Coherent chord computation and cross ratio for accurate ellipse detection

This paper presents a new method for detecting ellipses in images, which has many applications in pattern recognition and robotic tasks. Previous approaches typically use sophisticated arc grouping strategies or calculate differential such as tangents, and thereby they are less efficient or more sensitive to noise. In this work, we present a novel ellipse detector, based on the simple yet effective chord computation, and on the projective invariant cross ratio, which achieves promising performance in both accuracy and efficiency. First, elliptical arcs are extracted by fast vector computations along with the removal of straight segments to speed up detection. Then, arcs from the same ellipse are grouped together according to the relative location and the intersecting chord constraints, both are on coherent chord computation without differential. Additionally, an efficient additive principle is applied to further accelerate the grouping process. Finally, a novel and robust verification by area-deduced cross ratio is introduced to pick out salient ellipses. Compared with predecessor methods, cross ratio is not only simple for computation, but also has invariant properties (used to discriminate ellipses). Extensive experiments on seven public datasets (including synthetic and real-world images) are implemented. The results highlight the salient advantages of the proposed method compared to state-of-theart detectors: Easier to implementation, more robust against occlusion and noise, as well as attaining higher F-measure.