Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computation of discontinuous optical flow by domain decomposition and shape optimization
International Journal of Computer Vision
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Variational methods in image segmentation
Variational methods in image segmentation
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
Computer Vision and Image Understanding
A variational level set approach to multiphase motion
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Direct incremental model-based image motion segmentation for video analysis
Signal Processing - Video segmentation for content-based processing manipulation
SIAM Journal on Scientific Computing
Image Sequence Analysis via Partial Differential Equations
Journal of Mathematical Imaging and Vision
Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Level Set Model for Image Classification
International Journal of Computer Vision
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
Motion Competition: Variational Integration of Motion Segmentation and Shape Regularization
Proceedings of the 24th DAGM Symposium on Pattern Recognition
Smoothness in Layers: Motion segmentation using nonparametric mixture estimation.
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
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
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
A variational framework for image segmentation combining motion estimation and shape regularization
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Dense estimation and object-based segmentation of the optical flow with robust techniques
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Highly Accurate Optic Flow Computation with Theoretically Justified Warping
International Journal of Computer Vision
Dynamic Shape and Appearance Modeling via Moving and Deforming Layers
International Journal of Computer Vision
A Probabilistic Segmentation Scheme
Proceedings of the 30th DAGM symposium on Pattern Recognition
Bayesian approaches to motion-based image and video segmentation
IWCM'04 Proceedings of the 1st international conference on Complex motion
Distance regularized level set evolution and its application to image segmentation
IEEE Transactions on Image Processing
A variational framework for image segmentation combining motion estimation and shape regularization
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Dynamic shape and appearance modeling via moving and deforming layers
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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We present a novel variational approach for segmenting the image plane into a set of regions of piecewise constant motion on the basis of only two consecutive frames from an image sequence. To this end, we formulate the problem of estimating a motion field in the framework of Bayesian inference. Our model is based on a conditional probability for the spatio-temporal image gradient, given a particular velocity vector, and on a prior on the estimated motion field favoring motion boundaries of minimal length. The corresponding negative log likelihood is a functional which depends on motion vectors for a set of regions and on the boundary separating these regions. It can be considered an extension of the Mumford-Shah functional from intensity segmentation to motion segmentation. We propose an implementation of this functional by a multiphase level set framework. Minimizing the functional with respect to its dynamic variables results in an evolution equation for a vector-valued level set function and in an eigenvalue problem for the motion vectors. Compared to most alternative approaches, we jointly solve the problems of segmentation and motion estimation by minimizing a single functional. Numerical results both for simulated ground truth experiments and for real-world sequences demonstrate the capacity of our approach to segment several - possibly multiply connected - objects based on their relative motion.