Edge-preserving and scale-space filtering by saddle-node dynamics

Using maximum entropy principle and statistical mechanics, we derive and demonstrate the use of saddle-node dynamics for edge-preserving filtering. The nonlinear dynamics allows the clustering filter to achieve three tasks: a) removing noise; b) preserving edges and c) improved smoothing of nonimpulsive noise. For each datum in a signal, a neighborhood of weighted data is used for clustering. The cluster center becomes the filter output. This filter presents a new mechanism for preserving discontinuities differing from techniques based on local gradients and line processes. We demonstrate the filter using real images. This work provides a framework within which further image processing, image coding and computer vision problems can be investigated