模式识别中的透射变换与仿射变换

仿射变换和透射变换是两种基本的图像变换。本文详细研究了仿射变换和透射变换的性质，并推导出它们之间的关系。研究表明，在特殊情况下，非线性的透射变换退变为线性的仿射变换；在多数情况下，透射变换可以用仿射变换很好地近似，这为透射变换的目标识别指出了一条新的途径。一组新的由低阶中心矩构成的仿射不变量验证了本文推导的正确性

Projective Transformation and Affine Transformation in Pattern Recognition

Projective transformation and affine transformation are essential in the image transformation. In this paper, we studied them in detail and derived an equation which indicates the relation ship between them. It is found that, in some special cases, a nonlinear projective transformation degenerated into a linear affine transfromation. In general cases, the former can be approximated well to the latter, and it leads a new way in pattern recognition under the projective transformation. A new set of affine moment invariants was used to testify the formula derived in the paper.