Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Hands: a pattern theoretic study of biological shapes
Hands: a pattern theoretic study of biological shapes
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Alternating kernel and mixture density estimates
Computational Statistics & Data Analysis
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Using Prior Shapes in Geometric Active Contours in a Variational Framework
International Journal of Computer Vision
Gradient flows and geometric active contour models
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A topology-preserving level set method for shape optimization
Journal of Computational Physics
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
International Journal of Computer Vision
Efficient kernel density estimation of shape and intensity priors for level set segmentation
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Global Regularizing Flows With Topology Preservation for Active Contours and Polygons
IEEE Transactions on Image Processing
Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow
IEEE Transactions on Image Processing
Self-Repelling Snakes for Topology-Preserving Segmentation Models
IEEE Transactions on Image Processing
A combined segmentation and registration framework with a nonlinear elasticity smoother
Computer Vision and Image Understanding
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
The mean boundary curve of anatomical objects
ACIVS'12 Proceedings of the 14th international conference on Advanced Concepts for Intelligent Vision Systems
Alignment and morphing for the boundary curves of anatomical organs
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Robust diffeomorphic mapping via geodesically controlled active shapes
Journal of Biomedical Imaging
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In this study we present a geometric flow approach to the segmentation of three-dimensional medical images obtained from magnetic resonance imaging (MRI) or computed tomography (CT) scan methods, by minimizing a cost function. This energy term is based on the intensity of the original image, and its minimum is found following a gradient descent curve in an infinite-dimensional space of diffeomorphisms (Diff) to preserve topology. The general framework is reminiscent of variational shape optimization methods but remains closer to general developments on the deformable template theory of geometric flows. In our case, the metric that provides the gradient is defined as a right-invariant inner product on the tangent space ($\mathcal{V}$) at the identity of the group of diffeomorphisms, following the general Lie group approach suggested by Arnold [J. Méc., 5 (1966), pp. 29-43]. To avoid local solutions of the optimization problem and to mitigate the influence of several sources of noise, a finite set of control points is defined on the boundary of the template binary images, yielding a projected gradient descent on Diff.