September  2007, 6(3): 853-871. doi: 10.3934/cpaa.2007.6.853

The complete orthogonal V-system and its applications


Faculty of Information Technology, Macau University of Science and Technology, Macau, Macau


College of Sciences, North China University of Technology, Beijing 100041, China


School of Mathematics and Computer Sciences, Harbin Normal University, Harbin 150080, China

Received  May 2006 Revised  February 2007 Published  June 2007

Based on the function generator on [0,1], a class of complete orthogonal function system called as the V-system is studied in this paper. The V-system is composed by piecewise polynomials, and is capable of exactly describing the geometric information expressed by the popularly and widely used polynomial spline curves and surfaces. The V-system has all of the beautiful properties of the U-system: continuity, discontinuity, orthogonal completeness and reproducibility. In addition, the V-system also has the concise structure, compactly local support and multi-resolution capability. The V-system is the generalization of the well-known Haar function system, and is also a new class of practical and flexible wavelet bases. By utilizing the concepts of the energy and the descriptor of the V-system, we study the degree of similarity of geometric models which can be used in image analysis and processing.
Citation: Hui Ma, Dongxu Qi, Ruixia Song, Tianjun Wang. The complete orthogonal V-system and its applications. Communications on Pure & Applied Analysis, 2007, 6 (3) : 853-871. doi: 10.3934/cpaa.2007.6.853

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