The paper presents three edge grouping algorithms for finding a closed contour starting from a selected edge point and enclosing a fixation point. The algorithms search a shortest simple cycle in a graph derived from an edge image where a vertex is an end point of a contour fragment and an undirected arc is drawn between every pair of end-points whose visual angle from the fixation point is less than a threshold value (set to π/2 in our experiments). The first algorithm restricts the search space to shapes where no contour point seen from the fixation point is occluded by other contour points, and finds the shortest simply cycle. The second algorithm restricts the search space to shapes where the starting edge point neither occludes nor is occluded by other contour points, and finds a shortest simple cycle. The third algorithm is free from any constraints, but does not guarantee that the solution is a shortest cycle. The third algorithm, however, guarantees a solution no worse than that of the second algorithm. The paper demonstrates effectiveness of these algorithms with a number of natural images. Finally, the paper proposes a way to automate placement of a fixation point and a starting point so that the procedure runs in a fully automated manner.
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