Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithms for Computing Motion by Mean Curvature
SIAM Journal on Numerical Analysis
Subjective Surfaces: A Geometric Model for Boundary Completion
International Journal of Computer Vision
Segmentation by Adaptive Geodesic Active Contours
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A review of vessel extraction techniques and algorithms
ACM Computing Surveys (CSUR)
Breakdown-free GMRES for Singular Systems
SIAM Journal on Matrix Analysis and Applications
Semi-Implicit Covolume Method in 3D Image Segmentation
SIAM Journal on Scientific Computing
Composed Segmentation of Tubular Structures by an Anisotropic PDE Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Variational Method for Geometric Regularization of Vascular Segmentation in Medical Images
IEEE Transactions on Image Processing
Framelet-Based algorithm for segmentation of tubular structures
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Many different approaches have been proposed for segmenting vessels, or more generally tubular-like structures from 2D/3D images. In this work we propose to reconstruct the boundaries of 2D/3D tubular structures by continuously deforming an initial distance function following the Partial Differential Equation (PDE)-based diffusion model derived from a minimal volume-like variational formulation. The gradient flow for this functional leads to a non-linear curvature motion model. An anisotropic variant is provided which includes a diffusion tensor aimed to follow the tube geometry. Space discretization of the PDE model is obtained by finite volume schemes and semi-implicit approach is used in time/scale. The use of an efficient strategy to apply the linear system iterative solver allows us to reduce significantly the numerical effort by limiting the computation near the structure boundaries. We illustrate how the proposed method works to segment 2D/3D images of synthetic and medical real data representing branching tubular structures.