Level set segmentation using non-negative matrix factorization of brain MRI images

This paper presents a new level set method for image segmentation by integrating the level set formulation and the non-negative matrix factorization (NMF). The proposed model characterizes the histogram of the image by dividing the image into blocks and computing the histograms of the blocks as nonnegative combinations of basic histograms. This is achieved by using the NMF algorithm. The basic histograms form a clustering of the image into distinct regions. Our model also takes into account the intensity inhomogeneity or the bias field that usually corrupts medical images. In a level set formulation, this clustering criterion defines an energy in terms of the level set functions that represent a partition of the image domain. The image segmentation is achieved by minimizing this energy with respect to the level set functions and the bias field. Our method is compared, using synthetic and real images, to other state-of-the-art level set approaches that are based on localized clustering and local Gaussian distribution fitting. It is shown that the proposed approach is more robust to noise in the image and intensity inhomogeneity. These advantages stem from the fact that the proposed model i) depends on the distribution of pixels intensities (the histogram) rather than the direct intensity values and ii) does not introduce additional model parameters to be simultaneously estimated with the bias field and the level set functions.