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
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Region-based strategies for active contour models
International Journal of Computer Vision
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast level set method for propagating interfaces
Journal of Computational Physics
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
International Journal of Computer Vision
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
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
DEFORMOTION: Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
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
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Statistical Approach to Snakes for Bimodal and Trimodal Imagery
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Journal of Mathematical Imaging and Vision
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
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
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
Elastic-string models for representation and analysis of planar shapes
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Area and length minimizing flows for shape segmentation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Constraining active contour evolution via Lie Groups of transformation
IEEE Transactions on Image Processing
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Shape of Elastic Strings in Euclidean Space
International Journal of Computer Vision
International Journal of Computer Vision
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
Momentum Based Optimization Methods for Level Set Segmentation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
A Fast Optimization Method for Level Set Segmentation
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Geodesics in Shape Space via Variational Time Discretization
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Reconstructing Optical Flow Fields by Motion Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Variational B-spline level-set: a linear filtering approach for fast deformable model evolution
IEEE Transactions on Image Processing
Active Contour Method with Separate Global Translation and Local Deformation
ICIRA '09 Proceedings of the 2nd International Conference on Intelligent Robotics and Applications
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
A Computational Model of Multidimensional Shape
International Journal of Computer Vision
Generalized surface flows for deformable registration and cortical matching
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Journal of Mathematical Imaging and Vision
Converting level set gradients to shape gradients
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
A spherical harmonics shape model for level set segmentation
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
SIAM Journal on Imaging Sciences
New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows
Journal of Mathematical Imaging and Vision
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
A fully implicit framework for Sobolev active contours and surfaces
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape Space
Journal of Mathematical Imaging and Vision
SIAM Journal on Imaging Sciences
Time-Discrete Geodesics in the Space of Shells
Computer Graphics Forum
Multiple object tracking via prediction and filtering with a sobolev-type metric on curves
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
Active Contours with Free Endpoints
Journal of Mathematical Imaging and Vision
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All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L 2-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.