2024/04/04 by Martin Alkämper, Alkämper, Martin, Stephan Hilb +3 · 1 citation
Computer Science · #Advanced Image Processing Techniques #Advanced Vision and Imaging #FOS: Mathematics #Numerical Analysis (math.NA) #Optical measurement and interference techniques
paper · pdf · doi:10.48550/arxiv.2404.03125
openalex publication_date 2024/04/04 · openalex created_date 2024/04/07 · openalex updated_date 2026/07/28
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general L1-L2-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. The efficiency of our derived adaptive finite element scheme is demonstrated on image inpainting and the task of computing the optical flow in image sequences. In particular, for optical flow estimation we derive an adaptive finite element coarse-to-fine scheme which allows resolving large displacements and speeds-up the computing time significantly.