COMPUTING THE AREA, THE CIRCUMFERENCE, AND THE GENUS OF A BINARY DIGITAL IMAGE

Publisher Summary This chapter discusses a method for computing the area, the circumference, and the genus of a binary digital image. It shows a small binary digital image of resolution 8 × 7 consisting of 31 black and 25 white pixels. Pixels are considered here to be closed unit squares, although they are assumed to be implemented as elements of a binary matrix, as is often the case. The set union of the black pixels is called the figure of the image, and computing the area, the circumference, and the genus (or Euler number) of the image more precisely means computing these three important properties for the figure. The genus of a binary digital image often is defined as the number of connected components of the figure minus the number of holes. The chapter discusses a method which counts the number of vertices, sides, and extents of the black pixels in an image. The method is based on the fact that area, circumference, and genus can be understood as additive functionals.