Low-Rank and Sparse Splitting for Glyph Extraction

Abstract This paper is concerned with digital extraction of archaeological glyphs from a surface. The input surface is decomposed into a background component that represents the underlying general shape and a sparse component that captures the fine details, including the glyphs. We separate these components by using a novel variational framework that promotes low-rank background matrices via the nuclear norm minimization. Depending on the parameters, the resulting optimization problem can be either convex or non-convex. In particular, by considering $$\ell _q$$ ℓ q -quasi-norm sparsity penalties with $$0 0 < q < 1 , we obtain non-convex models that promote sparsity and often enhance the separation of fine structures more than an $$\ell _1$$ ℓ 1 -norm penalty. We evaluate the effectiveness of the proposed method when applied to synthetic as well as real-world data.