
[9] P. Papadakis, I. Pratikakis, S. Perantonis, and T. Theoharis. Efficient 3D
Shape Matching and Retrieval using a Concrete Radialized Spherical
Projection Representation. Pattern Recognition Journal, 40(9):2437–
2452, Sept. 2007.
[10] M. Ben-Chen and C. Gostman. Characterizing Shape Using Confor- mal
Factors. In Eurographics Workshop on 3D Object Retrieval, Crete,
Greece., April 2008.
[11] T. Tung and F. Schmitt. The augmented multiresolutionReeb graph
approach for content-based retrieval of 3D shapes. International Journal
of Shape Modeling (IJSM), 11(1):91–120, June 2005.
[12] S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno. Reeb graphs for
shape analysis and applications. Theoretical Computer Science, 392 (1-
3):5–22, 2008.22 hal-00538470, version 1 - 22 Nov 2010
[13] D.V. Vranic. 3D Model Retrieval. PhD thesis, University of Leipzig,
2004.
[14] M. Kazhdan, B. Chazelle, D. Dobkin, T. Funkhouser, and S.
Rusinkiewicz. A Reflective Symmetry Descriptor for 3D Models. Algorithmica,
38(1):201–225, 2003.
[15] J.W.H. Tangelder and R.C. Veltkamp, “A survey of content based 3D
shape retrieval methods,” Multimedia Tools and Applications, vol. 39,
no. 3, pp. 441–471, Sept. 2008.
[16] Gerig, G. Styner, M. Jones, D., Weinberger, D. Lieberman, J., 2001.
Shape analysis of brain ventricles using spharm. In: MMBIA , pp. 171-
178.
[17] René Lagrange, Polynômes et fonctions de Legendre coll. Mémorial des
sciences mathématiques, n° 97, Gauthier-Villars, 1939.
[18] W. E. Byerly. Spherical Harmonics, chapter 6, pages 195-218.New
York: Dover, 1959. An elementary treatise on fourier's series and
spherical, cylindrical, and ellipsoidal harmonics, with applications to
problems in mathematical physics.
[19] M. Mousa, R. Chaine, and S. Akkouche. Frequency-based representation
of 3d models using spherical harmonics. In WSCG’06 : Proceedings of
the 14th International Conference in Central Europe on Computer
Graphics, Visualization and Computer Vision, volume 14, pages 193–
200, Plzen, Czech Republic, January 30 - February 3 2006.
[20] T. Zaharia and F. Prêteux, “3D versus 2D/3D shape descriptors: A
comparative study,” in SPIE Conf. on Image Processing: Algorithms and
Systems III - IS & T/ SPIE Symposium on Electronic Imaging, Science
and Technology ’03, San Jose, CA, Jan. 2004, vol. 5298 [21] M. Chaouch and A. Verroust-Blondet, “A new descriptor for 2D depth
image indexing and 3D model retrieval,” in Proc. ICIP’07, vol. 6, 2007,
pp. 373–376.
[1] B.Cabral, N. Max and R. Springmeyer. Bidirectional Reflection
Functions from Surface Bump Maps SIGGRAPH 273-281, 1987
[2] Volker Schönefeld, Spherical Harmonics,1st July 2005
[3] Gerig, G. Styner, M. Jones, D., Weinberger, D. Lieberman, J., 2001.
Shape analysis of brain ventricles using spharm. In: MMBIA , pp. 171-
178.
[4] B.K.P Horn. Extended Gaussian Images. Proc. of the IEEE,
72(12):1671–1686, dec. 1984.
[5] http://scienceblogs.de/mathlog/2011/09/30/topologie-von-flachenclxxxvii/
[6] S.B. Kang and K. Ikeuchi. The complex EGI: a new representation for
3D pose determination. IEEE Trans. on Pattern Analysis and Machine
Intelligence, 16(3):249–258, March 1994.21, hal-00538470, version 1 -
22 Nov 2010
[7] Brecbuhler, Ch., Gerig, G., Kuhler, O., 1995. Parameterization of closed
surfaces for 3D shape description. Computer Image and Vision
Understanding 61 (2), 154-170.
