Euler Number is one of the most important characteristics in topology. In two-dimension digital images, the Euler characteristic
is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on
the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved
in this paper. It is a new idea to locally compute Euler Number of 2D image.
Keywords topology - Euler Number - binary image - 4-connected - 8-connected