Seng Luan Lee

A new multifilter design property for multiwavelet image compression

Approximation order, linear phase symmetry, time-frequency localization, regularity, and stopband attenuation are some criteria that are widely used in wavelet filter design. We propose a new criterion called good multifilter properties (GMPs) for the design and construction of multiwavelet filters targeting image compression applications. We first provide the definition of GMPs, followed by a necessary and sufficient condition for an orthonormal multiwavelet system to have a GMP order of at least 1. We then present an algorithm to construct orthogonal multiwavelets possessing GMPs, starting from any length-2N scalar CQPs. Image compression experiments are performed to evaluate the importance of GMPs for image compression, as compared to other common filter design criteria. Our results confirmed that multiwavelets that possess GMPs not only yield superior PSNR performances, but also require much lower computations in their transforms.

Smooth piecewise biquartic surfaces from quadrilateral control polyhedra with isolated n-sided faces

Abstract The modelling of surfaces by piecewise bipolynomial patches has important applications in computer-aided design and computer graphics. However, existing methods do not always work for control polyhedra with arbitrary topology. A method is proposed that uses only piecewise biquartics which will work for control polyhedra with mostly quadrilateral faces and isolated n -sided faces ( n ≠ 4). The surfaces are modelled by converting the control points to Bezier points for each patch using a blending matrix. The blending matrices are constructed from generalized biquartic B-spline blending functions. The domain of definition of these is a nonplanar rectangular surface mesh in 3D Euclidean space. The rectangular mesh consists of rectangular faces whose vertices can have an arbitrary number of edges. The construction of the generalized biquartic B-spline blending functions is described. The resulting surface is geometrically smooth around the extraordinary vertices and parametrically smooth otherwise. Furthermore, free parameters are available for manipulating the shape of the surface locally around the extraordinary points.

Construction of Schauder decomposition on banach spaces of periodic functions

This paper deals with Schauder decompositions of Banach spaces X 2π of 2π-periodic functions by projection operators P k onto the subspaces V k , k = 0,1,…, which form a multiresolution of X 2π ,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C 2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X 2π and a biorthogonal system for X 2π , and its dual X 2π . Decomposition and reconstruction algorithms are derived from the construction.

B-spline scale-space of spline curves and surfaces

We present iterative algorithms for B-spline scale-space smoothing of geometric data and recovery of high frequency information in the smoothing process. The scale-space representation is based on a directional smoothing process using B-splines. If the geometric data are approximated or modelled by uniform B-splines or box-splines then the scale-space smoothing produces B-spline curves or box-spline surfaces. The method is applicable to geometric data processing and geometric modelling of free-form curves and surfaces from quadrilateral polyhedra with extraordinary vertices.

Characterizations of wavelet bases and frames in Hilbert spaces

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