A feature-oriented forward–backward diffusion model for intensity image restoration based on level set motion

Abstract

In this paper, a new enhancing and smoothing partial differential equation coupled with time-delay regularization is presented, which is based on local geometric properties desired for image restoration. To reverse the process of image deterioration, a newly defined shock filter for edge enhancing is combined with a level set motion-based regularization equation. The balance between the backward process and the forward process is carried out by a weighting function coupled with time-delay regularization helping to identify boundary areas and homogeneous regions in a given image. The proposed model is well-posed in terms of viscosity solutions – the existence and uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical results for some kinds of grey-level images are demonstrated to confirm our anticipation.

Keywords:

• parabolic-hyperbolic equation
• shock filter
• periodic viscosity solution
• level set motion
• time-delay regularization
• image restoration

2000 AMS Subject Classifications :

• 35K65
• 35K15
• 35M20

Acknowledgements

We would like to thank the referees for useful remarks on the first version of the manuscript. This work was supported by NSAF of China (10576013) and by NSF of China (10531040).