Abstract
The framework of analyzing the image singularity based on the sub-pixel multifractal measure (SPMM) is presented in this paper. Performing SPMM can give the sub-pixel local distribution of image gradient and a more precise singularity exponent distribution of the image. And the MSM detected this way reflects the most important information of the image. Meantime, using singularity exponents and the most singular manifold, the image can be decomposed into a series of sets with different statistical and physical properties automatically and easily. Using the pavement surface crack image as an example, it shows that the physical and geometrical properties of the structures can be obtained by analyzing the distribution of singularity exponents and the most singularity exponent. Furthermore, the pavement surface images with or without crack can also be distinguished.
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