Another way of looking at monocular circle pose estimation

It is well known that there are generally two possible sets of pose parameters from one calibrated perspective view of a circle. What is the relation between these two possible sets? Where does this ambiguity arise from? In which case can this ambiguity be resolved? Considering these questions, we suggest a novel viewpoint toward circle pose estimation from a single view. Different from existing methods on the basis of analytical geometry, we originally develop the projective equation of a circle, based on which a closed form solution is developed and a brand new geometric explanation for the ambiguity of solutions is presented. Experimental results verify the correctness of our proposed method.