基于压缩映射不动点的图像几何不变特征提取

Extracting Geometric Invariant Feature of Images Based on Fixed Point Theory of Contractive Mappina

以Hilbert空间中压缩映射不动点理论为基础,建立了一种提取图像几何不变特征的框架。基本思想可表述为：在Hilbert空间中,首先以单参数变换群表示图像之间的几何形变,然后用压缩映射不动点迭代方法获得对该单参数变换群具有几何不变性的核函数,最后以此核函数提取图像中的不变特征,若变换不是压缩映射(变换),可通过正则坐标系间的转换,使单参数变换在新坐标系下具有压缩映射的性质。此框架为构造几何不变核函数提供了一条全新的思路,文中给出了对尺度缩放和旋转具有不变性的两个核函数实例,通过大量样本数据测试,验证了所建立的框架是正确有效的。

Extracting features which are invariant to geometric transformation has been disoussed widely. In this paper,a common framework based on the theory of fixed point of contractive mapping is proposed to find geometric invariant kernels, within which one-parameter group is used＇ to model the transformation between images, and any one-parameter group can be converted to a contractive mapping through a coordinate transformation from current canonical coordinate to another one, then the kernel can be considered as the fixed point of the contractive mapping which can be searched via iteration. Kernels invariant to scaling and rotating are constructed as examples of the framework and its ability to extracting invariant feature of image is proved in our experiments.