Intuition on boundaries, shocks and smoothing with PDEs

Abstract

When drawing or painting, many artists capture visual appearance with a coarse-to-fine sequence of boundaries and shadings. Many begin with a sketch of large, important scene features and then gradually add finer, more subtle details. Initial sketches of a painting may hold sharply defined boundaries around large, smoothly shaded regions for the largest, highest contrast and most important scene features. The artist then adds more shadings and boundaries to build up fine details, to fill in the visually empty regions and to capture rich detail everywhere. Such a procedure implicitly defines a hierarchical or coarse-to-fine scene decomposition, and we can use edge preserving filter operations such as the bilateral filters and PDEs to construct a similar decomposition for detail-preserving contrast reduction. This detail hierarchy is based on scene boundaries and shadings, an approach markedly different from the bandpass linear filter decompositions (e.g. image pyramids) that may suffer from halo artifacts. A suitable method for contrast reduction will produce no such halos.