Incorporation of physical constraints in optimal surface search for renal cortex segmentation

In this paper, we propose a novel approach for multiple surfaces segmentation based on the incorporation of physical constraints in optimal surface searching. We apply our new approach to solve the renal cortex segmentation problem, an important but not sufficiently researched issue. In this study, in order to better restrain the intensity proximity of the renal cortex and renal column, we extend the optimal surface search approach to allow for varying sampling distance and physical separation constraints, instead of the traditional fixed sampling distance and numerical separation constraints. The sampling distance of each vertex-column is computed according to the sparsity of the local triangular mesh. Then the physical constraint learned from a priori renal cortex thickness is applied to the inter-surface arcs as the separation constraints. Appropriate varying sampling distance and separation constraints were learnt from 6 clinical CT images. After training, the proposed approach was tested on a test set of 10 images. The manual segmentation of renal cortex was used as the reference standard. Quantitative analysis of the segmented renal cortex indicates that overall segmentation accuracy was increased after introducing the varying sampling distance and physical separation constraints (the average true positive volume fraction (TPVF) and false positive volume fraction (FPVF) were 83.96% and 2.80%, respectively, by using varying sampling distance and physical separation constraints compared to 74.10% and 0.18%, respectively, by using fixed sampling distance and numerical separation constraints). The experimental results demonstrated the effectiveness of the proposed approach.