Abstract
Images can be broadly classified into two types: isotropic and anisotropic. Isotropic images contain largely rounded objects while anisotropics are made of flow-like structures. Regardless of the types, the acquisition process introduces noise. A standard approach is to use diffusion for image smoothing. Based on the category, either isotropic or anisotropic diffusion can be used. Fundamentally, diffusion process is an iterated one, starting with a poor quality image, and converging to a completely blurred mean-value image, with no significant structure left. Though the process starts by doing a desirable job of cleaning noise and filling gaps, called under-smoothing, it quickly passes into an over-smoothing phase where it starts destroying the important structure. One relevant concern is to find the boundary between the under-smoothing and over-smoothing regions. The spatial entropy change is found to be one such measure that may be helpful in providing important clues to describe that boundary, and thus provides a reasonable stopping rule for isotropic as well as anisotropic diffusion. Numerical experiments with real fingerprint data confirm the role of entropy-change in identification of a reasonable stopping point where most of the noise is diminished and blurring is just started. The proposed criterion is directly related to the blurring phenomena that is an increasing function of diffusion process. The proposed scheme is evaluated with the help of synthetic as well as the real images and compared with other state-of-the-art schemes using a qualitative measure. Diffusions of some challenging low-quality images from FVC2004 are also analyzed to provide a reasonable stopping rule using the proposed stopping rule.
Highlights
1 Introduction In image processing problems, many times one comes across the task to enhance flow-like structures, for instance, the automatic assessment of wood surfaces or fabrics, fingerprint image analysis, scientific image processing in oceanography [1], seismic image analysis [2], or sonogram image interpolated for Fourier analysis [3]
After the completion of the linear anisotropic diffusion process, the entropy change graph is obtained as depicted in Fig. 8b,c, respectively
We look into their acquisition process process them for uniform background and later investigate their spatial entropy characteristic as the image evolves under linear anisotropic process
Summary
Many times one comes across the task to enhance flow-like structures, for instance, the automatic assessment of wood surfaces or fabrics, fingerprint image analysis, scientific image processing in oceanography [1], seismic image analysis [2], or sonogram image interpolated for Fourier analysis [3]. A remedy was pointed out by [12], that suggests the use of Gaussian smoothing before computing gradients This modification lays the foundation for a well-behaved nonlinear isotropic diffusion process. Our proposed linear anisotropic diffusion process will steer the non-uniform Gaussian to lay along the structure, but its size will remain constant regardless of the position. This observation paves the way to the hypothesis that peak entropy change will happen at the time instant on diffusion time axis when dominant image structures just start blending with the background right at their boundaries This finding, substantiated by extensive empirical evidence provided here, motivated us to put forward the idea that a maximum entropy change may well be posed as a good stopping time for the diffusion process.
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