Multiple contour finding and perceptual grouping as a set of energy minimizing paths

We address the problem of finding a set of contour curves in an image. We consider the problem of perceptual grouping and contour completion, where the data is a set of points in the image. A new method to find complete curves from a set of contours or edge points is presented. Our approach is an extension of previous work on finding a set of contours as minimal paths between end points using the fast marching algorithm. Given a set of key points, we find the pairs of points that have to be linked and the paths that join them. We use the saddle points of the minimal action map. The paths are obtained by backpropagation from the saddle points to both points of each pair. We also propose an extension of this method for contour completion where the data is a set of connected components. We find the minimal paths between each of these components, until the complete set of these "regions" is connected. The paths are obtained using the same backpropagation from the saddle points to both components.