Contour Completion Around a Fixation Point

The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived from an edge image where a vertex is an end point of a contour fragment and an undirected arc is drawn between a pair of end-points whose visual angle from the fixation point is less than a threshold value, which is set to $\pi/2$ in our experiments. The first algorithm restricts the search space by disregarding arcs that cross the line extending from the fixation point to the starting point. The second algorithm improves the solution of the first algorithm in a greedy manner. The algorithms were tested with a large number of natural images with manually placed fixation and starting points. The results are promising.