Operator based on surface curvatures for multiscale image analysis

This paper introduces a new operator called the Surface-Shape operator for describing image structure. An image function is considered as a bivariate surface, then the Surface-Shape operator is established for describing shape of each pixel comparing with its neighbourhood by utilizing surface curvatures. In the geometry viewpoint, types of surface shape are elliptic, hyperbolic, cylindrical, etc. To give clearer meanings in general, we label them based on the topographic structure such as hill, dale, ridge, valley, etc. By extending from single-scale image analysis, the Surface-Shape operator is used as a pre-processing for describing multiscale topographic structures in scale-space representation. The Surface-Shape operator has invariant properties under linear and monotonic gray tone transformations, and is insensitive to additive noises modelled by linear functions, so it has robustness with brightness variations and shading effects. We illustrate usefulness of the Surface-Shape operator for image analysis with the image classification application, and compare the proposed method with the popular methods used to-date: the Spatial Gray Level Dependence method, Laws' method for the single-scale approach, and the Multiresolution Simultaneous Autoregressive method for the multiscale approach. Results show that the proposed method works much better than the other methods. In particular, the proposed method based on multiscale analysis performs best.