Globally optimal co-segmentation of three-dimensional pulmonary ¹H and hyperpolarized ³He MRI with spatial consistence prior.

Pulmonary imaging using hyperpolarized (3)He/(129)Xe gas is emerging as a new way to understand the regional nature of pulmonary ventilation abnormalities in obstructive lung diseases. However, the quantitative information derived is completely dependent on robust methods to segment both functional and structural/anatomical data. Here, we propose an approach to jointly segment the lung cavity from (1)H and (3)He pulmonary magnetic resonance images (MRI) by constraining the spatial consistency of the two segmentation regions, which simultaneously employs the image features from both modalities. We formulated the proposed co-segmentation problem as a coupled continuous min-cut model and showed that this combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In particular, we introduced a dual coupled continuous max-flow model to study the convex relaxed coupled continuous min-cut model under a primal and dual perspective. This gave rise to an efficient duality-based convex optimization algorithm. We implemented the proposed algorithm in parallel using general-purpose programming on graphics processing unit (GPGPU), which substantially increased its computational efficiency. Our experiments explored a clinical dataset of 25 subjects with chronic obstructive pulmonary disease (COPD) across a wide range of disease severity. The results showed that the proposed co-segmentation approach yielded superior performance compared to single-channel image segmentation in terms of precision, accuracy and robustness.