Invariance is an attractive principle for specifying image processing algorithms. In this presentation, we concentrate on self-similarity—more precisely, shift, scale and rotation invariance—and identify the corresponding class of operators in d dimensions. For d = 1, there is no rotation and the scale-invariant differential operators are the fractional derivatives: ∂ γ τ ←→ (− jω) γ 2−τ( jω) γ...

and Applied Analysis 3 Wj and W̃j of Vj and Ṽj , respectively, satisfying Vj 1 Vj ̇Wj , Wj ⊥ Ṽj and Ṽj 1 Ṽj ̇W̃j , W̃j ⊥ Vj . The corresponding biorthogonal wavelets are given by ψj ∑ n∈Z −1 ã j 1−nφj 1 2 · −n , ψ̃j ∑ n∈Z −1 a j 1−nφ̃j 1 2 · −n . 1.4 A generalization of the biorthogonal wavelets of Cohen-Daubechies-Feuveau 1 was introduced that was based on exponential B-splines 12 . By generalizing...

While there are many possible choice of wavelets, splines have some clear advantages for biomedical imaging. First, unlike most other wavelet bases, they provide a continuous image representation that is easily computable at any spatial location — this property is crucial for implementing geometrical transformations. Second, they have the best approximation properties among all popular wavelet ...

This paper describes an approach to using compactly supported spline wavelets to model the residual signal in a real-time (frameby-frame) spectral modelling system. The outputs of the model are time-varying parameters (gain, centre frequency and bandwidth) for filters which can be used in a subtractive resynthesis system.

Wavelet-based analysis versus Gaussian smoothing in statistical parametric mapping (SPM) for detecting and analyzing brain activity from functional magnetic resonance imaging (fMRI) data is presented. Detection of activation in fMRI data can be performed in the wavelet domain by a coefficient-wise statistical t-test. The link between the wavelet analysis and SPM is based on two observations: (i...

Wavelet theory has become popular in modeling echo state network. One of the most promising directions is usage of the wavelets as membership activation functions of its reservoir. However, only Symlets wavelet seems to be suitable for hybrid wavelet-sigmoid activation functions. To enhance a systematic study of the field, we concentrate on developing more wavelets towards the typical ESN repre...

Building intuitive tools for manipulating curves and surfaces is a challenging task in the domains of geometric modelling and computer graphics. First, such tools need an appropriate mathematical model of the geometric objects. In addition, geometric constraints can enhance ergonomics, once they have been integrated into the editing tool. We investigate the integration of non linear constraints...