A new operator for describing topographical image structure

To develop a computer vision system, it is necessary to define a proper image structure representation to be used for interpreting images efficiently. In this paper, we propose a new operator called shape operator for describing topographical 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 eigenvalue of Hessian of an image function. It is expressed in an explicit form in terms of the second order partial derivatives of an image function. We show how to derive this operator, its interesting properties, and an application for texture classification. Experimental results show its good performance for discriminating texture imaged. Especially, it can give the same interpretation of an image reflected in different lighting conditions since it has the invariance properties under linear and monotonic gray tone transformations.