Since the works of Radon and Cormack on classical transform straight lines, several generalizations involving integrations conical surfaces have been studied. In this article, we introduce a new family with arbitrary vertices space axes through origin study corresponding transform. We derive its analytical inversion in two three dimensions. Numerical simulations are carried out for two-dimensio...

We propose new sets of Fourier-Mellin descriptors for color images. They are constructed using the Clifford Fourier Transform of Batard et al. (2010) and are an extension of the classical Fourier-Mellin descriptors for grayscale images. These are invariant under direct similarity transformations (translations, rotations, scale) and marginal treatment of colors images is avoided. An implementati...

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-bas...

This paper presents a novel kind of speech feature which is the modified Mellin transform of the log-spectrum of the speech signal (short for MMTLS). Because of the scale invariance property of the modified Mellin transform, the new feature is insensitive to the variation of the vocal tract length among individual speakers, and thus it is more appropriate for speaker-independent speech recognit...

We analyse a stack protocol of the Capetanakis-Tsybakov-Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a noncommutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration sem...

We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynom...

In this paper, we consider a q-analogue of the Dunkl operator on R, we define and study its associated Fourier transform which is a q-analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this q-Dunkl transform. Next, we study the q-Dunkl intertwining operator and its dual via the q-analogues of the Riemann-Liouv...

One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on valuations. It is shown that the classical Radon transform on smooth functions, and the well known Radon transform on constructible functions with respect to the Eul...