Computer Vision, Graphics, and Image Processing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On active contour models and balloons
CVGIP: Image Understanding
Feature extraction from faces using deformable templates
International Journal of Computer Vision
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Multiple Contour Finding and Perceptual Grouping using Minimal Paths
Journal of Mathematical Imaging and Vision
Real-Time Interactive Path Extraction with on-the-Fly Adaptation of the External Forces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
Geodesic active regions and level set methods for motion estimation and tracking
Computer Vision and Image Understanding
Fast Constrained Surface Extraction by Minimal Paths
International Journal of Computer Vision
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
An Implicit Method for Interpolating Two Digital Closed Curves on Parallel Planes
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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We introduce a novel implicit approach for single object segmentation in 3D images. The boundary surface of this object is assumed to contain two or more known curves (the constraining curves), given by an expert. The aim of our method is to find the desired surface by exploiting the information given in the supplied curves as much as possible. We use a cost potential which penalizes image regions of low interest (for example areas of low gradient). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. These paths globally minimize an energy which is defined from the cost potential. Our approach, although conceptually different, can be seen as an implicit extension to 3D of the minimal path framework already known for 2D image segmentation. As for this previous approach, and unlike other variational methods, our method is not prone to local minima traps of the energy. We present a fast implementation which has been successfully applied to 3D medical and synthetic images.