Object Labelling is the goal of uniquely labelling each pixel as being part of a connected object. It is related to the tasks of segmentation and thresholding, but when binary images are being discussed the task is usually refered to as labelling.
This apparently has a simple problem is probably the best illustration for the novice of some of the fundamental difficulties of doing vision on a serial computer. The Human Visual System can instantly perform counting with deceptive effortlessness. To understand the difficulty of getting a computer to do the same, remember that a computer can only 'look' at one pixel at a time. Try counting objects while looking at the world through a straw! It soon becomes clear that this needs an iterative solution.