The Hough transform for detecting parameterised shapes in images is still today mostly applied on binary images of contours or connected sets, which implies pre-processing of the images that may be costly and fragile. However the simple estimation of the spatial derivatives provides in every pixel the local geometry that can be used for dense voting processes, directly applied on the gray scale...

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...

High order spatial derivatives and stiff reactions often introduce severe temporal stability constraints on the time step in numerical methods. Implicit integration method (IIF) method, which treats diffusion exactly and reaction implicitly, provides excellent stability properties with good efficiency by decoupling the treatment of reactions and diffusions. One major challenge for IIF is storag...

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by m...

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing de...

The 2,4- and 2,5-dihydroxybenzamides (8, 9) were synthesized from their corresponding methyl esters. The structures and the spectral properties of investigated salicylic acid (1), 2,4- and 2,5-dihydroxy benzoic acids (2, 3), their methyl esters (4-6) and amides (7-9) were analyzed by means of FT-IR and one- and two-dimensional homo- and heteronuclear 1H and 13C NMR spectroscopies. Comparison of...

Research on the interpretation of image flow (or optical flow) until now has mainly focused on instantaneous flow fields. This limits the scope of the problems that one can address and the accuracy of the results. Here we extend a previous formulation of the problem to incorporate temporal variation of image flow. We illustrate our approach by solving specific cases which are of practical signi...

In this paper we develop descriptor techniques for modeling swirling hydrodynamic structures. Using the descriptor notation we obtain the generalized eigenvalue formulation for differential-algebraic equations describing the spatial stability of the fluid flow. We describe the general framework for spatial stability investigation of vortex structures in both viscous and inviscid cases. The disp...

Discretization of spatial derivatives is an important issue in meshfree methods especially when the derivative terms contain non-linear coefficients. In this paper, various methods used for discretization of second-order spatial derivatives are investigated in the context of Smoothed Particle Hydrodynamics. Three popular forms (i.e. ”double summation”, ”second-order kernel derivation”, and ”dif...

Research on the interpretation of image flow (or optical flow) until now has mainly focused on instantaneous flow fields. This limits the scope of the problems that one can address and the accuracy of the results. Here we extend a previous formulation of the problem to incorporate temporal variation of image flow. We illustrate our approach by solving specific cases which are of practical signi...