图像多重分形测度的速降函数投影方法与图像奇异性分析

该文给出了一个基于多重分形理论的图像奇异性分析框架.该框架通过定义在图像梯度级上的测度,证明了该测度在速降函数上的投影与尺度之间满足幂指数关系.给出了将图像分解为一系列具有不同奇异性指数和分数维的分形集合的分解算法.最后理论分析并提出了选择速降函数的基本原则,讨论了仅根据分形集合上的导数信息就可以重建该分形层面图像分量的重构算法.实验表明,该文给出的多重分形框架在图像奇异性检测和分析中具有十分重要的意义.

The Projection Method of Fast Decreasing Functions for Multifractal Measure and Image Singularity Analysis

The framework for image singularity analysis based on multifractal theory is presented in this paper. The measure is defined which gives the local distribution of the gradient of the image. The exponential formalism between the projection of fast decreasing functions of the defined measure and scale is proved. According to the exponential formalism, the paper also presented an algorithm, in which the nature image can be decomposed in a serial fractal sets with different singularity exponent and fractal dimension. Finally, some basic theoretical results of the choice for the fast decreasing functions are proposed. Also an investigation of how to reconstruct the different fractal image components with derivative , information contained in the different fractal sets is made. Experiments show that the multifractal formalism has significance in image singularity analysis and detection.