Piecewise Linearization Method for Arbitrary Curves by Relaxation Method to Line Label

Abstract

This paper proposes a new piecewise linearization method to approximate arbitrary curve and verifies the validity of the proposed method by experience. Previous methods are applied only to the sequence of points whose coordinate values are known. Furthermore, the sequence needs to be arranged into permutation. This is caused by the difficulty in extracting line segments from arbitrary curve. So, in this proposed method, first, by applying the group of patterns which is named ‘Angle pattern’, the sequence of point on each pixels is detected and the angle of the sequence is shown. Then, the angle on each pixels is divided into the group of labels which is named ‘Line segment label’ by using relaxation method. After labeling, line segments can be extracted. Because this proposed method is able to approximate arbitrary curve without pre-knowledge of the curve, it is considered that this method is quite effective method for feature detection in computer vision.