Construction of local nonlinear filter without staircase effect in image restoration

Abstract

This article introduces an innovative approach to the construction of a local nonlinear filter in image processing, which eliminates staircase effect. A local nonlinear filter changes its characteristics depending on the image content within a local area. Hence, it may preserve the image features. Due to its local property, the filtering algorithm has simple structure and fast performance. Two well-known local nonlinear filters are Yaroslavsky neighbourhood filter (also called sigma filter) and the bilateral filter (also called SUSAN filter). These filters produce very fast and effective denoising algorithms. But, unfortunately, they show staircase effect. To overcome their drawback, in this article we construct a new local nonlinear filter, called directional diffusion filter (DDF), which preserves image features and does not show staircase effect. We also study the DDF's properties and reveal the relation between DDF and Rudin–Osher–Fatemi's total variation model. Since the DDF denoising algorithm is very fast and uses very little read-only memory (ROM), it can be applied in the real-time processing for the devices without plenty of ROM, such as cell phones, security cameras and multispectral imagery sensors.

Keywords:

• nonlinear filters
• directional diffusion
• staircase effect
• image restoration
• total variation

AMS Subject Classifications::

• 94A08
• 93E14
• 68U10
• 3SK57
• 42C40

Acknowledgements

I would like to thank the referees for their valuable comments. The research was supported by NF Grant DAMS-07-12925.