Research On Manifold Based Linear Structure Exploring And Object Recognition Methods

With the rapid improvement of conveniency of information collection, the fields of pattern recognition and computer vision often involves many non-Euclidean data sets which lie on manifold. Analyzing in the manifold rather than Euclidean space can reveal essential nonlinear information of the data set, and has great significance for designing efficient data storage, visualization systems and pattern recognition system, and is one of the hot topics of pattern recognition and computer vision fields in recent years.When the structure of non-Euclidean data set is unknown, the manifold structure on which the data lie on need to be detected for further designing classification and decision systems. However, the existing methods haven’t given good performance for exploring manifold’s structure in observation space directly. This led the exploring of manifold structure to be a key issue of pattern recognition, data mining and other related fields. On the contrary, although the manifold analytic structures of some kinds of computer vision feature are known, designing more accurate recognition algorithm based on the analytical structure is still a difficult point in manifold based applications. For the above difficulty and the key issue, in-depth studies are done in this dissertation on the basis of analysis and summary of relevant research, and four algorithms are proposed as follows:(1) On solving the exploring problem of the linear structure of manifold on nonlinear data set, an exploring algorithm is proposed based on Grassmann geodesic similarity and Ant Colony clustering model. This algorithm can directly detect the nonlinear structure in the observation space which can’t be accomplished from manifold learning perspective. Experiments and analysis on several datasets showed that the proposed algorithm performed successfully on linear structure clustering compared with traditional algorithms. And by changing the number of clusters, the proposed algorithm can capture the local linear change in the data set.(2) On solving the fast mining problem of one dimensional linear manifold structure, an exploring algorithm based on density weight EM and splitting merging strategy is proposed, which can solve the parameter and nosie sensitive problem of the existing methods. Experiments showed that compared with traditional algorithms, the proposed algorithm can obtain a better result when the number of mining is not set as the same with the real line pattern number, and is able to correctly explore the one dimensional manifold structure of non-linear dataset under the noisy environment.(3) On solving2D affine invariant recognition problem, a matrix Langevin distribution and multi-components-scales contour Grassmann representing model based intrinsic boost algorithm is proposed. It solves the problem that classifying in Grassmann directly without Riemannian mapping. The theoretical analysis and experimental results show that, the proposed algorithm can still obtain a higher recognition rate under the situation of less contour sampling points. It has a superior performance than extrinsic methods and traditional methods, and also can deal with the situation that the contour has the noisy segment.(4) On solving the rotation invariant human detection problem involved in natural images and the monitoring scene, a new feature named as Polar-HOG covariance is proposed based on Histogram of oriented gradients (HOG). And then symmetric positive definite manifold was employed to design a rotation invariant human classification and detection algorithm. The proposed feature and algorithm solves the problem of traditional HOG and covariance feature that don’t have the rotation invariance. Compared with troditional methods, the proposed algorithm achieves better performance on dealing with the object rotation, and is able to obtain a higher classification and detection rates with a lower error rate and false alarm rate.The above research achievements supplied new methods for non-Euclidean data set structure exploring, and enriched the special analytic manifold applied research in computer vision. The related experiments demonstrated that the proposed algorithms are valid and advanced which laid a solid foundation for the further research in the new theory and algorithm of non-Euclidean pattern recognition and computer vision.