PDE-Based Three Dimensional Path Planning for Virtual Endoscopy

Abstract

Three dimensional medial paths or curve skeletons ( $\mathcal{CS}$) are an essential component of any virtual endoscopy (VE) system, because they serve as flight paths for a virtual camera to navigate the human organ and to examine its internal structures. In this paper, we propose a novel framework for computing flight paths of tubular structures for VE using partial differential equation (PDE). The method works in two passes. In the first pass, the overall topology of the organ is analyzed and its important topological nodes are identified, while in the second pass, the actual flight paths are computed by tracking them starting from each identified node. The proposed framework is robust, fully automatic, computationally efficient, and computes $\mathcal{CS}$ that are centered, connected, thin, and less sensitive to boundary noise. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several synthetic phantoms and clinical datasets.