Sparse representation of cast shadows via ℓ1-regularized least squares

Scenes with cast shadows can produce complex sets of images. These images cannot be well approximated by low-dimensional linear subspaces. However, in this paper we show that the set of images produced by a Lambertian scene with cast shadows can be efficiently represented by a sparse set of images generated by directional light sources. We first model an image with cast shadows as composed of a diffusive part (without cast shadows) and a residual part that captures cast shadows. Then, we express the problem in an ℓ₁-regularized least squares formulation, with nonnegativity constraints. This sparse representation enjoys an effective and fast solution, thanks to recent advances in compressive sensing. In experiments on both synthetic and real data, our approach performs favorably in comparison to several previously proposed methods.