Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Performance of optical flow techniques
International Journal of Computer Vision
Tracking level sets by level sets: a method for solving the shape from shading problem
Computer Vision and Image Understanding
Robust Tracking of Position and Velocity With Kalman Snakes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Computational Physics
Dense Estimation of Fluid Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational Optic Flow Computation with a Spatio-Temporal Smoothness Constraint
Journal of Mathematical Imaging and Vision
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Region Tracking via Level Set PDEs without Motion Computation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Variational Framework for Joint Segmentation and Registration
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Variational Space-Time Motion Segmentation
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Influence of the Noise Model on Level Set Active Contour Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods
International Journal of Computer Vision
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation
International Journal of Computer Vision
Highly Accurate Optic Flow Computation with Theoretically Justified Warping
International Journal of Computer Vision
Piecewise-Smooth Dense Optical Flow via Level Sets
International Journal of Computer Vision
Dynamical Statistical Shape Priors for Level Set-Based Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking Deforming Objects Using Particle Filtering for Geometric Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation
Journal of Mathematical Imaging and Vision
A Low Dimensional Fluid Motion Estimator
International Journal of Computer Vision
Variational dense motion estimation using the Helmholtz decomposition
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Variational motion segmentation with level sets
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Dense estimation and object-based segmentation of the optical flow with robust techniques
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Tracking Closed Curves with Non-linear Stochastic Filters
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
SIAM Journal on Imaging Sciences
Crowd flow characterization with optimal control theory
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
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In this paper, a new framework for the tracking of closed curves and their associated motion fields is described. The proposed method enables a continuous tracking along an image sequence of both a deformable curve and its velocity field. Such an approach is formalized through the minimization of a global spatio-temporal continuous cost functional, w.r.t a set of variables representing the curve and its related motion field. The resulting minimization process relies on optimal control approach and consists in a forward integration of an evolution law followed by a backward integration of an adjoint evolution model. This latter pde includes a term related to the discrepancy between the current estimation of the state variable and discrete noisy measurements of the system. The closed curves are represented through implicit surface modeling, whereas the motion is described either by a vector field or through vorticity and divergence maps depending on the kind of targeted applications. The efficiency of the approach is demonstrated on two types of image sequences showing deformable objects and fluid motions.