Symmetric PH and EP distributions and their applications to the probability Hough transform
type: Item
instance of: scholarly article
title: Symmetric PH and EP distributions and their applications to the probability Hough transform
zbMATH Open document ID: 1064.60022
DOI: 10.1016/S0898-1221(04)90067-3
author: Yuan Zhou
author: Quan-Lin Li
author: Guanghui Wang
publication date: 2005-03-08T00:00:00Z
review text: The aim of this paper is to investigate the properties of two novel distributions defined by the authors: a symmetric phase type (PH) distribution, and a symmetric exponential-polynomial type (EP) distribution based on the PH distribution. The contents of the paper are organized as follows: Section 2 introduces a univariate symmetric PH distribution and then proposes a univariate symmetric EP distribution based on the univariate symmetric PH distribution. Some graphical characteristics of the univariate PH and EP distributions are discussed. Section 3 illustrates the fact that the class of univariate symmetric EP distributions is large enough such that an arbitrary symmetric probability density function in \(L_2(-\infty,+\infty)\) (the space of square integrable functions on the real line) can be approximated in \((-\infty,+\infty)\) by a sequence of symmetric EP probability density functions. This result is proved using Laguerre and Hermite spectrum orthogonal decompositions. Section 4 provides a moment-based approach for simply constructing a sequence of symmetric EP density functions. Sections 5 and 6 propose two-dimensional, respectively multi-dimensional, symmetric EP and PH distributions and investigate their properties. Section 7 applies the symmetric PH and EP distributions to the study of probability Hough transform. Numerical algorithms and statistical behaviour of the class of symmetric PH and EP distributions have a large range of possible applications in pattern recognition, image analysis, computer vision etc.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62H35
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 68T45
zbMATH DE Number: 2142348
zbMATH Keywords: symmetric phase type distribution
zbMATH Keywords: symmetric exponential-polynomial type distribution
zbMATH Keywords: orthogonal basis
zbMATH Keywords: Laguerre polynomial
zbMATH Keywords: computer vision
zbMATH Keywords: pattern recognition
zbMATH Keywords: image analysis
zbMATH Keywords: probability Hough transform
zbMATH Keywords: numerical algorithms
MaRDI profile type: Publication
cites work: Q4733209
cites work: Q3923308
cites work: On the Limitations of Multivariate Phase-Type Families
cites work: Phase-type distributions: open problems and a few properties
cites work: Q5690357
cites work: Q5615180
cites work: Comparisons Among Estimators of a Scale Parameter of the Beta-Stacy Distribution
cites work: On the Laguerre Method for Numerically Inverting Laplace Transforms
cites work: Q4538148
cites work: The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes
cites work: On approximating higher order MAPs with MAPs of order two
cites work: A probabilistic algorithm for computing Hough transforms
cites work: Q4878842
cites work: Q5182969
cites work: Marked point processes as limits of Markovian arrival streams
cites work: Moment matching using a family of phase-type distributions
cites work: Multivariate Phase-Type Distributions
cites work: A New Class of Multivariate Phase Type Distributions
cites work: A formal definition of the Hough transform: properties and relationships
full work available at URL: s0898-1221(04)90067-3
OpenAlex ID: W2036187615
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142348