Curvature Operators in Geometric Image Processing

In this work 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 C. Zetzche, E. Barth and B. Wegmann ([15, 16]). We use curvature measures to detect edges and vertices (roughly two dimensional regions) and show that reconstruction is possible from these elements.