Lung segmentation based on Nonnegative Matrix Factorization

Abstract

In this paper, a new framework for 3D lung segmentation is proposed. The primary step of this framework is to model both the spatial interaction and first-order visual appearance of the lung tissue based on a new Nonnegative Matrix Factorization (NMF) approach that has the ability to handle the inhomogeneity in the lung regions caused by arteries, veins, bronchi, and possible pathological tissues. The performance of our framework is assessed on fourteen 3D CT images. Based on the Dice Similarity Coefficient (DSC), experimental results showed that the proposed approach outperforms other lung segmentation techniques.

3-D Lung Segmentation by Incremental Constrained Nonnegative Matrix Factorization

“…Because 3D lung CT images are extremely large and make the ALS computationally too expensive, the ALS-AS based NMF was applied in our previous work [20] separately to each axial 2D CT slice converted into a classical context image [34]. Each voxel of the latter is represented by a context vector, containing the original voxel-wise signal and signals from its selected neighbors, e.g., the 27-vector for the nearest 3 × 3 × 3 volume centered on the voxel.…”

“…This drawback is overcome by using the introduced below incremental constrained NMF (ICNMF), combining basic ideas of the earlier incremental NMF (INMF) [35] and constrained NMF (CNMF) [27], [28]. Voxel-by-voxel decomposition of the entire 3D context image with the INMF improves capturing the inter-slice spatial dependencies, while the lung and chest manifolds in the h-space learned by the CNMF are smoother and more discriminable than in [20]. To reduce the computational complexity, the large data matrix A for a 3D CT image is decomposed with the ICNMF slice-after-slice, so that factorizing each next axial CT slice is initialized with the basis and projection matrices, having been already obtained from all the preceding slices.…”

“…The algorithms for comparisons include the multi-resolution segmentation [42]; segmentation with iterative thresholding (IT) followed by morphological operations [15], and segmentation with a deformable boundary guided by the gradient vector flow (GVF) [43]. Table. III compares Algorithm 1 with our earlier NMFbased segmentation [20] on the 17 real and 7 synthetic data sets, using all three performance metrics. By the DSC, the algorithms differ insignificantly for the synthetic data, whereas Algorithm 1 demonstrates a small, but statistically significant improvement for the real data (the mean and standard deviation 0.96 ±0.01 vs. 0.95 ±0.02 ).…”

“…The conventional first-order signal models have gained wide-spread acceptance only because accurate modeling of higher-order spatial dependencies and computationally feasible embedding of such models into segmentation process are generally challenging problems. Nonetheless, recent applications of the nonnegative matrix factorization (NMF) to extract voxel-wise vectorial features quantifying high-order spatial signal dependencies for image segmentation [17], [18], [19], [20] hold much promise for better object discrimination.…”