Using Non-Parametric Kernel to Segment and Smooth Images Simultaneously

Piecewise constant and piecewise smooth Mumford-Shah (MS) models have been widely studied and used for image segmentation. More complicated than piecewise constant MS, global Gaussian intensity distribution within each partitioned region has also been studied. However, all these frameworks are limited in power and robustness in finding objects whose interiors have high noise level and/or complex multi-modal intensity distribution. To overcome these drawbacks,we propose a non-parametric kernel based model which is able to simultaneously segment and smooth images without adding extra smoothing terms. At each point within each partitioned smooth region, a Gaussian kernel with mean the intensity of the given to-be-segmented image at this point and a small local variance depending on the location is applied to create a nonparametric intensity statistics approximation. To save computation, a quadratic kernel involving simple calculation could replace the Gaussian kernel that involves expensive exponential calculation. We demonstrate the superiority of proposed model over other models by showing segmentation results from various images with different levels and types of noise.