A new method for manipulation of curves in several degrees is presented. When a point of curve is moved, it a ects a relative local segment, which size could depends of the propagation of the point through their lower resolution curves. So, for the same displacement of the point, could be generated relative local segments of di erent sizes, only varying a local parameter such sti ness constant....

This paper reports the work on a novel wavelet-based multi-scale filtering application used to generate very smooth subset of profiles known as Class-A curves. The multi-scale representation, based on B-spline wavelets, allows to split a spline curves in terms of a coarser least-square approximation and details coefficients. It raises that non-Class-A curves are determined by geometric imperfec...

We consider equidistant discrete splines S(j), j ∈ Z, which may grow as O(|j|s) as |j| → ∞. Such splines present a relevant tool for digital signal processing. The Zak transforms of Bsplines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation o...

Ruttimann et al. have proposed to use the wavelet transform for the detection and localization of activation patterns in functional magnetic resonance imaging (fMRI). Their main idea was to apply a statistical test in the wavelet domain to detect the coefficients that are significantly different from zero. Here, we improve the original method in the case of non-stationary Gaussian noise by repl...

We study a spline wavelet alternative direction implicit (SW-ADI) algorithm for solving two-dimensional reaction diffusion equations. This algorithm is based on a collocation method for PDEs with a specially designed spline wavelet for the Sobolev space H 2(I ) on a closed interval I. By using the tensor product nature of adaptive wavelet meshes, we propose a SW-ADI method for two-dimensional p...

We analyze the internal structure of the multiresolution analyses of L2(Rd) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V0 to be the closed linear span of the shifts of the scaling function and W0 that of the shifts of the wavelets. Finally, define V1 to be the dyadic dilation of V0. We characterize the condi...

We show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC. However, the phase distortion at the other frequencies can be much larger. We design a new class of real-valued, compactly supported, orthonormal, and nearly symmetric wavelets (we call them generalized...

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale twoand three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on subdivision. The -subdivision scheme only double...

We describe a new family of scaling functions, the (α, τ)fractional splines, which generate valid multiresolution analyses. These functions are characterized by two real parameters: α, which controls the width of the scaling functions; and τ , which specifies their position with respect to the grid (shift parameter). This new family is complete in the sense that it is closed under convolutions ...

We describe a wavelet based X-ray rendering method in the frequency domain with a smaller time complexity than wavelet splatting. Standard Fourier volume rendering is summarized and interpolation and accuracy issues are briefly discussed. We review the implementation of the fast wavelet transform in the frequency domain. The wavelet X-ray transform is derived, and the corresponding Fourier-wave...