Algebraic feature extraction for image recognition based on an optimal discriminant criterion

A novel algebraic feature extraction method for image recognition is presented. For the training image samples, a set of optimal discriminant projection vectors are calculated according to a generalized Fisher criterion function. On the basis of the optimal discriminant projection vector, the algebraic feature vectors of an image can be extracted by projecting the image onto all optimal discriminant projection vectors. Experimental results shows that the algebraic features extracted by the presented method have good recognition performance.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The small sample size (SSS) problem is one of the major problems encountered when traditional kernel discriminant analysis methods are applied to high-dimensional pattern recognition tasks. Different methods have been proposed to solve this problem. In this paper, we introduce a new kernel discriminant analysis algorithm, which is able to effectively address the SSS problem and extract a set of optimal discriminant vectors without any lose of useful discriminant information. Experiments performed on radar target recognition using range profiles indicate that the proposed method outperforms some existing kernel discriminant algorithms, such as generalized discriminant analysis and kernel direct discriminant analysis, in terms of recognition rate.

An analytical algorithm for determining the generalized optimal set of discriminant vectors

An efficient unsupervised feature selection method based on unsupervised optimal discriminant vector is developed to find the important features without using class labels. Features are ranked according to the feature importance measurement based on unsupervised optimal discriminant vector in the following steps. First, fuzzy Fisher criterion is adopted as objective function to derive the optimal discriminant vector in unsupervised pattern. Second, the feature importance measurement based on elements of unsupervised optimal discriminant vector is defined to determine the importance of each feature. The features with little importance measurement are removed from the feature subset. Experiments on UCI dataset and fault diagnosis are carried out to show that the proposed method is very efficient and able to deliver reliable results.

A new algebraic feature extraction method for image recognition is presented. The optimal transform of image matrices is proposed to extract the features from images. The Frobenius norm of matrices is first introduced as a measure of the distance between two matrices. Based on this, the within-class and between-class distances of image samples are defined. The ratio of the between-class and within-class distances of the transformed image sample set is taken as the criterion function J(T). The optimal transform matrix T is calculated by maximizing J(T) under some constraints. Experiments have been conducted to recognize both human face and handwritten character images. These results indicate that the algebraic features extracted by the present method possess a very strong discriminant power. An important conclusion about the present method is that the traditional linear discriminant method can be considered as a special case of the present feature method when image samples have only one column of vectors.

A new face recognition method via semi-discrete decomposition for one sample problem

Common Matrix (CM) fails to work when there is only one image available in the training set. In this paper, an approach to solve this problem is proposed. By using singular value decomposition (SVD) null space of the image matrices are obtained. By projecting the image matrix onto the null space, common matrices are obtained for each class. After obtaining the common matrices, optimal projection vectors will be those that maximize the total scatter of the common matrices.

In this talk, several feature extraction techniques will be introduced from two cues: algebraic feature extraction andgeometrical feature extraction methods. For algebraic feature extraction, Principal Component Analysis (PCA), LinearDiscriminant Analysis (LDA), Kernel Discriminant Analysis (KDA), Sparse representation and their variants will beintroduced. For geometrical feature extraction, Contour Points Distribution Histogram (CPDH), Active Shape Model (ASM),Active Appearance Model (AAM), ASM+AAM, and their variants will be presented. Typical applications of these featureextraction methods will be presented including face recognition, image fusion, image retrieval, and target tracking, etc. Themain aim of this talk is to introduce my main work in pattern recognition and computer vision, which hopefully ignitesdiscussions, and future development of feature extraction.

We investigate the feasibility of constructing a data-driven distance metric for use in null-hypothesis testing in the context of arms-control treaty verification. The distance metric is used in testing the hypothesis that the available data are representative of a certain object or otherwise, as opposed to binary-classification tasks studied previously. The metric, being of strictly quadratic form, is essentially computed using projections of the data onto a set of optimal vectors. These projections can be accumulated in list mode. The relatively low number of projections hampers the possible reconstruction of the object and subsequently the access to sensitive information. The projection vectors that channelize the data are optimal in capturing the Mahalanobis squared distance of the data associated with a given object under varying nuisance parameters. The vectors are also chosen such that the resulting metric is insensitive to the difference between the trusted object and another object that is deemed to contain sensitive information. Data used in this study were generated using the GEANT4 toolkit to model gamma transport using a Monte Carlo method. For numerical illustration, the methodology is applied to synthetic data obtained using custom models for plutonium inspection objects. The resulting metric based on a relatively low number of channels shows moderate agreement with the Mahalanobis distance metric for the trusted object but enabling a capability to obscure sensitive information.

An oriented particle level set method based on surface coordinates

We present UWSPSM, an algorithm of uncertainty weighted stereopsis pose solution method based on the projection vector which to solve the problem of pose estimation for stereo vision measurement system based on feature points. Firstly, we use a covariance matrix to represent the direction uncertainty of feature points, and utilize projection matrix to integrate the direction uncertainty of feature points into stereo-vision pose estimation. Then, the optimal translation vector is solved based on the projection vector of feature points, as well the depth is updated by the projection vector of feature points. In the absolute azimuth solution stage, the singular value decomposition algorithm is used to calculate the relative attitude matrix, and the above two stages are iteratively performed until the result converges. Finally, the convergence of the proposed algorithm is proved, from the theoretical point of view, by the global convergence theorem. Expanded into stereo-vision, the fixed relationship constraint between cameras is introduced into the stereoscopic pose estimation, so that only one pose parameter of the two images captured is optimized in the iterative process, and the two cameras are better bound as a camera, it can improve accuracy and efficiency while enhancing measurement reliability. The experimental results show that the proposed pose estimation algorithm can converge quickly, has high-precision and good robustness, and can tolerate different degrees of error uncertainty. So, it has useful practical application prospects.

A study of Liu-Storey conjugate gradient methods for vector optimization

Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian line packing problem. Best Complex Antipodal Spherical Codes (BCASCs) are the best vector sets with respect to the coherence. By extending methods used to find best spherical codes in the real-valued Euclidean space, the proposed approach aims to find BCASCs, and thereby, a complex-valued vector set with minimal coherence. There are many applications demanding vector sets with low coherence. Examples are not limited to several techniques in wireless communication or to the field of compressed sensing. Within this contribution, existing analytical and numerical approaches for coherence optimization of complex-valued vector spaces are summarized and compared to the proposed approach. The numerically obtained coherence values improve previously reported results. The drawback of increased computational effort is addressed and a faster approximation is proposed which may be an alternative for time critical cases.

Retinal vessel segmentation in colour fundus images using Extreme Learning Machine

The paper will present the original NBV (Nearest Boundary Vector) classifier whose structure has been inspired by the structure of CP (Counter Propagation) neural network, which uses the methods applied in the minimum-distance classification while in its operation drawn on the idea of functioning of SVM (Support Vector Machines) classifiers. The classification algorithm which is used by it relies on the original concept of a set of Boundary Vectors. It is characterized by the possibility of creation of various shapes of decision-making regions and it enables effective multi-class recognition. Recognition efficiency of NBV classifier will be confronted with efficiency of SVM classifiers.