Computational geometry: an introduction
Computational geometry: an introduction
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A central axis algorithm for 3D bronchial tree structures
ISCV '95 Proceedings of the International Symposium on Computer Vision
Liver registration for the follow-up of hepatic tumors
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Design of robust vascular tree matching: validation on liver
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Tree matching applied to vascular system
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
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Physiological measurements like branch angles, branch lengths, branch diameters and branch cross-sectional area of the 3-D pulmonary tree structures are clinically essential in evaluating the function of normal and diseased lung and during the breathing process. In order to facilitate these measurements and study relative structural changes, the 3-D lung tree volumes are reduced to a 3-D Euclidean straight line central axis tree.The central axis tree captures the branch topology and geometric features of the tree volume. Since matching 3-D tree volumes is complex, as they change in branch topology and geometry, we accomplish it designing an efficient algorithm that matches their corresponding central axis trees.The algorithm takes two binary central axis trees T_1=(V_1,E_1,W_1) and T_2=(V_2,E_2,W_2), where W_1 and W_2 are set of tuples containing geometric attributes corresponding to the nodes in T_1 and T_2, as inputs and returns the one-to-one matching function F of nodes in T_1 to T_2 that preserves the tree topology and closely matches the geometric attributes of these trees i.e. branch points, branch lengths, and branch angles between mapped nodes of T_1 and T_2. Since the topology match alone could result in many choices of the mapping function F, we prune these choices incorporating constraints on the geometric attributes of nodes in T_1 and T_2. We design a linear time algorithm that matches the branch topology and geometric features of T_1 and T_2. Our algorithm produced accurate matchings on various airway data sets of a dog lung obtained from Computed Tomography under simulated breathing conditions. T_1 and T_2 are obtained running a two-pass central axis algorithm on the tree volumes.