Affine invariant non-linear anisotropic diffusion smoothing strategy for vector-valued images

Abstract

The Gaussian noise introduced into the diffusion tensor images (DTIs) can bring serious impacts on tensor calculation and fibre tracking. To decrease the effects of the Gaussian noise, many Euclidean invariant gradient (EIG) based anisotropic diffusion denoising methods have been presented. In this paper, the effects of the Gaussian noise on calculated tensors were analysed and an affine invariant gradient (AIG) based non-linear anisotropic smoothing strategy was presented. The AIG based smoothing strategy is the development of the affine invariant non-linear anisotropic diffusion (AINAD) restoration model, introduced by Guillermo Sapiro, and adopted to restore vector-valued data. To evaluate the efficiency of the AINAD model in accounting for the Gaussian noise introduced into the vector-valued data, the peak to peak signal-to-noise ratio (PSNR) and signal-to-mean squared error ratio (SMSE) metrics are used. The experiment results acquired from the synthetic and real data prove the good performance of the presented filter.

Keywords:

• DIFFUSION TENSOR IMAGING
• AFFINE INVARIANT GRADIENT
• AFFINE INVARIANT NON-LINEAR ANISOTROPIC DIFFUSION
• SMOOTHING
• EUCLIDEAN INVARIANT GRADIENT