An Adaptive Approach for the Segmentation and the TV-Filtering in the Optic Flow Estimation

作者：Belhachmi Z^*; Hecht F

来源：Journal of Mathematical Imaging and Vision, 2016, 54(3): 358-377.

DOI：10.1007/s10851-015-0608-6

• Segmentation
• Optic flow estimation
• Video motion analysis
• Gamma-convergence
• Adaptivity
• Finite element
• Residual error indicators

We consider a variational model for the joint total variation filtering (TV) and the segmentation in the optic flow estimation. The model is based on a functional with a spatially varying regularization parameter to solve such an ill-posed problem. We present an adaptive approach based on a posteriori error indicators which allows us to select locally the optimal values of the diffusion coefficient in the functional. We show that the adaptive process applied to the linear part of the functional (with respect to the optic flow variable) fulfills the segmentation objective. Moreover, this adaptive approach provides an approximation of the Mumford-Shah functional in the sense of the-convergence of a family of discrete energies. The simultaneous filtering and segmentation are achieved within this approach with accuracy and a reduced number of degrees of freedom, which improves each task to obtain a reliable optic flow estimation. We present some numerical simulations to show the performances of the method for the segmentation and the simultaneous segmentation-filtering.

• 出版日期2016-3