具有平移、尺度和旋转不变性的小波变换

寻求具有平移、尺度和旋转不变性的小波变换,是应用小波分析进行模式识别需要重点解决的课题。普通的离散小波变换对信号的起始位置非常敏感,不具有平移不变性。本文通过坐标变换,采用方向能量函数确定图像主轴方位,并将其旋转到水平方向得到方向归一化图像。通过对图像的重整和正交小波基的位移、伸缩变换,消除位移和尺度的影响,得到具有平移、尺度和旋转不变性的小波变换。

A Wavelet Transform With Shift, Scale and Rotation Invariance

Constructing the wavelet transform with shift, scale and rotation invariance is a key problem of the application of wavelet transform in pattern recognition community. Traditional discrete wavelet transform, which is sensitive to the position of the signal, is not shiftable. In this paper, a wavelet transform with shift, scale and rotation invariance is presented. First, the orientation-normalized image is achieved by rotating its principal axis, defined by a directional energy function in polar coordinate, to horizontal direction. Then renormalized image is projected onto the multiresolution subspaces spanned by a set of shifted and dilated orthonormal wavelet basis functions to get translation and scale invariance.