Stopping criterion for linear anisotropic image diffusion: a fingerprint image enhancement case

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.