Differential Fly-Throughs (DFT): A General Framework for Computing Flight Paths

Abstract

In this paper, we propose a new variational framework based on distance transform and gradient vector flow, to compute flight paths through tubular and non-tubular structures, for virtual endoscopy. The proposed framework propagates two wave fronts of different speeds from a point source voxel, which belongs to the medial curves of the anatomical structure. The first wave traverses the 3D structure with a moderate speed that is a function of the distance field to extract its topology, while the second wave propagates with a higher speed that is a function of the magnitude of the gradient vector flow to extract the flight paths. The motion of the fronts are governed by a nonlinear partial equation, whose solution is computed efficiently using the higher accuracy fast marching level set method (HAFMM). The framework is robust, fully automatic, and computes flight paths that are centered, connected, thin, and less sensitive to boundary noise. We have validated the robustness of the proposed method both quantitatively and qualitatively against synthetic and clinical datasets.

Principal curves to extract vessels in 3D angiograms

“…, (8) where N (v i ) denotes a set of segment indices whose segment is adjacent to the vertex v i , P j (x) is the function given in Equation 7 for measuring the existence probability of tubular structure and P i (x) is a similar function but with the segment projection set S replaced by a vertex projection set V. The function δ · (·) returns the shortest Euclidean distance from a data point to a principal curve component (defined in Section 2.3). It is normalized by the local half width of the component…”

“…It is a piece of crucial information in advanced image analysis, viz. generating fly-throughs of virtual endoscopy [8], studying populations' vessel attributes [3] and making real-time 3D-2D vascular registration possible [7].…”

“…The automatic approach usually relies on a post-processing of the vascular segmentation. There were several methods worked along this line [15,22,16,8]. Nevertheless, if one wants to get a satisfactory centerline extraction, a topologically and morphologically correct segmention (with no handles and cavities) is compulsory which indeed is very difficult to obtain from clinical data.…”

Principal Curves for Lumen Center Extraction and Flow Channel Width Estimation in 3-D Arterial Networks: Theory, Algorithm, and Validation

“…The vessel centerline is as important as the segmentation. It is a piece of crucial information in advanced image analysis, processing and visualization, viz., virtual angioscopy [1], [2], population study of vessel attributes [3], real-time 3-D/2-D vascular registration [4], and vasculature visualization [5], [6]. Algorithms to extract vessel centerlines can be categorized into two classes, i.e., automatic and semiautomatic.…”

“…The latter needs at least a single user-supplied point to kick off the execution. An automatic approach usually relies on the postprocessing of the vascular segmentation [1], [2], [7], [8]. Nevertheless, if one wants to get a satisfactory centerline extraction, a topologically and morphologically correct segmentation (with no handles and cavities) is compulsory, which is indeed very difficult to obtain from clinical data.…”