<title>Algebraic feature extraction for image recognition</title>

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

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.

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.

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

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.

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.

In the image analysis via the general theory of moments, some shortcomings were discovered. The major disadvantages of the method of moments are that although the first few moments convey significant information for simple objects, they fail to do so for more complicated objects. The computed invariant moments are expected not to be strictly invariant in the presence of noise, and the computation of moment invariants is time-consuming. In this paper, an effective image analysis method based on the algebraic method is presented. First, a new coordinate transformation from an object image to an invariant matrix is proposed. The invariant matrix representation is independent of image translation, scaling, and rotation. On the basis of invariant matrix, a robust algebraic recognition method based on the projective image is developed. The projective coordinates of projective image on feature images are used as the feature vectors which represent the inherent attributes of objects. In order to test the efficiency of our method, it is used to solve the recognition problem of two-dimensional aircraft models. Theoretical and experimental results show that our method is very reliable for image analysis and the extracted algebraic features are invariant to image translation, scaling, and rotation.

In this paper, a novel face recognition method based on Gabor-wavelet and linear discriminant analysis (LDA) is proposed. Given training face images, discriminant vectors are computed using LDA. The function of the discriminant vectors is two-fold. First, discriminant vectors are used as a transform matrix, and LDA features are extracted by projecting original intensity images onto discriminant vectors. Second, discriminant vectors are used to select discriminant pixels, the number of which is much less than that of a whole image. Gabor features are extracted only on these discriminant pixels. Then, applying LDA on the Gabor features, one can obtain the Gabor-LDA features. Finally, a combined classifier is formed based on these two types of LDA features. Experimental results show that the proposed method performs better than traditional approaches in terms of both efficiency and accuracy.

In this paper, the possibility of using an orthonormal basis to train a collection of artificial neural networks (ANNs) in a face recognition task is discussed. This orthonormal basis is selected from a dictionary of orthonormal bases consisting of wavelet packets. Here, a basis is obtained by maximizing a certain discriminant measure (e.g., l/sup 2/) among classes of training images. Once such a basis is selected, its basis vectors are ordered according to their power of discrimination and the first N most local discriminant basis vectors are retained for image decomposition. By projecting all training images onto an individual basis vector of these N most discriminant basis vectors, N versions of the training set at different spatial/scale resolutions are then created. Next, N multilayer feedforward neural networks are trained independently by N different resolution-specific training sets. After networks have been trained, they are combined to form an ensemble of networks. In this paper, the more reliable estimate of the ensemble generalization error is achieved by applying the concept of cross-validation to local discriminant basis neural network ensembles. Finally, the previous and the extended results are given in order to show that the combination of disjoint training sets (cross-validation) and preprocessing (local discriminant basis) methods can improve the generalization error.

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.

The bases used in quantum mechanics, in general, are orthonormal. The relations in orthonormal basis vectors are simpler than those in nonorthogonal basis vectors. Also, the operators that represent different physical quantities are Hermitian and the eigenvectors of these operators belonging to different eigenvalues are orthonormal to each other. But, in many cases, such as sets of screened hydrogenic wavefunctions, nonorthogonal sets of basis vectors occur. It is, therefore, necessary to consider the representation of vectors and operators in nonorthogonal bases. Making use of the set of vectors reciprocal to the given set of nonorthogonal base vectors, the expression for the norms of vectors and for the matrix elements has been found. Also, adjoint and Hermitian matrices in nonorthogonal bases have been worked out using a set of reciprocal basis vectors.

Essence of this work is formulation of nonlinear dependencies, which allow to determine parameters of an optical system. Previous methods of the aberration correction have commonly used algebraic methods in a simple form for primary aberrations and thin lenses. Efficiency of those methods should be appreciated critically because they usually need a further aberration correction. Nowadays, progress in development professional mathematical software commercially available encourages to taking out works concerning algebraic correction methods. In this work aberration dependencies are investigated in their full complexity without simplification and approximation. Dependencies containing angles and ratios of dimensions have form of very complex trigonometric expressions. An optical system may be corrected by controlling these dependencies in the entire optical systems. Solution of the problem require the selection of number of unknowns, and expression of all residual relations as a function of these unknowns. Problem of the algebraic correction relies on solving of a non- linear equation system with separately described auxiliary functions which are nested up to certain depth. Radii of curvatures and eventual distances between surfaces are determined in the second final stage after solving the nonlinear equation system and taking account of the scale. Two simple numerical examples are presented.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

As an important part of the prefabricated building standard system, the evaluation standards for prefabricated buildings play an important guiding role in the construction and development of prefabricated buildings. However, at present, the national evaluation standards for prefabricated buildings are highly extensive and general, and some of their contents are not well considered, while local standards based on the national standard have been formulated in accordance with the actual situation in their respective regions, which makes the evaluation of prefabricated buildings in various regions more confusing, which also causes differences when calculating the prefabrication rate, restricting the development of prefabricated buildings. In order to promote the construction of a complete evaluation standard system for prefabricated buildings in China, this paper combs through the methods used for the calculation of the prefabrication rate of prefabricated buildings in 28 provincial-level administrative regions in China, conducts a comparative analysis and empirical research on the calculation of the prefabrication rate under different standards in four dimensions, and applies t-tests and simulated annealing algorithms to optimize the projection pursuit model to analyze the differences in the total scores of the prefabrication rate under different standards, as well as the key factors that affect them. The study shows that (1) the same building may have different prefabrication rates under different standards for prefabricated buildings, and the way of calculating the prefabrication rate and the scoring criteria of the evaluation items will result in significant differences in the calculated prefabrication rate. (2) Depending on the value of the optimal projection direction vector, it was found that among the evaluation criteria, the enclosure wall and the internal partition wall have the greatest influence on the total score value, while the main structure has the least influence on the total score value. (3) There are similarities as well as differences in the evaluation criteria of prefabricated buildings in each province. On this basis, by analyzing the reasons for these differences, corresponding suggestions are made for governments needing to formulate or revise local standards.

As a main carrier mode for the sustainable development of the construction industry in China, prefabricated building may lead to problems such as cost overruns, project delays, and waste of resources due to unreasonable selection of prefabricated components. Therefore, we quantitatively analyze the contribution rate of quality optimization of prefabricated components using QFD-SEM. Under the constraints of prefabrication rate, quality optimization contribution rate, and expected values of various sub-goals, we propose a multi-objective optimization method for prefabricated component combinations based on cost, duration, and carbon emissions. By using NSGA-II to solve the model, we can obtain a set of optimal Pareto solutions for prefabricated component combinations. Based on the optimal Pareto solution set, we establish a multi-objective evaluation model using simulated annealing optimization projection tracing method, and select the optimal prefabricated component combination solution according to the projected eigenvalues of the solutions. An empirical study is conducted using an eleven-story framed building in Shenzhen, Guangdong Province, China as a case study. The results show that: (1) Using this method, optimal solutions can be obtained in an unbounded solution space, with the optimal solution having advantages over both fully cast-in-place and fully prefabricated solutions. Compared to the fully cast-in-place solution, the duration and carbon emissions are reduced by 36.62% and 12.74% respectively, while compared to the fully prefabricated solution, costs are reduced by 4.15%. (2) There is a certain negative correlation between the cost of prefabricated component combinations and duration, carbon emissions, and quality optimization, while there is a certain positive correlation with the prefabrication rate. (3) The size of the optimal projection direction vector based on the optimization objectives indicates that carbon emissions have the greatest impact on the evaluation results of the solutions.

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