Closed contour is an important objectness indicator. We propose a new measure subject to the completeness and tightness constraints, where the optimized closed contour should be tightly bounded within an object proposal. The closed contour measure is defined using closed path integral, and we solve the optimization problem efficiently in polar coordinate system with a global optimum guaranteed. Extensive experiments show that our method can reject a large number of false proposals, and achieve

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... ver 6% improvement in object recall at the challenging overlap threshold 0.8 on the VOC 2007 test dataset.