Two Problems of Circle in Image

Circle is an important primitive in document images, which is contained in many scenes and shapes due to the aesthetic feeling. As it is known to all, three nonlinear points determine a circle, namely, the radius and the coordinates of circle can be calculated. However, three nonlinear points cannot determine a unique desirable circle occasionally in images. Circumferences consist of many pixels, what is the relation of radius size and number of pixels on the circumferences with and without redundancy? We mainly discuss the condition about how to make a unique desirable circle with three nonlinear pixels in images and the above-mentioned relation. Finally, the relation and condition have been found and testified by experiments.