  Image segmentation is a fundamental research topic in image processing and
computer vision. In the last decades, researchers developed a large number of
segmentation algorithms for various applications. Amongst these algorithms, the
Normalized cut (Ncut) segmentation method is widely applied due to its good
performance. The Ncut segmentation model is an optimization problem whose
energy is defined on a specifically designed graph. Thus, the segmentation
results of the existing Ncut method are largely dependent on a pre-constructed
similarity measure on the graph since this measure is usually given empirically
by users. This flaw will lead to some undesirable segmentation results. In this
paper, we propose a Ncut-based segmentation algorithm by integrating an
adaptive similarity measure and spatial regularization. The proposed model
combines the Parzen-Rosenblatt window method, non-local weights entropy, Ncut
energy, and regularizer of phase field in a variational framework. Our method
can adaptively update the similarity measure function by estimating some
parameters. This adaptive procedure enables the proposed algorithm finding a
better similarity measure for classification than the Ncut method. We provide
some mathematical interpretation of the proposed adaptive similarity from
multi-viewpoints such as statistics and convex optimization. In addition, the
regularizer of phase field can guarantee that the proposed algorithm has a
robust performance in the presence of noise, and it can also rectify the
similarity measure with a spatial priori. The well-posed theory such as the
existence of the minimizer for the proposed model is given in the paper.
Compared with some existing segmentation methods such as the traditional
Ncut-based model and the classical Chan-Vese model, the numerical experiments
show that our method can provide promising segmentation results.
