Dynamic Texture Analysis Based On Differential Geometry Methods

Dynamic textures are the image sequences with time-related stationary characteristics.They describe dynamic sceneries such as the waves, the waterfalls and the smokes. Featureextraction is one of the fundamental issues in pattern recognition. Firstly, we chose twoapproaches of feature extraction. One approach is based upon the features of the textures'spectral images. Another approach is based upon the features of the textures' gray levelco-currency matrices. Then we chose Support Vector Machine (SVM) as the classifier.SVM is chosen due to its nice performance at small sample sizes. The regular SVMclassification kernel functions have above 96% recognition rate for the features of thespectral images. Appropriate feature selection for the gray level co-currency matrices isnecessary because of their vast dimensions. We apply differential geometric methods toaddress this issue. First we extend the linear Principal Components Analysis (PCA) tocurves, that is, the Principal Curves method in differential geometry. The essence is 1-Dembedded manifold in the Euclidian space. Secondly, we use the tangent distance conceptin differential geometry, incorporate the tangent distances into the kernel functions, createtangent distance kernel functions, and further create tangent distance KPCA (KernelPrincipal Components Analysis). This approach of KPCA projects the original data into thehigher dimensional feature spaces by nonlinear projections, and implements thecorresponding linear operations in the higher dimensional feature spaces. For dynamictextures, the experiments in this thesis show that the results of KPCA are better than that ofthe linear PCA. Finally, we use the tangent distance kernel SVM to do classification for thedynamic textures.