For object analysis and recognition, an original shape often needs to be described by using a small number of vertices. Polygonal approximation is one of the useful methods for the description. In this paper, we propose the curvature-based polygonal approximation (CBPA) method that is an application of the weighted polygonal approximation problem which minimizes the number of vertices of an approximate curve for a given error tolerance (the weighted minimum number problem). The CBPA method considers the curvature information of each vertex of an input curve as the weight of the vertex, and it can be executed in O(n2) time where n is the number of vertices of the input curve. Experimental results show that this method is effective even in the case when relatively few vertices are given as an original shape of a planar object, such as handwritten letters, figures (freehand curves) and wave-form data.

Clothoid or cornu spiral segments were used as transition spirals forming C-and S-shaped curves between circles as well as straight lines in various situations of highway road design. These transitions are the center lines of rail, highway road design. The above C and S-shaped form curves consist one or more transition segments. We study the possibility of using the single transition spirals in the situations that use many transition spirals to form smooth transition spline between circles as well as straight lines. We also compute the bounds for the scaling of such single spirals using the practical equation. This paper is aimed to give a method avoiding non-linear equations by finding range for the scaling factor of the clothoids which can take initially an appropriate closer value from this range.

We propose a new algorithm for minimizing the number of vertices of an approximate curve by keeping the error within a given bound (min-# problem) with the parallel-strip error criterion. The best existing algorithm which solves this problem has O (n2 log n) time complexity. Our algorithm which uses the Cone Intersection Method does not have an improved time complexity, but does have a high efficiency. In particular, for practical data such as those which represent the boundaries or the skeletons of an object, the new algorithm can solve the min-# problem in nearly O(n2) time.

Various calculations of derivatives, dealing with specific spaces, have been studied to define cubic splines. Some Modified 3-Point Methods have been proposed which would reduce the amount of calculations required. These methods enable us to preceive the result from a computer by lines. Some theorems that are useful for the discussion of local calculations are given and examples are executed to compare our methods with the original cubic spline functions. The results given in this paper have demonstrated a relation to the interactive computer graphics as well as the interpolation of data points.

Locating corner points from an edge detected image is very important in view of simplifying the post processing part of a system that utilizes a corner information. In this paper, we propose a robust geometrical approach for corner detection. Unlike classical corner detection methods, which idealize corners as junction points of two line segments, our approach considers the possibility of multiple line segments intersecting at a point. Moreover, junctions caused by two or more curved segments of different curvature are thought of as a corner point. The algorithm has been tested and proved competence with different types of images demonstrating its ability to detect and localize the corners in the image, though we found it to be best suited for images with relatively few curved segments. With the help of non-maximum response suppression technique our approach yields comparatively better result than any other method.

Generation of line-drawing images in intelligent terminals seems to be an important theme in the area of computer graphics because of the recent architectures of computer systems. Required operations for the image generation should be local (or incremental), and each operation has to be carried out with limited amount of calculations and memories. The authors have reported the five-point method for this purpose. In this paper, the three-point method is newly investigated as a further study on this line. Traditional three-point methods cannot be applicable as their undulations" owing to the truncation of data points for local processing appear. Therefore, several types of estimations" are introduced in order to compensate the truncation; they are compared in view of derived results and required calculational steps, and one of the methods is recommended as the most useful local algorithm.

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.