基于类似形原理从单幅透视图识别平面立体

Recognizing Polyhedrons from a Perspective Drawing Based on Principle of Homograph

根据透视不变性提出了5个描述多边形形状的拓扑特征和几何特征,以这些特征作为约束条件给出透视投影下类似形的定义。根据类似形的定义提出了识别多边形是类似形的新方法。据此提出了基于类似形原理从单幅透视投影线图识别平面立体的新方法。新定义的类似形能将平面立体中的表面分类。匹配过程限制在类似形内进行,大大减少了搜索范围。用拓扑结构对类似形进行定性分析,对噪音不敏感,用几何特征进行定量分析,则能反应平面立体形状的细微差别。该识别方法不仅能识别不同形状的平面立体目标,而且还可以区分形状相同但大小、比例不同的平面立体目标。实验结果表明该方法是有效的。

In this paper, two problems are researched. First, we propose five topology characteristics and geometry characteristics that are invariant under perspective transformation to describe polygon. Then the definition of homograph is given in terms of these characteristics. On the basis of this definition, we give a procedure for recognizing homographs. Second, a new algorithm for recognizing polyhedrons from a perspective line drgwing based on principle of homograph is presented. Homograph as defined by us can be employed to distinguish between surfaces with different characteristics and to classify the surfaces of polyhedron. As homographs＇ categories are few in number and as it is only necessary to put the polygon to be recognized in one of these few categories, efficiency of recognition is greatly raised. We introduced the topological structure to analyze homograph qualitatively, therefore the algorithm is insensitive to noises; and employ geometrical structure to analyze homograph quantitatively, thus the algorithms can show fine discrimination between polyhedrons. Thus, it can not only recognize polyhedrons of different shape but also distinguish between polyhedrons that are of the same shape but their sizes and proportions are different. Comparing with other recognition algorithms, our algorithm has obtained obvious improvement. The effectiveness of the algorithm is demonstrated preliminarily by computer simulation.