A new approach to compute the Euler Number of 3D image

The Euler-Poincare characteristic of image is one of the most important characteristics in digital topology and many computing methods have been proposed in unceasing exploration. The connectivity of the 3D binary image was deeply researched in order to understand the essence of Euler number and to compute the Euler number of 3D image conveniently. A formula for locally computing the Euler number of 3D image was proposed based on the definitions of foreground run and neighbor number. This description was different from former ones between pixels and connectivity. It is a new idea to locally compute the Euler number of 3D image.