基于径向希尔伯特变换的图像边缘增强特性研究

Properties of Image Edge Enhancement Using Radial Hilbert Transform

研究了基于螺旋相位频谱滤波器滤波的径向希尔伯特变换对不同边缘分布图像的增强特性.给出了拓扑荷n=1的有限孔径螺旋相位滤波器点扩散函数的解析表达式,并利用圆孔、汉字和人像等三幅不同边缘分布密度的图像进行了边缘增强的模拟计算.结果表明,基于螺旋相位频谱滤波的径向希尔伯特变换会使边缘增强图像具有立体浮雕效果,并且随着输入图像的边缘分布密度变大,立体浮雕效果会越显著.通过理论分析得出,这一现象是由螺旋相位滤波器点扩散函数中的次极大分布与输入图像边缘卷积引起的.这一结论为图像的信息处理提供了一些有利的手段.

The properties of edge enhancement for different marginal distribution density image based on radial Hilbert transform with a spiral phase filter were studied.The analytical expression to describe the point spread function of a finite-radius spiral phase filter with topological charge n=1 was given and the edge enhancement for different marginal distribution image such as circular aperture,Chinese character and portraits were simulated.The results show that the edge enhanced images using radial Hilbert transform have three-dimensional relief effect,and the more intensive marginal distribution of input image,the more significant relief effect.Theoretical analysis found that this property derives from convolution between the input image and subsidiary maximum in the point spread function.This conclusion will be beneficial as a way for image processing.