We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.

In this paper, a new algorithm for content− based image indexing and retrieval is presented. The proposed method is based on a combination of multiresolution analysis and color correlation histogram of the image. According to the new algorithm, wavelet coefficients of the image are computed first using Daubechies wavelets. A quantization step is then applied before computing horizontal and vert...

Classifying color textures under varying illumination sources remains challenging. To address this issue, this paper introduces a new descriptor for color texture classification, which is robust to changes in the scene illumination. The proposed descriptor, named Color Intensity Local Mapped Pattern (CILMP), incorporates relevant information about the color and texture patterns from the image i...

In this article, we propose a new method that combines the use of a global threshold and a window-based scheme for computing local thresholds. The latter scheme compares the contrast of gray values within a neighborhood whose size varies with the scale of the objects being examined. To compute the scale quantity, a new wavelet model entitled Hadamard multiresolution analysis is also proposed. W...

There exists a strong conceptual relation between Multiresolution Analysis, a theory mainly used in Wavelet Theory, and Indistinguishability Operators, a theory mainly used in Fuzzy Sets Theory. In this work a first approach to find a formal link between both theories is tried. It will be shown that, in some cases, a multiresolution analysis allows to build a family of Indistinguishability Oper...

The paper is concerned with the introduction and study of multiresolution analysis based on the up function, which is an innnitely diierentiable function supported on 0 2]. Such analysis is, necessarily, nonstationary. It is shown that the approximation orders associated with the corresponding spaces are spectral, thus making the spaces attractive for the approximation of very smooth functions.

Large terrain databases require a great number of polygons and textures. In consequence, transmission of terrain data over slow networks is still worrying. Multiresolution models allow progressive transmission, that is, the transmission of a simple model followed by successive refinements. In this work we describe a new multiresolution model called Geometric-Textured Bitree (GTB) that enables p...

In this work, the bands of a Sentinel-2A image with spatial resolutions of 20 m and 60 m are sharpened to a spatial resolution of 10 m to obtain visible and near-infrared (VNIR) and shortwave infrared (SWIR) spectral bands with a spatial resolution of 10 m. In particular, we propose a two-step sharpening algorithm for Sentinel-2A imagery based on modified, selected, and synthesized band schemes...

Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the res...