A Detection Method Of Plane Curve Based On Finite Mixture Models

Curve detection is an important research subjects among image processing and machine vision,in which line(line segment)detection and circular curve(including arc)detection are the most widely used technology.Curve detection technology has been applied in various fields in real life.At present,detection technologies commonly used mainly include: 1)Hough transform and the corresponding improved algorithms;2)the recognition method based on multi-objective optimization algorithm;3)the recognition method based on boundary tracking;4)the recognition method based on fuzzy clustering,etc.In this paper,the finite mixture model is used to study the problem of plane curve detection.Firstly,according to the geometric characteristics of straight line and circular curve and the distribution of data points in different directions,we derive the probabilistic model to describe single straight line and circular curve,respectively.An algorithm for estimating the maximum likelihood estimation of model parameters is given.Then,based on the probabilistic model of single curve,we derive the probabilistic mixture models of multiple curves.Using Lagrange multiplier method and Newton method,the EM algorithm for the parameter estimation of the mixture models is derived,and the maximum likelihood estimation of all the parameters in the model is calculated.In addition,we also give a clustering analysis method for target data sets.Finally,in order to complete the curve detection when the number of mixture models branches is unknown,this paper combines the curve mixture models with the EM algorithm based on the minimum message coding length criterion and the dynamic regularization of Bayesian Ying-Yang harmony learning.Then,based on two different ideas,curve detection algorithms for automatically estimating the number of branches is derived.Numerical experiments and real image experiments prove that these two algorithms can complete the task of curve detection and cluster analysis.Two comparative experiments with other commonly used algorithms illustrate the advantages and disadvantages of this algorithm.The advantage is that there is no need for complex image pre-processing work and prior knowledge.The disadvantage is that they run slower.