Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
A 3D 6-subiteration thinning algorithm for extracting medial lines
Pattern Recognition Letters
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Relative critical sets in RR(N) and applications to image analysis
Relative critical sets in RR(N) and applications to image analysis
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Non-Linear Model Fitting to Parameterize Diseased Blood Vessels
VIS '04 Proceedings of the conference on Visualization '04
An interior algorithm for nonlinear optimization that combines line search and trust region steps
Mathematical Programming: Series A and B
3D Dendrite Reconstruction and Spine Identification
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Piecewise linear cylinder models for 3-dimensional axon segmentation in brainbow imagery
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
Detecting boundaries in a vector field
IEEE Transactions on Signal Processing
Rapid automated three-dimensional tracing of neurons from confocal image stacks
IEEE Transactions on Information Technology in Biomedicine
Median-based robust algorithms for tracing neurons from noisy confocal microscope images
IEEE Transactions on Information Technology in Biomedicine
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In this study, we compare two vectorial tracing methods for 3D color images: (i) a conventional piecewise linear generalized cylinder algorithm that uses color and edge information and (ii) a principal curve tracing algorithm that uses the gradient and Hessian of a given density estimate. We tested the algorithms on synthetic and Brainbow dataset to show the effectiveness of the proposed algorithms. Results indicate that the proposed methods can successfully trace multiple axons in dense neighborhoods.