Abstract: Through the research about invariants under similarity transformations（rotation,scale and translation）,the proof of the fact that the center of gravity of an image and two endpoints of its major axis are such invariants under similarity transformations is stated,and a geometric feature-based shape descriptor θ invariant to rotation,scale and translation is proposed in this paper.θ is the included angle between the line segments connecting center of gravity and two endpoints of major axis.The theoretical analysis and experiments both show that the shape descriptor is efficient and simple,and gains desirable matching results.

Key words: pattern recognition, shape descriptor, shape matching, invariant

摘要： 通过对平移旋转和伸缩变换下的不变量进行研究,证明了形状的长轴端点和重心是该变换下的不变量,提出了长轴两端点与重心所成的夹角这一几何特征的形状描述子,该形状描述子具有平移旋转和伸缩变换不变性,理论分析和实验结果表明该描述子简单高效,具有较好的形状匹配结果。

关键词: 模式识别, 形状描述子, 形状匹配, 不变量