A primal-dual adaptive finite element method for total variation based motion estimation
<|reference_start|>A primal-dual adaptive finite element method for total variation based motion estimation: Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically generating an adaptive grid we introduce indicators based on a-posteriori error estimates. Further we discuss data interpolation methods on unstructured grids in the context of image processing and present a pixel-based interpolation method. For the computation of optical flow we derive an adaptive finite element coarse-to-fine scheme for resolving large displacements. The coarse-to-fine scheme speeds-up the computing time tremendously.<|reference_end|>
@article{alkämper2024a,
    title={A primal-dual adaptive finite element method for total variation based
  motion estimation},
    author={Martin Alk"amper, Stephan Hilb, Andreas Langer},
    journal={arXiv preprint arXiv:2404.03125},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03125},
    primaryClass={math.NA cs.NA}
}