Curvature operators in geometric image processing

We study the problem of reconstructing an image from a perceptual segmentation based on a geometric classification of its points using non-linear curvature filters. We give a mathematical proof that an image can be reconstructed from the regions of non-zero Gaussian curvatures. This result provides the theoretical background for a new theory of non-linear two dimensional signal processing as proposed by Zetzche et al. (1990, 1993). We use curvature measures to detect edges and vertices (roughly two dimensional regions) and show that reconstruction is possible from these elements.