Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
Journal of Computational Physics
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
Finding Shortest Paths on Surfaces Using Level Sets Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimal Paths in 3D Images and Application to Virtual Endoscopy
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Multiple Contour Finding and Perceptual Grouping as a Set of Energy Minimizing Paths
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Vessel Axis Determination Using Wave Front Propagation Analysis
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Level Set Based Segmentation with Intensity and Curvature Priors
MMBIA '00 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
ICPR '96 Proceedings of the International Conference on Pattern Recognition (ICPR '96) Volume III-Volume 7276 - Volume 7276
A review of vessel extraction techniques and algorithms
ACM Computing Surveys (CSUR)
Geodesic Remeshing Using Front Propagation
International Journal of Computer Vision
International Journal of Computer Vision
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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This paper presents new methods to segment thin tree structures, which are, for example present in microglia extensions and cardiac or neuronal blood vessels. Many authors have used minimal cost paths, or geodesics relative to a local weighting potential P, to find a vessel pathway between two end points. We utilize a set of such geodesic paths to find a tubular tree structure by seeking minimal interaction. We introduce a new idea that we call geodesic voting or geodesic density. The approach consists of computing geodesics from a set of end points scattered in the image which flow toward a given source point. The target structure corresponds to image points with a high geodesic density. The ''Geodesic density'' is defined at each pixel of the image as the number of geodesics that pass over this pixel. The potential P is defined in such way that it takes low values along the tree structure, therefore geodesics will migrate toward this structure thereby yielding a high geodesic density. We further adapt these methods to segment complex tree structures in a noisy medium and apply them to segment microglia extensions from confocal microscope images as well as vessels.