Based on projective geometry , the research works about 3d invariance ' s extraction and application have been done in this thesis as following : ( 1 ) the basic theories and concepts in projective geometry are systematically summarized . it includes : the camera models of perspective imaging , projective collineation , cross ratio , a simple compare about invariance ( invariant ) among some geometry transformations , fundamental matrix , epipolar and epipolar line in epipolar geometry , and so on . ( 2 ) the calculation methods for 2d projective transformation are extended from points to multi - element , which includes points , lines , points lines and so on , to get the relationship between two projective planes 基于射影几何理论，论文围绕3d不变特征的提取和应用进行了如下的研究工作： ( 1 )系统总结了射影几何中的若干基础概念，包括：透视成像的相机模型、射影对应、交比不变量、基于不同几何变换下的不变量的简单对比、对极几何中的基础矩阵、对极点、对极线等。
For bilateral symmetry objects , the techniques on symmetry - point detection and symmetry - axis extraction are presented based on harmonic conjugation relationship . for rotated symmetry objects , the techniques on rotated units description and rotated symmetry center extraction are presented based on center invariants of objects . further more , by using 3d invariants and 2d projective transformation , an approach to recover shape from part symmetry objects is realized on some conditions ( 3 )深入分析了2d对称性目标透视成像的几何特点，将共点四线交比用于目标轮廓上的关键点的特性描述中；利用调和共轭关系，提出了一种针对左右对称型目标的对称点检测和对称轴提取的算法；利用交比关系构造了目标的形心不变量，提出了一种针对旋转对称型目标的旋转对称单元判定、旋转中心提取的算法；进一步利用3d不变量和2d射影变换，实现了一定条件下的对称性目标的形状恢复技术。
