Solid shape
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
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
Extremal feature extraction from 3-D vector and noisy scalar fields
Proceedings of the conference on Visualization '98
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 4
Fast Constrained Surface Extraction by Minimal Paths
International Journal of Computer Vision
Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths
Journal of Mathematical Imaging and Vision
Fast Image Inpainting Based on Coherence Transport
Journal of Mathematical Imaging and Vision
Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images
Journal of Mathematical Imaging and Vision
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We introduce a novel implicit approach for surface patch segmentation in 3D images starting from a single point. Since the boundary surface of an object is locally homeomorphic to a disc, we know that the boundary of a small neighboring domain intersects the surface of interest on a single closed curve. Similarly to active surfaces, we use a cost potential which penalizes image regions of low interest. First, Using a front propagation approach from the source point chosen by the user, one can see that the closed curve corresponds to a valley line of the arrival time from the source point. Next, we use an implicit 3D segmentation method. It assumes that the object boundary contains two known constraining curves. In our case, the first curve is reduced to a point and the other one is automatically detected by our approach. A partial differential equation is introduced and its solution is used for segmentation. The zero level set of this solution contains the valley line and the source point as well as the set of minimal paths joining them. We present a fast implementation which has been successfully applied to 3D biomedical and synthetic images.