Euler number of image is one of the most important characteristics in digital topology. The connectivity of the binary image was deeply researched in order to understand the essence of Euler number. The relationship between Euler number and the neighbor number of foreground run was proposed as a formula based on the two basic concepts of Euler number and neighbor number. It is a new idea to part computed Euler number of two dimesion image. It has been applied to count the number of objects with irregular shape.