In developing an automatic system of a single tooth length measurement on x-ray image, since a tooth shape is assumed to be straight and curve, an algorithm which can accurately deal with straight and curve is required. This paper proposes an automatic algorithm for measuring the length of single straight and curve teeth. In the algorithm consisting of control point determination, curve fitting, and length measurement, PCA is employed to find the first and second principle axes as vertical and horizontal ones of the tooth, and two terminal points of vertical axis and the junction of those axes are determined as three first-order control points. Signature is then used to find a peak representing tooth root apex as the forth control point. Bezier curve, Euclidean distance, and perspective transform are finally applied with determined four control points in curve fitting and tooth length measurement. In the experiment, comparing with the conventional PCA-based method, the average mean square error (MSE) of the line points plotted by the expert is reduced from 7.548 pixels to 4.714 pixels for tooth image type-I, whereas the average MSE value is reduced from 7.713 pixels and 7.877 pixels to 4.809 pixels and 5.253 pixels for left side and right side of tooth image type-H, respectively.

In this paper, we propose a novel incremental method for discovering latent variables from multivariate data with high efficiency. It integrates non-Gaussianity and an adaptive incremental model in an unsupervised way to extract informative features. Our proposed method discovers a small number of compact features from a very large number of features and can still achieve good predictive performance in EEG signals. The promising EEG signal classification results from our experiments prove that this approach can successfully extract important features. Our proposed method also has low memory requirements and computational costs.

Locally linear embedding (LLE) is a well-known method for nonlinear dimensionality reduction. The mathematical proof and experimental results presented in this paper show that the neighborhood sizes in LLE must be smaller than the dimensions of input data spaces, otherwise LLE would degenerate from a nonlinear method for dimensionality reduction into a linear method for dimensionality reduction. Furthermore, when the neighborhood sizes are larger than the dimensions of input data spaces, the solutions to LLE are not unique. In these cases, the addition of some regularization method is often proposed. The experimental results presented in this paper show that the regularization method is not robust. Too large or too small regularization parameters cannot unwrap S-curve. Although a moderate regularization parameters can unwrap S-curve, the relative distance in the input data will be distorted in unwrapping. Therefore, in order to make LLE play fully its advantage in nonlinear dimensionality reduction and avoid multiple solutions happening, the best way is to make sure that the neighborhood sizes are smaller than the dimensions of input data spaces.

An extension of the traditional color-based visual tracker, i.e., the continuously adaptive mean shift tracker, is given for improving the convenience and generality of the color-based tracker. This is achieved by introducing a probability density function for pixels based on the hue histogram of object. As its merits, the direction and size of the tracked object are easily derived by the principle component analysis (PCA), and its extension to three-dimensional case becomes straightforward.

In this letter we propose a simple adaptive algorithm which solves the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates single parameter normalization which is computationally much simpler. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

In this paper, we proposed a new Two-Dimensional Linear Discriminant Analysis (2DLDA) method, based on Two-Dimensional Principle Component Analysis (2DPCA) concept. In particular, 2D face image matrices do not need to be previously transformed into a vector. In this way, the spatial information can be preserved. Moreover, the 2DLDA also allows avoiding the Small Sample Size (SSS) problem, thus overcoming the traditional LDA. We combine 2DPCA and our proposed 2DLDA on the Two-Dimensional Linear Discriminant Analysis of principle component vectors framework. Our framework consists of two steps: first we project an input face image into the family of projected vectors via 2DPCA-based technique, second we project from these space into the classification space via 2DLDA-based technique. This does not only allows further reducing of the dimension of feature matrix but also improving the classification accuracy. Experimental results on ORL and Yale face database showed an improvement of 2DPCA-based technique over the conventional PCA technique.