A Local Nonparametric Model for Simultaneous Image Segmentation and Adaptive Smoothing

Parametric and nonparametric region based active contour models have been widely used in image segmentation and showed promising results. However, since segmentation processing in these models are driven by intensity probability density functions (p.d.f.), intensity inhomogeneity and higher level of noise are always challenging problems that need to be addressed. In this paper we present a novel local nonparametric model for simultaneous image segmentation and adaptive smoothing. We treat the smoothed image intensity at each point as a random variable, whose realizations are the intensities of the observed noisy image in a neighborhood of this point. The neighborhood size varies from point to point depending on image gradients. A nonparametric p.d.f. estimation is applied to the smoothed image to get likelihood estimations for both object and background. Then, the simultaneous smoothing and segmentation is achieved by minimizing the negative log-likelihood estimations together with total length of the region boundaries. By the choice of the local adaptive neighborhoods the smoothing does not across the boundaries and is less at the locations where image gradient is higher. The proposed model is implemented using its level set formulation. The experimental results on synthetic data, T1 weighted human brain MRI images, FLAIR MRI brain images, and echocardiographic images indicate the advantages of the proposed model in dealing with higher level noise and intensity inhomogeneity. The existence of a solution to the proposed model is also discussed.