Automated Robust Image Segmentation: Level Set Method Using Nonnegative Matrix Factorization with Application to Brain MRI

We address the problem of fully automated region discovery and robust image segmentation by devising a new deformable model based on the level set method (LSM) and the probabilistic nonnegative matrix factorization (NMF). We describe the use of NMF to calculate the number of distinct regions in the image and to derive the local distribution of the regions, which is incorporated into the energy functional of the LSM. The results demonstrate that our NMF-LSM method is superior to other approaches when applied to synthetic binary and gray-scale images and to clinical magnetic resonance images (MRI) of the human brain with and without a malignant brain tumor, glioblastoma multiforme. In particular, the NMF-LSM method is fully automated, highly accurate, less sensitive to the initial selection of the contour(s) or initial conditions, more robust to noise and model parameters, and able to detect as small distinct regions as desired. These advantages stem from the fact that the proposed method relies on histogram information instead of intensity values and does not introduce nuisance model parameters. These properties provide a general approach for automated robust region discovery and segmentation in heterogeneous images. Compared with the retrospective radiological diagnoses of two patients with non-enhancing grade 2 and 3 oligodendroglioma, the NMF-LSM detects earlier progression times and appears suitable for monitoring tumor response. The NMF-LSM method fills an important need of automated segmentation of clinical MRI.