Research On Image Classification Methods Based On Symmetric Positive Definite Manifolds

Image classification is a popular intersection research direction in multiple fields such as computer vision,pattern recognition and machine learning.It aims to extract discriminative features from images or video sequences and use classification algorithms to classify them.Symmetric Positive Definite(SPD)matrices have strong representation ability and can provide powerful representations for image sets.However,since the SPD matrix lies on a specific Riemannian manifold,the metric based on the Euclidean structure cannot guarantee the accuracy of the manifold data structure.Therefore,how to perform feature extraction and image classification while maintaining the geometric structure of SPD manifolds is a difficult challenge in current research.Based on this,this thesis proposes a feature extraction method and an image classification method based on manifold learning using the Riemann metric defined on SPD manifolds,respectively.(1)To address the problem of information loss that may occur when using traditional feature extraction methods,this thesis utilizes manifold tangent space for discriminative learning to preserve the nonlinear structure of the data.Specifically,using the Log-Euclidean Metric(LEM)on the SPD manifold,the Two-Dimensional Discriminant Locality Preserving Projection(2D-DLPP)feature extraction method is generalized to the tangent space of the manifold to obtain more discriminative features.Then,the nearest neighbor classifier and geodesic distance on the manifold are used as classification standard to classify the extracted low-dimensional features.The effectiveness of the proposed method is verified by comparison experiments on the face dataset.(2)Utilizing the LEM and the positive definite Riemannian kernel function derived from it,the SPD manifold data are mapped into the high-dimensional Reproducing Kernel Hilbert Space(RKHS).Combining with the collaborative representation algorithm,a Laplacian matrix is constructed to preserve the semantic and neighborhood information of the manifold data,so that the distances of semantically identical nearest neighbors in the kernel space are as small as possible,while the distances of semantically dissimilar nearest neighbors are as large as possible,thus improving the classification accuracy.By comparing with the algorithm based on Euclidean metric and Riemannian metric respectively,the proposed algorithm is shown to achieve good performance in image classification tasks.