Neighborhood coding for image representation and neighborhood operations

Neighborhood coding is a binary image representation method that has been performing successfully for a variety of applications such as features extraction for image recognition, shape descriptor, and image compression. Despite the success of this coding method, the representation lacked a formal notation. Here, we proposed a formal mathematical notation to represent any binary image into a neighborhood coding scheme. Using this representation we also introduce the concept of neighborhood operations, a procedure akin to mathematical morphology, however having a lower computational cost.