Computation of discontinuous optical flow by domain decomposition and shape optimization
International Journal of Computer Vision
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
Computer Vision and Image Understanding
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Numerical Analysis
Direct incremental model-based image motion segmentation for video analysis
Signal Processing - Video segmentation for content-based processing manipulation
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 Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
A multiphase level set framework for motion segmentation
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Dense estimation and object-based segmentation of the optical flow with robust techniques
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
The MPM-MAP algorithm for motion segmentation
Computer Vision and Image Understanding
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation
International Journal of Computer Vision
International Journal of Computer Vision
An integrated dynamic scene algorithm for segmentation and motion estimation
EURASIP Journal on Applied Signal Processing
Computer Vision and Image Understanding
Robotics and Autonomous Systems
A Geometric Framework and a New Criterion in Optical Flow Modeling
Journal of Mathematical Imaging and Vision
Bayesian approaches to motion-based image and video segmentation
IWCM'04 Proceedings of the 1st international conference on Complex motion
A multiphase level set framework for motion segmentation
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Implicit free-form-deformations for multi-frame segmentation and tracking
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Motion detection using wavelet analysis and hierarchical markov models
SCVMA'04 Proceedings of the First international conference on Spatial Coherence for Visual Motion Analysis
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Based on a geometric interpretation of the optic flow constraint equation, we propose a conditional probability on the spatio-temporal image gradient. We consistently derive a variational approach for the segmentation of the image domain into regions of homogeneous motion. The proposed energy functional extends the Mumford-Shah functional from gray value segmentation to motion segmentation. It depends on the spatio-temporal image gradient calculated from only two consecutive images of an image sequence. Moreover, it depends on motion vectors for a set of regions and a boundary separating these regions. In contrast to most alternative approaches, the problems of motion estimation and motion segmentation are jointly solved by minimizing a single functional. Numerical evaluation with both explicit and implicit (level set based) representations of the boundary shows the strengths and limitations of our approach.