Visual Feature Embedding And Object Recognition In Statistical Manifold Framework

As the basic visual features, color, texture and shape are usually adopted to describe image properities and applied to object recognition tasks. Gabor filter and Gaussian derivative filter are two kinds of tools to construct multispectral texture and local shape descriptors of image. For any input image, the collection of filtered images outputted from a bank of Gabor filters or Gaussian derivative filters used to be viewed as a multichannel or multispectral image for alanysis and application. This sort of multichannel image owns the global high-dimensional and local multi-dimensional natures similar to common color image. Global approaches are accustomed to concatenating all channels of pixel-by-pixel filtered responses to form a high-dimensional vector. But, the high-dimensional nature of feature vectors tends to cause "the curse of dimensionality" in a learning or recognition task, which makes algorithm invalid or only output suboptimal result. Although sampling and other compression techniques can solve the problem to certain extent, it is often at the cost of multitudinous information loss. A co-occurrence matrix is essentially a discrete probability distribution that describes image texture with spatial co-occurrence information of pixel features. The classical methods use Haralick features, but then the complete information of the co-occurrence matrix can not be summarized into these features. Histograms are a kind of widely used image descriptors, but the response sets obtained by convoluting an image with a bank of Gabor or Gaussian derivative filters have complex distributions in most cases. Then it is necessary to extract discriminative histograms and endow them with appropriate information metric. In addition, the non-Euclidean structured histograms determine that it is hard to get satisfactory results as applying a Euclidean metric-based learning algorithm to histograms-representing frequency data. Aiming to the problems of above visual features appeared in the processes of recognition and learning, we consider the probabilistic generative models of pixel-by-pixel features or co-occurring features of images (or filtered images) in the framework of statistical manifolds. By using the techniques of the models’discretization (only to nonparametric probability models) and the compactified embedding, the similarity metrics of generative models are built by the Fisher-Riemannian geometries on multinomial manifolds. We present the recognition methods of matching generative models of features or co-occurring features, and the learning method based on stochastic histogram embedding in the framework of statistical manifold. The novelties and main results of the associated work in this thesis include: (1) Object representation in the form of probabilistic generative model of features or co-occurring features is presented. That is, objects are represented as (product) the points of a nonparameteric (product) statistical manifold with the joint (or marginal) generative models of pixel-by-pixel feature sets of object images or the filtered images. Using the generative models of co-occurring features on object images or filtered images, objects are represented as the points on a (product) multinomial manifold. The presented object representations are the foundations to formulate our recognition algorithms in this thesis.(2) Theoretically, we prove the rationality to study a submanifold of a nonparemeteric statistical manifold by the Fisher geometry on multinomial manifold. As to application, we present the partition scheme on feature space with the quantiles learned in unsupervised manner. For designing model geometry-adaptive information metric, the techniques of maximum likelihood embedding and compactified embedding are adopted for the discretized models. In addition, we equip the embedded (product) submanifold with the information metric built by the geodesic distance metrics of factor multinomial manifolds. In this way, we present the object recognition method by matching probabilistic generative models of images’ features. Experiments showed that the method gained the better recognition performances on several different types of object databases by using multichannel Gabor features or Gaussian differential features.(3) Object recognition approach matching gray level co-occurrence matrix or color co-occurrence matrices on (product) multinomial manifold is presented, by introducing (product) co-occurrence matrix (matrices) embedding and the compactification. In order to generalize the approach, a novel image descriptor, i.e. Gabor magnitude co-occurrence matrix was designed in this thesis. Using the extension technique of geodesic distance metrics on multinomial manifolds, we also generalized the method for object recognition by matching Gabor magnitude co-occurrence matrices on product multinomial manifold with boundary. Experimental results showed that these methods significantly outperformed classic (kernel) subspace methods and Haralick features based method with the higher recognition accuracy.(4) The statistical manifold learning method based on stochastic histogram embedding is presented. This method does not pursue the optimal histogram binning scheme, but stress the extraction of multiple low-resolution stochastic histograms and information integration on product multinomial manifold based on the compactified embedding. The classical manifold learning algorithms and the intrinsic dimension estimation algorithms can be adjusted to the derived metric-adaptive form, for learning on the embedded product submanifold for lower-dimensional Euclidean embedding. Experimental results show this learning algorithm can gain promising performances on feature extraction and data visualization.