A method for temporal analysis and reconstruction of video sequences based on the time-frequency analysis and Hermite projection method is proposed. The S-method-based time-frequency distribution is used to characterize stationarity within the sequence. Namely, a sequence of DCT coefficients along the time axes is used to create a frequency-modulated signal. The reconstruction of nonstationary ...

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fract...

This paper proposes a Hermite-kernel realization of the conjugate filter oscillation reduction (CFOR) scheme for the simulation of fluid flows. The Hermite kernel is constructed by using the discrete singular convolution (DSC) algorithm, which provides a systematic generation of low-pass filter and its conjugate high-pass filters. The high-pass filters are utilized for approximating spatial der...

The Hermite transform is introduced as an image representation model that can be used to tackle the problem of fusion in multimodal medical imagery. This model includes some important properties of human visual perception, such as local orientation analysis and the Guassian derivative model of early vision. Local analysis is achieved by windowing the image with a Gaussian function, then a local...

Let wλ(x) := (1−x2)λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying ∫ 1 −1 wλ(x)P (λ) n (x)E (λ) n+1(x)x dx { = 0, 0 ≤ m < n+ 1, = 0, m = n+ 1. In this paper, we show uniform convergence of the Hermite–Fejér interpolation polynomials Hn+1[·] and H2n+1[·] based on the zeros of the Sti...

Bivariate interpolatory Hermite subdivision schemes have recently been applied to build free-form subdivision surfaces. It is well known to geometric modelling practitioners that interpolatory schemes typically lead to “unfair” surfaces—surfaces with unwanted wiggles or undulations—and noninterpolatory (a.k.a. approximating in the CAGD community) schemes are much preferred in geometric modellin...

Methods approaching the problem of the Hermite Birkhoff interpolation of scattered data by combining Shepard operators with local interpolating polynomials are not new in literature [1–4]. In [3] combinations of Shepard operators with bivariate Hermite-Birkhoff local interpolating polynomials are introduced to increase the algebraic degree of precision (polynomial reproduction degree) of Shepar...

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.