A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
SIAM Review
Multiple Contour Finding and Perceptual Grouping using Minimal Paths
Journal of Mathematical Imaging and Vision
Optimal Algorithm for Shape from Shading and Path Planning
Journal of Mathematical Imaging and Vision
An $\cal O(N)$ Level Set Method for Eikonal Equations
SIAM Journal on Scientific Computing
Short note: O(N) implementation of the fast marching algorithm
Journal of Computational Physics
Geodesic Remeshing Using Front Propagation
International Journal of Computer Vision
IEEE Transactions on Image Processing
From a Single Point to a Surface Patch by Growing Minimal Paths
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Airway Tree Extraction with Locally Optimal Paths
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Approximate shortest paths in simple polyhedra
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Journal of Biomedical Imaging - Special issue on Mathematical Methods for Images and Surfaces 2011
Globally minimal path method using dynamic speed functions based on progressive wave propagation
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part II
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In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the minimal path approach. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. This approach can also be used for finding an open curve giving extra information as stopping criteria. Detection of a variety of objects on real images is demonstrated. Using a similar idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.