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The complete orthogonal V-system and its applications
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2007
Year
EngineeringLinear SystemOrthogonal CompletenessMatrix TheoryFunctional AnalysisMulti-resolution MethodImage AnalysisPattern RecognitionEdge DetectionFunction GeneratorComputational GeometryApproximation TheoryGeometric ModelingGeometric InterpolationComplete Orthogonal V-systemMultidimensional Signal ProcessingMatrix AnalysisWavelet TheoryNatural Sciences
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.