A multiresolution image representation is presented in which iterative morphological filters of many scales hut identical shape serve as basis functions. Structural pattern decomposition is achieved by subtracting successive layers in the multiresolution representation. The representation differs from established techniques in that the code elements have a well defined location and size. The re...

Given a frame multi-resolution analysis of L2(Rd) with a set of multiple scaling functions that is a quasi-stable generating set for V0, we give some neccessary and su cient conditions under which the standard generating set for V1 is also a quasi-stable generating set. We also give some equivalent conditions for W0 to admit a quasi-stable generating set by means of the re nement equation mask,...

We present a multiresolutional algorithm that segments a compound document and uses the results of the segmentation for document enhancement in copier applications. The document is initially segmented into halftone and non-halftone areas. Based on this segmentation the location of the edges due to text, graphics, and images (and not due to halftone dots) are detected on halftone as well as on n...

The notion of a weak multiresolution analysis is defined over an arbitrary field in terms of cyclic modules for a certain affine group ring. In this setting the basic properties of weak multiresolution analyses are established, including characterizations of their submodules and quotient modules, the existence and uniqueness of reduced scaling equations, and the existence of wavelet bases. Thes...

Twenty five years after the seminal work of Jean Morlet, the wavelet transform, multiresolution analysis, and other spacefrequency or space-scale approaches are considered standard tools by researchers in image processing. Many applications that point out the interest of these techniques have been proposed. We review the recent published work dealing with industrial applications of the wavelet ...

Signal processing community has recently shown interest in Ramanujan sums which was defined by S.Ramanujan in 1918. In this paper we have proposed Orthogonal Ramanujan Sums (ORS) based on Ramanujan sums. In this paper we present two novel application of ORS. Firstly a new representation of a finite length signal is given using ORS which is defined as Orthogonal Ramanujan Periodic Transform.Seco...

This paper describes a novel approach of using multi-resolution analysis (MRA) for automatic speech recognition. Twodimensional MRA is applied to the short-time log spectrum of speech signal to extract the slowly varying spectral envelope that contains the most important articulatory and phonetic information. After passing through a standard cepstral analysis process, the MRA features are used ...