Alternative way to compute the euler number of a binary image

In this paper an alternative way to compute the (E) Euler number of a binary image via information about its pixels is presented. The P perimeter of the objects in the image, their P_c contact perimeter and the T-type pixel are used to obtain this important invariant. This is the second time the Euler number is described in terms of the contact perimeter of the objects in an image but with new results. The first paper that reports computing the Euler number of a binary shape in terms of the P and P_c is in [E. Bribiesca, Computation of the Euler number using the contact perimeter, Computers and Mathematics with Applications 60:1364-137 (2010)]. Bribiesca's proposal is useful only for unit-width shapes. In this paper, we extend Bribiesca's method for non-unit-width shapes.