NonLocal via Local-NonLinear via Linear: A New Part-coding Distance Field via Screened Poisson Equation

Interesting phenomena in shape perception is nonlocal and nonlinear. Thus, it is crucial that a shape perception system exhibits a nonlocal and nonlinear behaviour. From the computational point of view, however, neither nonlinearity nor nonlocality is desired. We propose a repeated use of Screened Poisson PDE (leading to a sparse linear system) to compute a part coding and extracting distance field, a mapping from the shape domain to the real line. Despite local and linear computations, the field exhibits highly nonlinear and nonlocal behaviour, leading to efficient and robust coding of both the local and the global structures. The proposed computation scheme is applicable to shapes in arbitrary dimensions as well as shapes implied by fragmented partial contours. The local behaviour is independent of the image context in which the shape resides.