Multiscale methods have become an important tool in mathematical analysis and applications, in particular in the area of signal and image processing as well as in numerical analysis. The mathematical background has been reinforced with the introduction of wavelet bases in the mid-1980's. Our goal is to give a short survey of these methods and show their speciic advantages, as well as their inhe...

In this paper we have shown how a common multiscale morphological paradigm can be used to solve various image processing problems. We have implemented the schemes by using morphological tower which is based on multiscale operations satisfying causality and edge localization properties. The efficacy of the technique is illustrated for noise smoothing, contrast enhancement and multimodal image fu...

This paper presents a framework to define an objective measure of the similarity (or dissimilarity) between two images for image processing. The problem is twofold: 1) define a set of features that capture the information contained in the image relevant for the given task and 2) define a similarity measure in this feature space. In this paper, we propose a feature space as well as a statistical...

Multiresolution triangulation meshes are widely used in computer graphics for 3-d modeling of shapes. We propose an image representation and processing framework using a multiscale triangulation of the grayscale function. Triangles have the potential of approximating edges better than the blocky structures of tensorproduct wavelets. Among the many possible triangulation schemes, normal meshes a...

Coherent Multiscale Image Processing using Quaternion Wavelets by Wai Lam Chan This thesis develops a quaternion wavelet transform (QWT) as a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant tight frame representation whose coefficients sport a magnitude and three phases: two phases encode local image shifts while the third contains textural informati...

In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a two-sweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illus...

Landscapes are Complex Systems, which by their very nature necessitate a multiscale approach in their monitoring, modeling and management. To assess such broad extents, remote sensing technology is the primary provider of landscape sized data sets, and while tremendous progress has been made over the last thirty years in terms of improved resolution, data availability, and public awareness, the...

The description of the object shape is an important characteristic of the image. In image processing and pattern recognition, several different shape descriptors are used. In human visual perception, the shapes are processed in multiple resolutions. Therefore multiscale shape representation is essential in the shape based image classification and retrieval. In the description of the object shap...