A Method for Classification of Convex Polygons Ping Guo, Yan-Xia Wang
A Method for Classification of Convex Polygons Ping Guo, Yan-Xia Wang School of Computer Science, Chongqing University, Chongqing, 400044, China
[email protected] Abstract Based on the planar polygon shape classification, we propose a method—Standardized Binary String Descriptor of Convex Polygon—for classification of convex polygons, making it more precise. Thus, the model database space is pruned and the number of shape models compared with, when doing match query and similarity query, is reduced. Furthermore, the number of equivalence class of convex polygon formula based on SBSDCP classification is presented.
inquiries more effectively and make shape recognition more accurate. This paper is organized as follows. In Section 1, it gives the significance of the study of the polygon, application and the status quo. Several basic definitions and theorems for our discussion are presented in Section 2. We describe the idea of BSD and the computation of Standardized Binary Shape Descriptor (SBSD) in Section 3 which is a major part of the thesis. Conclusion is made in Section 4.
2. Correlative Concepts
1. Introduction
First, some basic definitions are presented as follows.
An arbitrary planar graph’s border without holes can form a simple closed curve and become a polygon after quantified, for example, the boundary of map, cursive handwriting, the outline of cell. There is a method of classification about plane polygon in reference [1], all convex polygon has been divided into one kind by that way. The shape character of image border is essential for pattern recognition. How a shape can be represented in terms of its shape properties and whether the representation of shape is invariant to translation, scale, and orientation, which is desirable for the description of shape [3]. The comparison of different objects can be accomplished by describing their structural characters through match query algorithm [4]. The application of inquiries and matching based on the shape of graphics is very extensive, for example pattern recognition, image database system Handwritten character recognition system . Chuang [5] uses the template shape with the largest growth for shape matching. Mehrotra and Gray [6] normalize the coordinates of vertices of polygonal shapes and measure similarity of polygonal shapes by the Euclidean Distance of two coordinate lists. The proposed method makes the classification of a convex polygon more precise that it can better organize and store graphics data to perform shape
A polygon is represented by an ordered list of vertices P={v1,v2,…,vn } where n is the number of vertices of the polygon and vi∈R2
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Definition 1. A polygon is simple if no two edges of the polygon cross each other. Definition 2. If any interior angle of a polygon is less than 180 deg , the polygon is defined as a convex polygon . Definition 3. A convex polygon is non-degenerate if an arbitrary three adjacent vertices are not in a collinear. Theorem 1. An arbitrary convex polygon in plane has at most three acute angles. Proof : Suppose a convex polygon has n vertices, the corresponding exterior angles are resigned as α1, α2, …, αn . As n
∑α
i
= 360o
i =1
Suppose the polygon has k obtuse angles in its exterior angles αi1, αi2, …, αik , then n
k
i =1
j =1
360o = ∑ α i >∑ α kj ≥ k × 90o So k
