Multiresolution shape representation is a very effective way to decompose surface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while preserving the detail information. Many schemes for modeling with multiresolution decompositions based on splines, polygonal meshes and subdivision surfaces have been propos...

BACKGROUND Ultrasound images are usually affected by speckle noise, which is a type of random multiplicative noise. Thus, reducing speckle and improving image visual quality are vital to obtaining better diagnosis. METHOD In this paper, a novel noise reduction method for medical ultrasound images, called multiresolution generalized N dimension PCA (MR-GND-PCA), is presented. In this method, t...

This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on electronic structure, the advances described are useful for non-linear problems in the physical sciences in general. Among the reviewed developments is the con...

This paper studies the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hex...

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topologica...

This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for state of the art filters for denoising, feature detection or phase analysis in N-dimensions. It focus on reusability, and highly decoupled modules for easy exten...

Many multiresolution methods have been proposed. Most of them emphasize accuracy and hence are slow. Some methods may be fast, but they may not preserve the geometry of the model. Although there are a few real-time multiresolution methods available, they are developed mainly for handling large terrain models. In this paper, we present a very efficient multiresolution method for continuously red...

In this paper, we present CoMRI, Compressed MultiResolution Index, our system for fast sequence similarity search in DNA sequence databases. We employ Virtual Bounding Rectangle (VBR) concept to build a compressed, grid style index structure. An advantage of grid format over trees is subsequence location information is given by the order of corresponding VBR in the VBR list. Taking advantage of...

This paper concerns the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for he...

We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasiaffine counterparts a...