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.

We propose a practical local and global path-planning algorithm for an autonomous vehicle or a car-like robot in an unknown semi-structured (or unstructured) environment, where obstacles are detected online by the vehicle's sensors. The algorithm utilizes a probabilistic method based on particle filters to estimate the dynamic obstacles' locations, a support vector machine to provide the critical points and Bezier curves to smooth the generated path. The generated path safely travels through various static and moving obstacles and satisfies the vehicle's movement constraints. The algorithm is implemented and verified on simulation software. Simulation results demonstrate the effectiveness of the proposed method in complicated scenarios that posit the existence of multi moving objects.

We propose the extended Bezier spiral in this paper. The spiral is useful for both design purposes and improved aesthetics. This is because the spiral is one of the Bezier curves, which play an important role in interactive curve design, and because the assessment of the curve is based on the human reception of the curve. For the latter purpose we utilize the logarithmic distribution graph that quantifies the designers' preferences. This paper contributes the unification of the two different curve design objectives (the interactive operation and so called "eye pleasing" result generation); which have been independently investigated so far.