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

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.

Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)