Image Reconstruction And Classification Based On T-algebra

Each pixel in the visual data is not independent,and there is a constraint relationship between local pixels.Making better use of neighborhood pixels' spatial structure and constraints in visual data to process and analyze visual data effectively has become an essential topic in pattern analysis and machine vision.Traditional image analysis algorithms,such as principal component analysis,usually expand images into vectors,which destroys image inherent structure and makes it difficult to use the neighborhood information of images effectively.The recently proposed t-algebra extends scalars to t-scalars and uses the extended t-scalars to construct new types of matrices and tensors for elements.The shortcomings of traditional image analysis algorithms can be avoided to some extent by using t-algebra.The t-algebra is used to improve the image reconstruction and recognition algorithm.On this basis,new optimization methods are proposed to improve the performance of the tensorial algorithm on the original basis.1)While using t-algebra to extend and improve the image reconstruction algorithm based on singular value decomposition,fast Fourier transform of generalized scalar can significantly speed up the operation time.Inspired by this,we carry out the fast Fourier transform,discrete cosine transform,and unitary matrix transform on t-scalars and compare these transformations' effects on the image reconstruction via the tensorial singular value decomposition in the numerical experiments of image reconstruction.Finally,the experiments show the tensorial singular value decomposition via any of the three transformations mentioned above outperforms the canonical singular value decomposition in terms of the quality of image reconstructions.Among the outperforming image reconstructions,the one via DCT(Discrete Cosine Transform)performs at the same level as the one via Discrete Fourier transform or slightly better than the latter.2)The influence of the order and size of t-scalars on the image reconstruction algorithm's performance based on the tensorial principal component analysis is studied,besides using the t-algebra to extend and improve the canonical algorithms.In this thesis,two different neighborhood strategies are employed for determining generalized scalars' order and size.Tensorial principal component analysis with different sizes and orders of generalized scalars is used to reconstruct public-available images.Our experiments show that the tensorial principal component analysis outperforms the traditional principal component analysis for image reconstruction.Under some condition,one can increase the performance of a tensorial reconstruction algorithm by increasing the scalar entries of each generalized scalar.3)The t-algebra is employed to generalize the hyperspectral image classification method modeled on the Grassmann manifold.In this thesis,the angles between subspaces are used to characterize the geodesic distance between two points on the Grassmann manifold.The angle-based metric is employed for the supervised classification of pixels in hyperspectral images.To improve the manifold-based classifier's performance,we use different subspace dimensions for numerical experiments.The classification accuracies by three different norms are compared.Also,the notions of subspace,Grassmann manifold,and vector norms are generalized over the t-algebra,and the process of constructing compound pixels in the forms of t-vectors from each pixel neighborhood of hyperspectral images is discussed.To verify the generalized Grassmannian classifier's effectiveness and superiority,we compare its classification accuracies with those by the canonical Grassmannian classifier and different variants of the convolutional neural network,respectively.The results show that the generalized Grassmannian classifier compares favorably with its rivals in classifying hyperspectral images.The image reconstructors and classifiers over the t-algebra have improved performance.The applications of image analysis and machine vision are closely related to the t-algebra,which is based on the theory of rings.The applications verify the theory's correctness,while the latter provides the necessary theoretical basis and descriptive tools for its applications.