Machine Vision and Applications
On minimal energy trajectories
Computer Vision, Graphics, and Image Processing
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
Using Prior Shapes in Geometric Active Contours in a Variational Framework
International Journal of Computer Vision
Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Global Minimum for Active Contour Models: A Minimal Path Approach
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
On Smoothness Measures of Active Contours and Surfaces
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Gradient flows and geometric active contour models
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Conformal Metrics and True "Gradient Flows" for Curves
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
More-Than-Topology-Preserving Flows for Active Contours and Polygons
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Designing Spatially Coherent Minimizing Flows for Variational Problems Based on Active Contours
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Tracking With Sobolev Active Contours
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
On similarity-invariant fairness measures
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Consistency and stability of active contours with Euclidean and non-Euclidean arc lengths
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Dynamic Texture Detection Based on Motion Analysis
International Journal of Computer Vision
New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows
Journal of Mathematical Imaging and Vision
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
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Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric out-performs the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important. Some interesting properties of Sobolev gradient flows are that they stabilize certain unstable traditional flows, and the order of the evolution PDEs are reduced when compared with traditional gradient flows of the same energies. In this paper, we explore new possibilities for active contours made possible by Sobolev active contours. The Sobolev method allows one to implement new energy-based active contour models that were not otherwise considered because the traditional minimizing method cannot be used. In particular, we exploit the stabilizing and the order reducing properties of Sobolev gradients to implement the gradient descent of these new energies. We give examples of this class of energies, which include some simple geometric priors and new edge-based energies. We will show that these energies can be quite useful for segmentation and tracking. We will show that the gradient flows using the traditional metric are either ill-posed or numerically difficult to implement, and then show that the flows can be implemented in a stable and numerically feasible manner using the Sobolev gradient.