3-D Lung Segmentation by Incremental Constrained Nonnegative Matrix Factorization

Abstract

Accurate lung segmentation from large-size 3-D chest-computed tomography images is crucial for computer-assisted cancer diagnostics. To efficiently segment a 3-D lung, we extract voxel-wise features of spatial image contexts by unsupervised learning with a proposed incremental constrained nonnegative matrix factorization (ICNMF). The method applies smoothness constraints to learn the features, which are more robust to lung tissue inhomogeneities, and thus, help to better segment internal lung pathologies than the known state-of-the-art techniques. Compared to the latter, the ICNMF depends less on the domain expert knowledge and is more easily tuned due to only a few control parameters. Also, the proposed slice-wise incremental learning with due regard for interslice signal dependencies decreases the computational complexity of the NMF-based segmentation and is scalable to very large 3-D lung images. The method is quantitatively validated on simulated realistic lung phantoms that mimic different lung pathologies (seven datasets), in vivo datasets for 17 subjects, and 55 datasets from the Lobe and Lung Analysis 2011 (LOLA11) study. For the in vivo data, the accuracy of our segmentation w.r.t. the ground truth is 0.96 by the Dice similarity coefficient, 9.0 mm by the modified Hausdorff distance, and 0.87% by the absolute lung volume difference, which is significantly better than for the NMF-based segmentation. In spite of not being designed for lungs with severe pathologies and of no agreement between radiologists on the ground truth in such cases, the ICNMF with its total accuracy of 0.965 was ranked fifth among all others in the LOLA11. After excluding the nine too pathological cases from the LOLA11 dataset, the ICNMF accuracy increased to 0.986.

Sparse feature learning for image analysis in segmentation, classification, and disease diagnosis.

“…(6) and (7) is not convex in both W and H, it is convex in either W or H, corresponding to Eqs. (14) and (15), respectively.…”

“…Moreover, the number of clusters are highly sensitive to the distance parameter of algorithm, which is directly related to the sparseness and smoothness of the decomposition space H. These drawbacks are overcome in [6] by using an introduced below ICNMF, which combines basic ideas of the INMF [91] and Constrained NMF (CNMF) [93,94]. The ICNMF decomposes every large data matrix A in a slice-by-slice mode, such that factorization of each next axial CT slice in a 3D CT image is initialized with the basis and decomposition matrices, having been already obtained from all the preceding slices.…”

“…Signal distributions for segmented voxels in the original 27-dimensional space (a) and the r-dimensional spaces reduced with the NMF (b) and ICNMF (c) visualized using the t-SNE projection [7]. The better ICNMF performance is exemplified by signal distributions and segmentation results for pathologies on the lung-chest border [6]. segmentation, as the sparseness of H affecting the accuracy more, than the smoothness of W. At the same time, the accuracy varies insignificantly for many weight combinations, so that selecting the best pair requires a too long experimentation.…”

“…Algorithm 5 adapts successfully to such pathologies. Lungs segmented with Algorithm 5 using the 3 × 3 × 3 neighborhood on pulmonary CT in the cases of airspace consolidation (a); tree-in-bud and micro-nodules (b); usual nodules (c); cancer (d); ground-glass opacity and juxtapleural nodules (e); honeycomb (f); diffuse consolidation (g), and cavity (h) [6]. five other segmentation algorithms, by comparing the means and standard deviations of their DSC values using the statistical paired t-tests.…”

“…Computed Tomographic (CT) images for lung segmentation [1,2,6]. Then image classification is investigated for understandable feature extraction in deep networks based on AE [16] and Convolutional Autoencoder (CAE).…”