Multiple Contour Finding and Perceptual Grouping using Minimal 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 based on a previous work on finding contours as minimal paths between two end points using the fast marching algorithm (L. D Cohen and R. Kimmel, International Journal of Computer Vision, Vol. 24, No. 1, pp. 57xe2x80x9378, 1997). 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  a :141,second part, we propose a scheme that does not need key points for initialization. A set of key points is automatically selected from a larger set of admissible points. At the same time, saddle points between pairs of key points are extracted. Next, paths are drawn on the image and give the minimal paths between selected pairs of points. The set of minimal paths completes the initial set of contours and allows to close them. We illustrate the capability of our approach to close contours with examples on various images of sets of edge points of shapes with missing contours.

A Scoring Model of Figural Goodness and Its Application to Contour Completion Problems This paper models the concept of figural goodness of a shape and apply the model to solving the visual occlusion problem. Based on the observation that u0027goodnessu0027 of figure is influenced by local and global shape contexts, we model simplicity and regularity of a shape, and define a figural goodness score by linearly combining these two. To evaluate the usefulness and limitation of the proposed scoring, we applying the model to solving a contour completion problem. In the application, various completion paths of occluded contours are generated by a computer using different kinds of completion algorithms. To the generated paths, the best one is selected as the contour completion result by comparing their figural goodness scores. Experimental results have shown that the scoring model of figural goodness works effectively for the contour completion problem.