[8] R. Ohbuchi, T.Minamitani, and T .Takei. Shape-similarity search of 3D
models by using enhanced shape functions. In Int. J. of Computer
Applications inTechnology (IJCAT), 23(3/4/5):70-85, 2005.
[9] P. Papadakis, I. Pratikakis, S. Perantonis, and T. Theoharis. Efficient 3D
Shape Matching and Retrieval using a Concrete Radialized Spherical
Projection Representation. Pattern Recognition Journal, 40(9):2437–
2452, Sept. 2007.
[10] M. Ben-Chen and C. Gostman. Characterizing Shape Using Confor- mal
Factors. In Eurographics Workshop on 3D Object Retrieval, Crete,
Greece., April 2008.
[11] T. Tung and F. Schmitt. The augmented multiresolutionReeb graph
approach for content-based retrieval of 3D shapes. International Journal
of Shape Modeling (IJSM), 11(1):91–120, June 2005.
[12] S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno. Reeb graphs for
shape analysis and applications. Theoretical Computer Science, 392 (1-
3):5–22, 2008.22 hal-00538470, version 1 - 22 Nov 2010
[13] D.V. Vranic. 3D Model Retrieval. PhD thesis, University of Leipzig,
2004.
[14] M. Kazhdan, B. Chazelle, D. Dobkin, T. Funkhouser, and S.
Rusinkiewicz. A Reflective Symmetry Descriptor for 3D Models. Algorithmica,
38(1):201–225, 2003.
[15] J.W.H. Tangelder and R.C. Veltkamp, “A survey of content based 3D
shape retrieval methods,” Multimedia Tools and Applications, vol. 39,
no. 3, pp. 441–471, Sept. 2008.
[16] Gerig, G. Styner, M. Jones, D., Weinberger, D. Lieberman, J., 2001.
Shape analysis of brain ventricles using spharm. In: MMBIA , pp. 171-
178.
[17] René Lagrange, Polynômes et fonctions de Legendre coll. Mémorial des
sciences mathématiques, n° 97, Gauthier-Villars, 1939.
[18] W. E. Byerly. Spherical Harmonics, chapter 6, pages 195-218.New
York: Dover, 1959. An elementary treatise on fourier's series and
spherical, cylindrical, and ellipsoidal harmonics, with applications to
problems in mathematical physics.
[19] M. Mousa, R. Chaine, and S. Akkouche. Frequency-based representation
of 3d models using spherical harmonics. In WSCG’06 : Proceedings of
the 14th International Conference in Central Europe on Computer
Graphics, Visualization and Computer Vision, volume 14, pages 193–
200, Plzen, Czech Republic, January 30 - February 3 2006.
[20] T. Zaharia and F. Prêteux, “3D versus 2D/3D shape descriptors: A
comparative study,” in SPIE Conf. on Image Processing: Algorithms and
Systems III - IS & T/ SPIE Symposium on Electronic Imaging, Science
and Technology ’03, San Jose, CA, Jan. 2004, vol. 5298 [21] M. Chaouch and A. Verroust-Blondet, “A new descriptor for 2D depth
image indexing and 3D model retrieval,” in Proc. ICIP’07, vol. 6, 2007,
pp. 373–376.
@article{"International Journal of Information, Control and Computer Sciences:68915", author = "S. Hellam and Y. Oulahrir and F. El Mounchid and A. Sadiq and S. Mbarki", title = "3D Objects Indexing Using Spherical Harmonic for Optimum Measurement Similarity", abstract = "In this paper, we propose a method for three-dimensional
(3-D)-model indexing based on defining a new
descriptor, which we call new descriptor using spherical harmonics.
The purpose of the method is to minimize, the processing time on the
database of objects models and the searching time of similar objects
to request object.
Firstly we start by defining the new descriptor using a new
division of 3-D object in a sphere. Then we define a new distance
which will be used in the search for similar objects in the database.
", keywords = "3D indexation, spherical harmonic, similarity of 3D
objects.", volume = "9", number = "1", pages = "241-6", }
