A localized piecewise constant model with kernel mapping and convex optimization for image segmentation

This paper presents a localized piecewise constant model for image segmentation. By taking the local image characteristics into account, the proposed model can effectively segment images with intensity inhomogeneity. Due to the introduction of a kernel-induced non Euclidean distance to its objective functional, our model is more robust to noise and outliers. Its objective functional includes two terms: a data term which evaluates the deviation of the image data from the local region-based piecewise constant model by kernel mapping, and a classic length regularization term for smoothing region boundaries. In order to obtain the global optimal and make the segmentation results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. The promising experimental results on synthetic and real images validate the effectiveness of the proposed model.