Abstract
A method of counting the number of objects of an arbitrary shape and a size, in a visual field, is presented.
Euler number is a well known topological invariant and can easily be counted as the difference between the number of maximal points (convexities) and the number of minimal points (concavities) to some fixed direction. When the objects have no loop, i.e., each object is simply connected, the number of objects coincides with Euler number, while if there were objects having some loops, Euler number becomes the number of objects minus the number of loops. Thus the number of objects can be counted as the sum of Euler number and the numbr of loops.
Detecting loops is concerned with the problem of connectedness property, which is one of the macroscopic properties of geometrical patterns. In order to secure a grobal point of view, a register named connectedness register is introduced.
Extremal points are detected and counted by scanning witn two detector cells from the upper left corner of the visual field, as with a television raster, and with the aid of connectedness register, loops are also detected and counted. The number of objects is then calculated at the end of scanning of a single field, as the number of upper ends (upper convexities) minus the number of cups (upper concavities) plus the number of loops.
Simulations on a digital computer proved the varidity of this counting method. It has many applications such as dust counting, blood corpuscule counting, surface defection test, size distribution measurement, and so on.
