2019/03/12 by Miroslav Bačák, Bačák, Miroslav, Johannes Hertrich +5
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1903.04873
openalex publication_date 2019/03/12 · openalex created_date 2019/03/22 · openalex updated_date 2026/08/01
This paper deals with extensions of vector-valued functions on finite graphs fulfilling distinguished minimality properties. We show that so-called lex and L-lex minimal extensions are actually the same and call them minimal Lipschitz extensions. Then we prove that the solution of the graph p-Laplacians converge to these extensions as p→ ∞. Furthermore, we examine the relation between minimal Lipschitz extensions and iterated weighted midrange filters and address their connection to ∞-Laplacians for scalar-valued functions. A convergence proof for an iterative algorithm proposed by Elmoataz et al.~(2014) for finding the zero of the ∞-Laplacian is given. Finally, we present applications in image inpainting.