EFFICIENT QUATERNION MOMENTS FOR REPRESENTATION AND RETRIEVAL OF BIOMEDICAL COLOR IMAGES

Biomedical color (BMC) images are being used on a wide scale by physicians, where their diagnosis would be more accurate. Hence, it is recommended to develop new approaches that are able to represent and retrieve the BMC images efficiently. This work proposes two methods to represent BMC images: Quaternion Associated Laguerre. Moments (Q_ALMs), and Quaternion Chebyshev Moments (Q_CMs). Q_ALMs and Q_CMs are derived by extending the ALMs and CMs to the quaternion field. ALMs and CMs represent discrete orthogonal moments, and they are defined using the Associated Laguerre Polynomials (ALPs) and Chebychev Polynomials, respectively. Hospitals and medical institutes everywhere in the world create and store a large variety of datasets of BMC images during the routine clinical practices; hence, the mastery to retrieve the BMC images correctly is crucial for precise diagnoses and also for the researchers in medical sciences. So that in this study, we also introduced two image retrieval systems for BMC images based on the Q_CMs and Q_ALMs approaches. Our approaches extensively assessed with two standard benchmark datasets: LGG Segmentation dataset for brain magnetic resonance MR images and NEMA-CT for the computed tomography (CT) images. The performance of the proposed retrieval systems is assessed through three performance metrics: Average retrieval precision (ARP), average retrieval rate (ARR), and F_score. Results have shown the outperformance of Q_CMs over Q_ALMs in both the cases of representing and retrieval of BMC images.

Symmetric functions of binary products of fibonacci and orthogonal polynomials

In this paper, we introduce a new operator in order to derive some new symmetric properties of Fibonacci numbers and Chebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for Fibonacci numbers and Chebychev polynomials of first and second kinds.

Polynomial fitting of nonlinear sources with correlating inputs

Purpose – The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs. Design/methodology/approach – The polynomial fitting is improved by amplitude normalization, reducing the order of the model, utilizing Chebychev polynomials and finally perturbing the correlating controlling voltage spectra. The fitting process is estimated by the reliability figure and the condition number. Findings – It is shown in the paper that perturbing one of the controlling voltages reduces the correlation to a large extend especially in the cross-terms of the multi-input polynomials. Chebychev polynomials reduce the correlation between the higher-order spectra derived from the same input signal, but cannot break the correlation between correlating input and output voltages. Research limitations/implications – Optimal perturbations are sought in a separate optimization loop, which slows down the fitting process. This is due to the fact that each nonlinear source that suffers from the correlation needs a different perturbation. Originality/value – The perturbation, harmonic balance run and refitting of an individual nonlinear source inside a device model is new and original way to characterize and fit polynomial models.

Effect of surface elasticity on an interface crack in plane deformations

We consider the effect of surface elasticity on an interface crack between two dissimilar linearly elastic isotropic homogeneous materials undergoing plane deformations. The bi-material is subjected to either remote tension (mode-I) or in-plane shear (mode-II) with the faces of the (interface) crack assumed to be traction-free. We incorporate surface mechanics into the model of deformation by employing a version of the continuum-based surface/interface theory of Gurtin & Murdoch. Using complex variable methods, we obtain a semi-analytical solution valid throughout the entire domain of interest (including at the crack tips) by reducing the problem to a system of coupled Cauchy singular integro-differential equations, which is solved numerically using Chebychev polynomials and a collocation method. It is shown that, among other interesting phenomena, our model predicts finite stress at the (sharp) crack tips and the corresponding stress field to be size-dependent. In particular, we note that, in contrast to the results from linear elastic fracture mechanics, when the bi-material is subjected to uniform far-field stresses (either tension or in-plane shear), the incorporation of surface effects effectively eliminates the oscillatory behaviour of the solution so that the resulting stress fields no longer suffer from oscillatory singularities at the crack tips.

Circular Digraph Walks, $k$-Balanced Strings, Lattice Paths and Chebychev Polynomials

We count the number of walks of length $n$ on a $k$-node circular digraph that cover all $k$ nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths. We observe that the results also count so-called $k$-balanced strings of length $n$, generalizing a 1996 Putnam problem.