Partitioning 2D Images into Prototypes of Slope Region

A gray scale digital image can be represented as a 2.5D surface where the height of the surface corresponds to the gray value of the respective pixel. Analysis of the gray scale image can be efficiently done by exploiting the properties of the plane graph embedded in the 2.5D sur-face. The vertices of the graph can be easily categorized into critical and non-critical points by use of Local Binary Patterns (LBPs). Well defined graph operations such as contraction and removal of edges are used to eliminate the non-critical points and preserve the critical points thereby reducing the size of graph. In this process, it is important to preserve the structural and topological properties of the regions of a gray scale image. After analysing the topological properties of a well composed image, we provide two prototypes of the slope region and the necessary conditions for their existence. Also we prove that every slope region conforms to either of the two prototype. Conversely the prototypes may be used to generate an image with a required topological properties.