Applications Of Partial Differential Equations On Images Recognition

This paper mainly studies the application of Partial Differential Equations(PDEs)on large-sized images(illumination and shelter)recognition.This paper is divided into 4chapters.In the first chapter,related theories of Support Vector Machine(SVM),Twin Support Vector Machine(TSVM),Canonical Correlation Analysis(CCA),Principal Component Analysis(PCA),Linear Discriminant Analysis(LDA),and PDEs are introduced briefly.Regularized SVM(RSVM)based on PDEs is proposed in the second chapter,and the influence of PDEs for parameters selection with RSVM is researched.According to a series of experimental results,evolutions of PDEs can weaken the effect of parameters,so that parameters selection can be avoided effectively.In the third chapter,Twin Boundary SVM(TBSVM)based on PDEs is proposed,and its effect on parameters selections of TBSVM is studied.Experimental results indicate that evolutions of PDEs with appropriate times can weaken the effect of parameters on classification accuracies when penalty parameters are no less than regularization parameters,even parameters selections can be avoided.For large-sized images recognition,a novel dimensionality reduction method named Minimized CCA(MCCA)is proposed in the fourth chapter.MCCA can process different-sized images with high dimensions,and shows superiority over classic CCA,PCA and LDA.On the basis,as for the large-sized images(illumination and shelter),the effect of MCCA based on PDEs on image recognition and feature extraction are researched.Experimental results indicate that accuracies can be improved to the best by evolutions of PDEs with appropriate times when images are dimension-reduced by CCA to smaller-sizes.