Abstract
In this paper, we propose a novel U-System-based approach for representing and matching similar shapes. U-system is a complete orthogonal piecewise k-degree polynomials in L 2[0,1]and it has some good properties,such as regeneration,convergence by group. Using U-system with finite items, it can be realized to accurate representation of shapes. This paper make shapes analysis in theory. We experimentally demonstrate that U descriptors are more suitable for representing and matching 2D shapes than Fourier descriptors.
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References
Pavlidis, T.: A Review of Algorithms for Shape Analysis. Computer Vision, Graphics, and Image Processing 7, 243–258 (1978)
Rui, Y., She, A.C., Huang, T.S.: Modified Fourier Descriptors for Shape Representation-A Practical Approach. In: Proc. First Int’l Workshop Image Databases and Multi Media Search, pp. 22–23 (August 1996)
Ma, W.-Y., Manjunath, B.S.: NeTra:A Toolbox for Navigating Large Image Databases. Multimedia Systems 7(3), 184–198 (1999)
Berretti, S., Del Bimbo, A., Pala, P.: Retrieval by Shape Similarity with Perceptual Distance and Effective Indexing. IEEE Trans. Multimedia 2(4), 225–239 (2000)
Bartolini, I., Ciaccia, P., Patella, M.: WARP: Accurate Retrieval of Shapes Using Phase of Fourier Descriptors and Time Warping Distance. IEEE Transactions on Pattern Analysis And Machine Intelligence 27(1), 142–147 (2005)
Zhongkan, C.: Orthogonal functions and its applications (1982)
Harmuth, H.F.: Sequency Theory Foundations and Applications (1977)
Feng, Y., Qi, D.: A Sequence of Piecewise Orthogonal Polynomials. J. of SIAM J. Math. Anal. 15(4), 834–844 (1984)
Micchelli, C.A., Xu, Y.: Using the Matrix Refinement Equation for the Construction of Wavelets on Invariant Sets. Applied and Computational Harmonic Analysis 1, 391–401 (1994)
Battle, G.: Wavelets of Federbush-Lemarie type (preprint, 1993)
Federbush, P.: A mass zero cluster expansion. Part 1, The expansion, Comm.Math.Phys. 81, 327–340 (1981)
Dongxu, Q., Yuyu, F.: On the Convergence of Fourier-U Series. J. of University of Science and Technology of China, Issue of Math. 5, 7–17 (1983)
Dongxu, Q., Yuyu, F.: On the Orthogonal Complete system U. Acta.Scientiarum Naturalium Universitatis Jilinensis 2, 21–31 (1984)
Qishan, Z., Youguang, Z.: The Theory of Bridge Function and Its Application. National Defence Industry Press, Beijing (1992) (in Chinese)
Qi, D.: Frequency Spectrum Analysis in Digital Geometry (Special report), Hefei City (2005)
Qi, D., Tao, C., Song, R., Ma, H., Sun, W., Cai, Z.: Representation for a Group of Parametric Cures Based on the Orthogomal Complete U-system. J. of Computer (accepted, 2005)
Ma, H., Song, R., Tao, C., Qi, D.: Orthogonal Complete U-system and Its Application in CAGD. The first Korea-Chin Joint Conference on Geometric and Visual Computing (accepted, 2005)
Song, R., Ma, H., Qi, D.: A New Class of Complete Orthogonal Functions and Its Applications Based on U-system. In: The 4th International Conference on Wavelet Analysis and Its Applications (accepted, 2005)
Feng, Y.Y., Qi, D.X.: On the Harr and Walsh Systems on a Triangle.MRC Technical Summary Report No.2235, University of Wisconsin-Madison (1981)
Kauppinen, H., Seppanen, T., Pietikainen, M.: An Experimental Comparison of Autoregressive and Fourier-Based Descriptors in 2D Shape Classification. IEEE Trans. Pattern Analysis and Machine Intelligence 17(2), 201–207 (1997)
Zhang, D., Lu, G.: A Comparative Study of Fourier Descriptors for Shape Representation and Retrieval. In: Proc. Fifth Asian Conf. Computer Vision(ACCV 2002), pp. 646–651 (January 2002)
Pelillo, M., Siddiqi, K., Zucker, S.: Matching hierarchical structures using association graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(11), 1105–1120 (1999)
Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing shock graphs. In: Proceedings of the 8th International Conference on Computer Vision (2001), pp. 755–762 (2001)
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Cai, Z., Sun, W., Qi, D. (2006). Matching 2D Shapes Using U Descriptors. In: Nishita, T., Peng, Q., Seidel, HP. (eds) Advances in Computer Graphics. CGI 2006. Lecture Notes in Computer Science, vol 4035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784203_18
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DOI: https://doi.org/10.1007/11784203_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35638-7
Online ISBN: 978-3-540-35639-4
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