Robust local estimation in anisotropic diffusion process

Abstract

In this work we propose to use an anisotropic diffusion process using robust statistics. We show that smoothing, while preserving edges, helps the segmentation of upper limb bones (shoulder) in MRI data bases. The anisotropic diffusion equation is mainly controlled using an automatic edge stopping function based on Tukey's biweight function, which depends on the values of gradients pixels. These values are divided into two classes: high gradients for pixels belonging to edges or noisy pixels, low ones otherwise. This process also depends on a threshold gradient parameter which splits both former classes. So a robust local estimation method is proposed to better eliminate the noise in the image while preserving edges. Firstly, the efficiency of the model in the noise reduction is quantified using an entropy criterion on synthetic data with different noise levels to evaluate the smoothing of the regions. Secondly, we use the Pratt's Figure of Merit (FOM) method to evaluate edges preservation. Eventually, a qualitative edge evaluation is given on a MRI volume of the shoulder joint.

Robust and effective automatic parameter choice for medical image filtering.

“…Perona and Malik [30] suggested to fix β by trial and error, or using a noise estimator as described in [6]. Alternative approaches have been proposed, such as using the p-norm of the image intensity [36], or through linking robust local statistics estimators and diffusion [20,5].…”