This work proposes some mathematical methods used in the design of a class of two-dimensional recursive filters, with an orientation-selective frequency response. We propose an analytical design method based on a given 1D digital prototype filter and a frequency transformation determined using Chebyshev-Padé approximations and the bilinear transform. These filters may find useful applications i...

Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation reduced form the constructed by Painleve analysis. Based on transformation, some exact non-differentiable solutions are obtained. To gain more insights obtained solutions, two constrain...

Polynomials in differentiation operators are considered. The Darboux transformations covariance determines non-Abelian entries to form the coefficients of the polynomials. Joint covariance of a pair of such polynomials (Lax pair) as a function of one-field is studied. Methodically, the transforms of the coefficients are equalized to Frechet derivatives (first term of the Taylor series on prolon...

Visual recognition faces the difficult problem of recognizing objects despite the multitude of their appearances. Ample neuroscientific evidence shows that the cortex uses a topographic code to represent visual stimuli. We therefore develop a bilinear probabilistic model that learns transformations to build an invariant topographic code in an unsupervised way. Simulations for the simple over-co...

The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two...

We present a novel framework for polyhedral mesh editing with face-based projective maps, that preserves planarity by definition. Such meshes are essential in the field of architectural design and rationalization. By using homogeneous coordinates to describe vertices, we can parametrize the entire shape space of planar-preserving deformations with bilinear equations. The generality of this spac...

The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: the iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrab...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. The analagous result also holds for switched linear systems. In this note we show that, for any sampling time, diago...

the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p