Geometric property based ellipse detection method

In this paper a simple but effective and robust ellipse detection method based on geometric property is developed, which mainly utilizes the following two aspects of ellipse geometric information: (1) Points on ellipse contour are position-symmetric and the gradient vectors of one pair of symmetric points are parallel or anti-parallel, the fact of which can be used for ellipse center location. In this part, the inner product in mathematics is introduced to evaluate the extent of parallelism of two gradient vectors, and then two concepts, inner product symmetrical energy (IPSE) and inner product consistent energy (IPCE), is defined to compute the probability of a position as a symmetric center. (2) The sum of distances of one contour point far from ellipse's two foci is a constant. For two given positions, by computing the distribution of the sum of distances we can validate if they are the correct positions of ellipse foci. Furthermore, ellipse's semi-major axis can be also estimated from distance distribution on the positions of ellipse foci. After determining the center, foci and semi-major axis of an ellipse candidate, other parameters can be easily deduced by resolving the elliptic equation directly. Compared with existing methods, the proposed method detects the ellipse using the geometric properties directly while avoiding the complicated application of the ellipse parameter space or fitting step, and it is simple, effective and robust. In addition, the ideas proposed in this paper can be extended for other features extraction, such as general symmetry center location and other shapes detection, and extensive experiments show the good availability of the proposed ideas.