Image Classification Based On Riemannian Manifolds And Statistical Learning Methods

Image classification is one of the most important topics in computer vison.With the extensive applications of digital imaging devices, image classification technologys play an indispensable role in daily life, medical imaging, commercialuse, security and military. Due to changes in views and environment of imagingand motion blur, noise, the images from the same class have significant variations. Meanwhile, the inter-calss variations between images are often unobvious. These make image classification more challenging.First of all, this thesis presents a method of extracting local image featuresunder Log-Euclidean Riemannian framework. It calculates a covariance matrix ateach pixel of the image, and maps the covariance matrices to the Euclidean space through matrix logarithm operation. Then statistical modeling on the proposed local features can be obtained by using the traditional methods in Euclidean space.Secondly, this thesis proposes a Log-Euclidean kernels-based method to map the space of covariance matrices to the Reproducing Kernel Hilbert Space, for solving the problem of sparse representation and dictionary learning on covariance matrices. Image matching plays an important role in image classification, and thisthesis proposes a novel EMD methodology for image matching with Gaussian mixture models, which compares two Gaussian mixture models with the sparse representation-based Earth Mover’s Distance (SR-EMD), and develops an effective metric learning method to further improve the performance. Finally, in order to overcome thelimition that the traditional pairwise constrainted metric learning methodsuse fixed bound based constraints, the shrinkage-expansion adaptive constraints is proposed for pairwise constrainted metric learning methods.This thesis evaluates the proposed image classification methods across over10image databases, which contain more than200,000images in total. Meanwhile, the proposed methods are applied to a variety of image classification tasks, such as texture classification, scene categorization, face verification and image retri eval which is closely related to image classification. Experimental results show that the proposed methods achieve better performances than their competing counterparts.