A new operator for image structure analysis

In this paper, we propose a new operator called shape operator for describing image structure. We consider an image function as a surface, then describe a shape of each pixel comparing with its neighbourhood in terms of topographical shapes such as hill, dale, ridge, valley, etc. The shape operator is established by utilizing the eigenvalues of Hessian of an image function. We show how to derive this operator, and its interesting properties. Finally, we illustrate by examples how the shape operator can give the same interpretation of an image although the image is corrupted by shading effects, and how it can give the same interpretation of an image viewed in different viewpoints.