Image Classification Based On Heat Kernel Embedding

The heat-kernel method is a very important method widely used in the mathematics and physics.The main core of the method is to extract from a spectral function the information of operator itself or the background information where the operator is defined. Due to it can fully reflect the geometric characteristics of the image,it has been gradually applied to the field of image processing,And this thesis bases on the geometric characteristics of heat-kernel proposed a method of using heat-kernel features to conduct the SVM classification to achieve image classification purposes.Firstly,this thesis describes in detail the process of establishing the image coordinates of the heat-kernel embedding.Including the feature point detection, Delaunay triangulation, and the establishment of adjacency matrix and the Laplacian matrix. Finally, this thesis gets the heat-kernel embedding coordinates of the image.Secondly,this thesis conducts a study according to the Harris-Laplace method causing the feature points missed detection.Through the comparative analysis of the advantages and disadvantages of Harris-Laplace and Canny-Harris feature points detection algorithms , this thesis proposes the improved feature points detection algorithm which combines these two feature points detection algorithms.In order to verify the improvement of feature point detection algorithm is better than the first two algorithms, this thesis uses abo three kinds of feature points detection to get the feature points then established heat-kernel features.Through heat-kernel conducts PCA model space mapping experiment, and to compare the results of mapping space.The experimental results show that the improved feature points detection is better than Harris-Laplace and Canny-Harris detection algorithms.Finally, in the process of using the heat-kernel feature to SVM classification experiment,there are two factors that impact on the classification accuracy.They are heat-kernel feature column vector truncated dimensions and the time parameter of the heat-kernel feature.The experimental results show that the heat-kernel feature input vector dimensions selection 18 and Time parameters of heat-kernel feature selection t=1.Then according to these two selections this thesis uses SVM for heat-kernel feature classification,and comparing with the results of spectral features SVM classification and heat-kernel feature SVM classification of the image.The experimental results show that the accuracy of classification by using heat-kernel feature is higher than by using spectral feature,at the same time,using the improved feature point detection algorithm to establish heat-kernel feature for SVM classification will achieve relatively better classification accuracy.