Factor Analysis And Its Application In Image Binarization

In many image processing methods,such as edge extraction,shape description,and object recognition,the image can be first binarized for preprocessing,and follow up the subsequent processing.Therefore,image binarization is very important as a basic method in image processing.In this thesis,several common methods for estimating factor loading matrices in the orthogonal factor analysis model are introduced:These methods include principal component method,iterative principal factor method,iterative maximum likelihood estimation method,gravity center method,generalized least squares method,unweighted least squares method,and Alpha factor method.The advantages and weakness of above methods are discussed,at the same time,the connection between these methods are indicated and the applicable conditions of each method are given.This thesis also studies the image binarization method,and proposes a method of image block binarization based on factor analysis.First divide the M×N image into k×k blocks,perform factor analysis on each k×k image block,and then according to the image-forming principle,select two common factors,namely the incident light intensity and the object reflectivity.The principal component method is applied to estimate the factor load matrix for each k×k image block,and the estimated factor load matrix is used to binarize the image using four methods as follows.(1)The similarity of matrix is used to calculate the similarity between any two factor load matrices.According to the given threshold,the foreground and the background of the image are separated,and the binary image is obtained.This method is suitable for natural lighting images where the light is uneven or where the gray of background and object area do not differ significantly.(2)Hierarchical clustering is used to calculate the mean,variance,and skewness of each factor load matrix first,which regard these as the feature vector of a k × k size image block.The image is then binarized using the OTSU method.Second,binarized images are divided into three categories:background blocks,foreground blocks,and mixed blocks.For each mixed block,find the corresponding feature vector and use the hierarchical clustering method to cluster it into two groups to obtain the final binary image.This method is suitable for the image types whose background and object regions have distinct gray.(3)A logistic regression model is employed to calculate the mean,variance,and skewness of each factor load matrix as the feature vector of the k×k image block.The OTSU method was used to binarize the image.Then,for binarized images,the probability of taking 1 for each k×k image block is calculated,and the image is divided into foreground,background and mixed blocks according to probability.Secondly,for the mixed image blocks,finding the corresponding feature vector,using Logistic regression model to give the initial grouping,and adjusting the initial group by iteration to obtain the final binary image.This method is suitable for distorted images of multiplicative Gaussian noise.(4)A new linear model is established,to give the initial grouping of image,and the initial grouping is adjusted through iteration to obtain the final binary image.This method is suitable for JPEG compressed distorted images.Using four different methods to experiment with different types of images,the results show that the binary image of theses algorithms are better than that of the OTSU methods.