Multiresolution analysis with GRASS

The theory of matrix-valued multiresolution analysis frames

Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the ...

New GRASS modules for multiresolution analysis with wavelets

The recognition and the study of several spatial phenomena strongly depends on the resolution at which the analysis is carried out. The availability of an efficient way to represent the same phenomena at different resolutions is therefore very important (from both a mathematical and a computational point of view). Wavelets, families of base functions generated by dilation and translation of a m...

MRA parseval frame multiwavelets in L^2(R^d)

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

A Multiscale Approach to Contour Detection by Texture Suppression

In this paper we propose a multiscale biologically motivated technique for contour detection by texture suppression. Standard edge detectors reacts to all the local luminance changes, irrespective whether they are due to the contours of the objects represented in the scene, rather than to natural texture like grass, foliage, water, etc. Moreover, edges due to texture are often stronger than edg...