Reconnection of Interrupted Curvilinear Structures via Cortically Inspired Completion for Ophthalmologic Images

Objective: In this paper, we propose a robust, efficient, and automatic reconnection algorithm for bridging interrupted curvilinear skeletons in ophthalmologic images. Methods: This method employs the contour completion process, i.e., mathematical modeling of the direction process in the roto-translation group SE(2) = R-2 x S-1 to achieve line propagation/completion. The completion process can be used to reconstruct interrupted curves by considering their local consistency. An explicit scheme with finite-difference approximation is used to construct the three-dimensional (3-D) completion kernel, wherewe choose the Gamma distribution for time integration. To process structures in SE(2), the orientation score framework is exploited to lift the 2-D curvilinear segments into the 3-D space. The propagation and reconnection of interrupted segments are achieved by convolving the completion kernel with orientation scores via iterative group convolutions. To overcome the problem of incorrect skeletonization of 2-D structures at junctions, a 3-D segment-wise thinning technique is proposed to process each segment separately in orientation scores. Results: Validations on 4 datasets with different image modalities show that our method achieves an average success rate of 95.24% in reconnecting 40 457 gaps of sizes from 7 x 7 to 39 x 39, including challenging junction structures. Conclusion: The reconnection approach can be a useful and reliable technique for bridging complex curvilinear interruptions. Significance: The presented method is a critical work to obtain more complete curvilinear structures in ophthalmologic images. It provides better topological and geometric connectivities for further analysis.