Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Face detection and facial component extraction by wavelet decomposition and support vector machines

Abstract: Quite recently the support vector machine (SVM) has shown a great potential in the area of automatic face detection. Generally the SVM based methods fall into two categories: component-based and whole face-based. However there exist some limitations to each category. In this paper we present a two-stage method using both SVM categories based on multiresolution wavelet decomposition (MWD). In the first stage, the whole face-based SVMs are used for coarse location of faces from small sub-images of low resolution. Then a set of component-based SVMs are applied to verify the extracted candidates in subsequent larger sub-images of higher resolutions. Experimental results show that this wavelet-SVM based method takes the advantage of the effectiveness of both categories of SVM-based methods and the computation efficiency.

Iris recognition using fourier-wavelet features

Abstract: This paper presents an effective iris recognition system for iris localization, feature extraction, and matching. By combining the shift-invariant and the multi-resolution properties from Fourier descriptor and wavelet transform, the Fourier-Wavelet features are proposed for iris recognition. A similarity measure is adopted as the matching criterion. Four wavelet filters containing Haar, Daubechies-8, Biorthogonal 3.5, and Biorthogonal 4.4 are evaluated and they all perform better than the feature of Gaussian-Hermite moments. Experimental results demonstrate that the proposed features can provide promising performance for iris recognition.

Contourlets and sparse image expansions

Abstract: Recently, the contourlet transform has been developed as a true two-dimensional representation that can capture the geometrical structure in pictorial information. Unlike other transforms that were initially constructed in the continuous-domain and then discretized for sampled data, the contourlet construction starts from the discrete-domain using filter banks, and then convergences to a continuous-domain expansion via a multiresolution analysis framework. In this paper we study the approximation behavior of the contourlet expansion for two-dimensional piecewise smooth functions resembling natural images. Inspired by the vanishing moment property which is the key for the good approximation behavior of wavelets, we introduce the directional vanishing moment condition for contourlets. We show that with anisotropic scaling and sufficient directional vanishing moments, contourlets essentially achieve the optimal approximation rate, O ((log M ) 3 M -2 ) square error with a best M -term approximation, for 2-D piecewise smooth functions with C 2 contours. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.

Length preserving multiresolution editing of curves

Abstract: In this paper a method for multiresolution deformation of planar piecewise linear curves that preserves the curve length is presented. In a wavelet based multiresolution editing framework, the curve can be deformed at any level of resolution through its control points. Enforcing the length constraint is carried out in two steps. In a first step the multiresolution decomposition of the curve is used in order to approximate the initial curve length. In a second step the length constraint is satisfied exactly by iteratively smoothing the deformed curve. Wrinkle generation is an application the paper particularly focuses on. It is shown how the multiresolution definition of the curve allows to explicitly and intuitively control the scale of the generated wrinkles.

A fast adaptive diffusion wavelet method for Burger’s equation

Abstract: A fast adaptive diffusion wavelet method is developed for solving the Burger’s equation. The diffusion wavelet is developed in 2006 (Coifman and Maggioni, 2006) and its most important feature is that it can be constructed on any kind of manifold. Classes of operators which can be used for construction of the diffusion wavelet include second order finite difference differentiation matrices. The efficiency of the method is that the same operator is used for the construction of the diffusion wavelet as well as for the discretization of the differential operator involved in the Burger’s equation. The diffusion wavelet is used for the construction of an adaptive grid as well as for the fast computation of the dyadic powers of the finite difference matrices involved in the numerical solution of Burger’s equation. In this paper, we have considered one dimensional and two dimensional Burger’s equation with Dirichlet and periodic boundary conditions. For each test problem the CPU time taken by fast adaptive diffusion wavelet method is compared with the CPU time taken by finite difference method and observed that the proposed method takes lesser CPU time. We have also verified the convergence of the given method.