Computing Polynomial Segmentation through Radial Surface Representation

 

Leticia Flores-Pulido¹, Gustavo Rodríguez-Gómez², Oleg Starostenko³, Vicente Alarcón³, and Alberto Portilla¹

 

¹ PCSCE, Universidad Autónoma de Tlaxcala, Tlaxcala, Mexico (e-mail: leticia.florespo@udlap.mx, alberto.portilla@udlap.mx).

² Coordinación de Ciencias Computacionales, Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, Mexico (e-mail: grodrig@inaoep.mx).

³ Escuela de Ingeniería, Universidad de las Amerícas Puebla, Mexico (e-mail: oleg.starostenko@udlap.mx, vicente.alarcon@udlap.mx).

 

Manuscript received on December 17, 2012
Revised version on June 6, 2014
Accepted for publication on June 12, 2014.

 

Abstract

The Visual Information Retrieval (VIR) area requires robust implementations achieved trough mathematical representations for images or data sets. The implementation of a mathematical modeling goes from the corpus image selection, an appropriate descriptor method, a segmentation approach and the similarity metric implementation whose are treated as VIR elements. The goal of this research is to found an appropriate modeling to explain how its items can be represented to achieve a better performance in VIR implementations. A direct method is tested with a subspace arrangement approach. The General Principal Component Analysis (GPCA) is modified inside its segmentation process. Initially, a corpus data sample is tested, the descriptor of RGB colors is implemented to obtain a three dimensional description of image data. Then a selection of radial basis function is achieved to improve the similarity metric implemented. It is concluded that a better performance can be achieved applying powerful extraction methods in visual image retrieval (VIR) designs based in a mathematical formulation. The results lead to design VIR systems with high level of performance based in radial basis functions and polynomial segmentations for handling data sets.

Key words: Subspace arrangement, data modeling, segmentation, polynomial function, radial basis surface representation.

 

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References

[1] S. Little and S. Rueger, "Conservation of effort in feature selection for image annotation," in IEEE Workshop on Multimedia Signals Processing, (MMSP 2009), Rio de Janeiro, Brazil, 2009, pp. 5-7.         [ Links ]

[2] C. D. Manning, P. Raghavan, and H. Schutze, An Introduction to Information Retrieval. Cambridge, England: Cambridge university Press, 2009.         [ Links ]

[3] K. Shearer, S. Venkatesh, and H. Bunke, "Rapid similarity retrieval from image and video," in Multimedia Image and Video Processing, L. Guan, S. Y. Kung, and J. Larsen, Eds. CRC Press, 2001, ch. 15, pp. 437-466.         [ Links ]

[4] M. Y. Yang, H. Derksen, and R. Fossum, "Estimation of subspace arrangements with applications in modeling and segmenting mixed data," SIAM Review, vol. 50, no. 3, pp. 413-458, August 2008.         [ Links ]

[5] A. Bjorner, I. Peeva, and J. Sidman, "Subspace arrangements defined by products of linear forms," J. London Math. Soc., vol. 2, no. 71, pp. 273-288, 2005.         [ Links ]

[6] H. Derksen, "Series of subspace arrangements," preprint, 2005. [Online]. Available: http://arxiv.org/abs/math/0510584         [ Links ]

[7] R. Vidal and J. Piazzi, "A new GPCA algorithm for clustering subspaces by fitting," in Differentiating and Dividing Polynomials, CVPR, 2004, pp. 510-514.         [ Links ]

[8] D. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, pp. 1289-1306, April 2006.         [ Links ]

[9] R. Duda, P. Hart, and D. Stork, Pattern Classification, 2nd ed. WILEY, 2001.         [ Links ]

[10] Y. Sugaya and K. Kanatani, "Outlier removal for motion tracking by subspace separation," IEICE Trans. Inform, vol. E86-D, pp. 1095-1102, 2003.         [ Links ]

[11] A. Yang, S. Rao, and Y. Ma, "Robust statistical estimation and segmentation of multiple subspaces," in Workshop on 25 years of RANSAC, IEEE International Conference on Computer Vision and Pattern Recognition, 2006, pp. 99-106.         [ Links ]

[12] K. Kanatani, "Motion segmentation by subspace separation and model selection," in The 8th International Conference in Computer Vision, vol. 2, Vancouver, Canada, July 2001, pp. 586-591.         [ Links ]

[13] -, "Geometric inference from images, what kind of statistical model is necessary?" Systems and Computers in Japan, vol. 35, no. 6, pp. 1-9, 2006.         [ Links ]

[14] S. Roweis and L. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science, vol. 290, pp. 2323-2326, 2000.         [ Links ]

[15] K. Huang, A. Wagner, and Y. Ma, "Identification of hybrid linear time-invariant systems via subspace embedding and segmentation," in Proceedings of the IEEE Conference on Decision and Control, vol. 3, 2004, pp. 3227-3234.         [ Links ]

[16] Y. Ma and R. Vidal, "A closed form solution to the identiication of hybrid ARX models via the identification of algebraic varieties," in Proceedings of the International Conference on Hybrid Systems Computation and Control, 2005, pp. 449-465.         [ Links ]

[17] S. Rao, A. Yang, A. Wagner, and Y. Ma, "Segmentation of hybrid motions via hybrid quadratic surface analysis," in Proceedings of IEEE International Conference on Computer Vision, 2005, pp. 2-9.         [ Links ]

[18] R. Vidal, Y. Ma, and S. Sastry, "Generalized principal component analysis (GPCA)," IEEE Trans. Pattern Anal. Machine Intelligence, vol. 27, pp. 1-15, 2003.         [ Links ]

[19] L. Flores-Pulido, Data Segmentation Modeling for Visual Information Retrieval Systems. Puebla, Mexico: Universidad de las Americas, 2011.         [ Links ]

[20] L. Flores-Pulido, W. E. Estrada-Cruz, and J. A. Chavez-Aragon, "An image retrieval system based on feature extraction for machine vision using three similarity metrics," in Congreso Internacional Cars Fof 2007, 23rd ISPE International Conference on Cad/Cam, Robotics Factories of the Future, Universidad Militar De Nueva Granada, Bogota, Colombia, August 2007.         [ Links ]

[21] A. Iske, Multiresolution Methods in Scattered Data Modeling, ser. Lecture Notes in Computational Science and Engineering. Springer, 2004, vol. 37.         [ Links ]