This paper introduces a novel class of length-4N orthonormal scalar wavelets, and presents the theory, implementational issues, and their applications to image compression. We first give the necessary and sufficient conditions for the existence of this class. The parameterized representation of filters with different lengths are then given. Next, we derive new and efficient decomposition and reconstruction algorithms specifically tailored to this class of wavelets. We show that the proposed discrete wavelet transformations are orthogonal and have lower computational complexity than conventional octave-bandwidth transforms using Daubechies' (1989) orthogonal filters of equal length. In addition, we also verify that symmetric boundary extensions can be applied. Finally, our image compression results further confirm that improved performance can be achieved with lower computational cost.

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.

The Gaussian kernel has long been used in the classical multiscale analysis. The purpose of the paper is to propose the uniform B-spline as an alternative for the visual modeling. A general framework for various scale-space representations is formulated using the B-spline approach. In particular, the evolution of the wavelet models can be well understood from such an approach. Most of the wavelet representations can be factored into B-spline bases and hence can be implemented efficiently using the spline technique. Besides, it is shown that the B-spline scale-space representations not only inherit most of the properties of the Gaussian scale-space but also have many advantages with respect to the efficiency, compactness and parallel structure.

This paper presents a new multiscale curvature-based shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to efficiently estimate the multiscale curvature functions. Based on the curvature scale-space image, we introduce a coarse-to-fine matching algorithm which automatically detects the dominant points and uses them as knots for curve interpolation.

This paper proposes a scale-space theory based on B-spline kernels. Our aim is twofold: 1) present a general framework, and show how B-splines provide a flexible tool to design various scale-space representations. In particular, we focus on the design of continuous scale-space and dyadic scale-space frame representations. A general algorithm is presented for fast implementation of continuous scale-space at rational scales. In the dyadic case, efficient frame algorithms are derived using B-spline techniques to analyze the geometry of an image. The relationship between several scale-space approaches is explored. The behavior of edge models, the properties of completeness, causality, and other properties in such a scale-space representation are examined in the framework of B-splines. It is shown that, besides the good properties inherited from the Gaussian kernel, the B-spline derived scale-space exhibits many advantages for modeling visual mechanism including the efficiency, compactness, orientation feature and parallel structure.

Two classes of closed piecewiee bicubic surfaces are considered.These surfaces are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points.Furthermore, free parameters are available for manipulating the shape of the surface without changing the control polyhedron.The control is local for a large control polyhedron.