Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

Image registration and image interpolation in volume rendering of cross sections

We outline a method for registration of images of cross sections using the concepts of The Generalized Hough Transform (GHT). The approach may be useful in situations where automation should be a concern. To overcome known problems of noise of traditional GHT we have implemented a slight modified version of the basic algorithm. The modification consists of eliminating points of no interest in the process before the application of the accumulation step of the algorithm. This procedure minimizes the amount of accumulation points while reducing the probability of appearing of spurious peaks. Also, we apply image warping techniques to interpolate images among cross sections. This is needed where the distance of samples between sections is too large. Then it is suggested that the step of registration with GHT can help the interpolation automation by simplifying the correspondence between points of images. Some results are shown.

HTS: A new shape descriptor based on Hough Transform

In this paper we propose a novel method for shape analysis called HTS (Hough Transform Statistics), which uses statistics from Hough Transform space in order to characterize the shape of objects in digital images. Experimental results showed that the HTS descriptor is robust and presents better accuracy than some traditional shape description methods. Furthermore, HTS algorithm has linear complexity, which is an important requirement for content based image retrieval from large databases. © 2013 IEEE.

Ridge-based fingerprint matching using hough transform

Despite the efficacy of minutia-based fingerprint matching techniques for good-quality images captured by optical sensors, minutia-based techniques do not often perform so well on poor-quality images or fingerprint images captured by small solid-state sensors. Solid-state fingerprint sensors are being increasingly deployed in a wide range of applications for user authentication purposes. Therefore, it is necessary to develop new fingerprint-matching techniques that utilize other features to deal with fingerprint images captured by solid-state sensors. This paper presents a new fingerprint matching technique based on fingerprint ridge features. This technique was assessed on the MSU-VERIDICOM database, which consists of fingerprint impressions obtained from 160 users (4 impressions per finger) using a solid-state sensor. The combination of ridge-based matching scores computed by the proposed ridge-based technique with minutia-based matching scores leads to a reduction of the false non-match rate by approximately 1.7% at a false match rate of 0.1%. © 2005 IEEE.

On Some Generalizations of Classical Integral Transforms

MSC 2010: 44A15, 44A20, 33C60

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

Uma proposta de slam com determinação de informações geométricas do ambiente

PEDROSA, Diogo P. F. ; MEDEIROS, Adelardo A. D. ; ALSINA, Pablo J. . Uma Proposta de SLAM com Determinação de Informações Geométricas do Ambiente. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 16, Salvador, BA, 2006. Anais... Salvador: CBA, 2006. v. 1. p. 1704-1709

Mapeamento de ambientes estruturados com extração de informações geométricas através de dados sensoriais

The objective of this thesis is proposes a method for a mobile robot to build a hybrid map of an indoor, semi-structured environment. The topological part of this map deals with spatial relationships among rooms and corridors. It is a topology-based map, where the edges of the graph are rooms or corridors, and each link between two distinct edges represents a door. The metric part of the map consists in a set of parameters. These parameters describe a geometric figure which adapts to the free space of the local environment. This figure is calculated by a set of points which sample the boundaries of the local free space. These points are obtained with range sensors and with knowledge about the robot s pose. A method based on generalized Hough transform is applied to this set of points in order to obtain the geomtric figure. The building of the hybrid map is an incremental procedure. It is accomplished while the robot explores the environment. Each room is associated with a metric local map and, consequently, with an edge of the topo-logical map. During the mapping procedure, the robot may use recent metric information of the environment to improve its global or relative pose

Uma proposta de slam com determinação de informações geométricas do ambiente

PEDROSA, Diogo P. F. ; MEDEIROS, Adelardo A. D. ; ALSINA, Pablo J. . Uma Proposta de SLAM com Determinação de Informações Geométricas do Ambiente. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 16, Salvador, BA, 2006. Anais... Salvador: CBA, 2006. v. 1. p. 1704-1709

Uma proposta de slam com determinação de informações geométricas do ambiente

PEDROSA, Diogo P. F. ; MEDEIROS, Adelardo A. D. ; ALSINA, Pablo J. . Uma Proposta de SLAM com Determinação de Informações Geométricas do Ambiente. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 16, Salvador, BA, 2006. Anais... Salvador: CBA, 2006. v. 1. p. 1704-1709

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.