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The ability to find the average of a set of contours has several applications in computer vision including prototype formation and computational atlases. While contour averaging can be handled in an informal manner, the formal formulation within the framework of generalized median as an optimization problem is attractive. In this work we will follow this line. A special class of contours is considered, which start from the top, pass each image row exactly once, and end in the last row of an image. Despite of the simplicity they frequently occur in many applications of image analysis. We propose a dynamic programming approach to exactly compute the generalized median contour in this domain. Experimental results will be reported on two scenarios to demonstrate the usefulness of the concept of generalized median contours. In the first case we postulate a general approach to implicitly explore the parameter space of a (segmentation) algorithm. It is shown that using the generalized median contour, we are able to achieve contour detection results comparable to those from explicitly training the parameters based on known ground truth. As another application we apply the exact median contour to verify the tightness of a lower bound for generalized median problems in metric space.

A Class of Generalized Median Contour Problem with Exact Solution