Automation of object counting in digital images has received significant attention in the last 20 years. Objects under consideration varied from cells, bacteria, trees, fruits, pollen, insects to people. These applications cast light on the importance of shape identification and object counting. We developed an algorithm and methodology for detection of mathematically well-defined shapes and calculated the probability of shapes crossing equally spaced lines. Simulations for detection and counting of regular mathematical shapes such as lines and circles were performed in a random environment. Simulation results are compared with the empirical probability calculations. Results seem promising as they converge to the empirical calculations with the increase in number of shapes.