Planar Visualization of Treelike Structures

We present a novel method to create planar visualizations of treelike structures (e.g., blood vessels and airway trees) where the shape of the object is well preserved, allowing for easy recognition by users familiar with the structures. Based on the extracted skeleton within the treelike object, a radial planar embedding is first obtained such that there are no self-intersections of the skeleton which would have resulted in occlusions in the final view. An optimization procedure which adjusts the angular positions of the skeleton nodes is then used to reconstruct the shape as closely as possible to the original, according to a specified view plane, which thus preserves the global geometric context of the object. Using this shape recovered embedded skeleton, the object surface is then flattened to the plane without occlusions using harmonic mapping. The boundary of the mesh is adjusted during the flattening step to account for regions where the mesh is stretched over concavities. This parameterized surface can then be used either as a map for guidance during endoluminal navigation or directly for interrogation and decision making. Depth cues are provided with a grayscale border to aid in shape understanding. Examples are presented using bronchial trees, cranial and lower limb blood vessels, and upper aorta datasets, and the results are evaluated quantitatively and with a user study.