Blind image restoration based on the theory of high-dimensional space geometry

In practical situations, the causes of image blurring are often undiscovered or difficult to get known. However, traditional methods usually assume the knowledge of the blur has been known prior to the restoring process, which are not practicable for blind image restoration. A new method proposed in this paper aims exactly at blind image restoration. The restoration process is transformed into a problem of point distribution analysis in high-dimensional space. Experiments have proved that the restoration could be achieved using this method without re-knowledge of the image blur. In addition, the algorithm guarantees to be convergent and has simple computation.

High dimensional imagery geometry and it's applications

Because of information digitalization and the correspondence of digits and the coordinates, Information Science and high-dimensional space have consanguineous relations. With the transforming from the information issues to the point analysis in high-dimensional space, we proposed a novel computational theory, named High dimensional imagery geometry (HDIG). Some computational algorithms of HDIG have been realized using software, and how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is demonstrated in this paper. As the applications, two kinds of experiments of HDIG, which are blurred image restoration and pattern recognition ones, are given, and the results are satisfying.

An algorithm for removing facial makeup disturbances based on high dimensional imaginal geometry

In this paper, a novel algorithm for removing facial makeup disturbances as a face detection preprocess based on high dimensional imaginal geometry is proposed. After simulation and practical application experiments, the algorithm is theoretically analyzed. Its apparent effect of removing facial makeup and the advantages of face detection with this pre-process over face detection without it are discussed. Furthermore, in our experiments with color images, the proposed algorithm even gives some surprises.

Phylogeny of SARS-CoV based on high-dimensional information geometry

We proposed a novel methodology, which firstly, extracting features from species' complete genome data, using k-tuple, followed by studying the evolutionary relationship between SARS-CoV and other coronavirus species using the method, called "High-dimensional information geometry". We also used the mothod, namely "caculating of Minimum Spanning Tree", to construct the Phyligenetic tree of the coronavirus. From construction of the unrooted phylogenetic tree, we found out that the evolution distance between SARS-CoV and other coronavirus species is comparatively far. The tree accurately rebuilt the three groups of other coronavirus. We also validated the assertion from other literatures that SARS-CoV is similar to the coronavirus species in Group I.

A novel image restoration algorithm based on high-dimensional space geometry

A novel image restoration approach based on high-dimensional space geometry is proposed, which is quite different from the existing traditional image restoration techniques. It is based on the homeomorphisms and "Principle of Homology Continuity" (PHC), an image is mapped to a point in high-dimensional space. Begin with the original blurred image, we get two further blurred images, then the restored image can be obtained through the regressive curve derived from the three points which are mapped form the images. Experiments have proved the availability of this "blurred-blurred-restored" algorithm, and the comparison with the classical Wiener Filter approach is presented in final.

A novel image restoration approach based on point location in high-dimensional space geometry

The goal of image restoration is to restore the original clear image from the existing blurred image without distortion as possible. A novel approach based on point location in high-dimensional space geometry method is proposed, which is quite different from the thought ways of existing traditional image restoration approaches. It is based on the high-dimensional space geometry method, which derives from the fact of the Principle of Homology-Continuity (PHC). Begin with the original blurred image, we get two further blurred images. Through the regressive deducing curve fitted by these three images, the first iterative deblured image could be obtained. This iterative "blurring-debluring-blurring" process is performed till reach the deblured image. Experiments have proved the availability of the proposed approach and achieved not only common image restoration but also blind image restoration which represents the majority of real problems.

A face detection algorithm based on high dimensional space geometry

In this paper, a face detection algorithm which is based on high dimensional space geometry has been proposed. Then after the simulation experiment of Euclidean Distance and the introduced algorithm, it was theoretically analyzed and discussed that the proposed algorithm has apparently advantage over the Euclidean Distance. Furthermore, in our experiments in color images, the proposed algorithm even gives more surprises.

A novel image restoration algorithm based on high-dimensional space geometry

A novel image restoration approach based on high-dimensional space geometry is proposed, which is quite different from the existing traditional image restoration techniques. It is based on the homeomorphisms and "Principle of Homology Continuity" (PHC), an image is mapped to a point in high-dimensional space. Begin with the original blurred image, we get two further blurred images, then the restored image can be obtained through the regressive curve derived from the three points which are mapped form the images. Experiments have proved the availability of this "blurred-blurred-restored" algorithm, and the comparison with the classical Wiener Filter approach is presented in final.

Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Geometry property of multi-degree of freedom neurons

In this paper, we study a problem of geometric inequalities for a Multi-degree of Freedom Neurons. Some new geometric inequalities for a Multi-degree of Freedom Neurons are established. As special cases, some known inequalities are deduced.

A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

Differences and commonalities between connectionism and symbolicism

The differences between connectionism and symbolicism in artificial intelligence (AI) are illustrated on several aspects in details firstly; then after conceptually decision factors of connectionism are proposed, the commonalities between connectionism and symbolicism are tested to make sure, by some quite typical logic mathematics operation examples such as "parity"; At last, neuron structures are expanded by modifying neuron weights and thresholds in artificial neural networks through adopting high dimensional space geometry cognition, which give more overall development space, and embodied further both commonalities.

Keyword spotting system based on biomimetic pattern recognition

The mandarin keyword spotting system was investigated, and a new approach was proposed based on the principle of homology continuity and point location analysis in high-dimensional space geometry theory which are both parts of biomimetic pattern recognition theory. This approach constructed a hyper-polyhedron with sample points in the training set and calculated the distance between each test point and the hyper-polyhedron. The classification resulted from the value of those distances. The approach was tested by a speech database which was created by ourselves. The performance was compared with the classic HMM approach and the results show that the new approach is much better than HMM approach when the training data is not sufficient.

A new development on ANN in China - Biomimetic pattern recognition and multi weight vector neurons

A new model of pattern recognition principles-Biomimetic Pattern Recognition, which is based on "matter cognition" instead of "matter classification", has been proposed. As a important means realizing Biomimetic Pattern Recognition, the mathematical model and analyzing method of ANN get breakthrough: a novel all-purpose mathematical model has been advanced, which can simulate all kinds of neuron architecture, including RBF and BP models. As the same time this model has been realized using hardware; the high-dimension space geometry method, a new means to analyzing ANN, has been researched.