In many applications, e.g. medical, industrial and military systems, it is of interest to fit a circle to scattered data points belonging to a complete or incomplete circular arc. As an example, circle fitting can be applied in the industry, for quality control, when investigation is required to verify if a manufactured circular object has the desired radius or not. A variety of methods have been developed to handle the circle fitting problem. Some methods are relatively complex and provide more accurate circle fitting, whereas some are simple and fast but lacks accuracy. Furthermore, some methods handle circle fitting better on incomplete circular objects. However, for practical machine vision implementations, there seems to be a lack of study when it comes to circle fitting on largely incomplete circular arcs. Largely incomplete circular arcs refer to short arcs having corresponding angles of few degrees, e.g. less than 10°. Hence, this thesis deals with design and implementation of circle fitting on largely incomplete circular objects. The goal is to investigate the shortest circular arc, i.e. the shortest possible angle that, can be fitted to a circle with an accuracy of at least 98%. The approach includes studying related work, developing a vision based algorithm for circle fitting on incomplete circular objects and conducting experiments using live stream 2D images. We designed and implemented an algorithm, based on a circle fitting algorithm, called Hyper fit. Our experimental set-up, with a 5-Megapixel camera, showed that it is possible to fit a circle, with an accuracy of 98%, to a short circular arc with an angle of only 1.95° of a complete circle. 1.95° corresponds to 0.54% of a complete circles circumference. Results showed that, using a high-resolution camera, it is possible to fit accurate circles on largely incomplete circular arcs. Moreover, the implementation achieved the real-time requirement, as it could process at least 3 fps (frames per second).