Variations in the projection of objects on a 2D image, e.g., due to
occlusions and articulations, lead to edge maps which are noisy, contain
gaps and spurious elements, and are deformed versions of the object
boundaries. The use of edge salience to embed the regularity of contour
continuity is typically faced with two drawbacks. First, salience measures take
advantage of boundary continuity, but not of shape continuity, which
includes continuity of the interior. Second, while each edge element can
only belong to one object boundary, in the computation of salience measures, it
often freely contributes to the salience of edges in competing grouping hypotheses. We identify
both drawbacks with the lack of an explicit intermediate representation
between the edge map and grouped object boundaries.
We propose that (i) a symmetry map can fully represent the initial edge map so
that both boundary and regional continuities can be represented via
skeletal continuity; (ii) a re-organization of the edge map in the form of
completing gaps, discarding spurious elements, smoothing and partitioning a
contour (grouped set of edge elements) can be represented by
transformations on the symmetry map; (iii) the optimal grouping corresponds
to the least action path consisting of a sequence of symmetry
transforms. The focus of this paper is to define transformations on
the symmetry map and illustrate results for it. Specifically, we illustrate how a set
of grouped edge elements can be smoothed and partitioned by iteratively
applying these symmetry transforms. Results show smoothing without removing
the corners, which are significant, e.g. for the identification of parts.

    Boundary Smoothing:
          Example1:
                1. Movie (150K)
         Example2:
               1. Movie (320K)

    Edge Grouping:
           Example:
               1.Movie (45K)
 
    Removal of Edge Elements:
           Example:
                1. Movie (29K)

    Occlusion Transform:
            Example:
                1.Movie (19K)

    Part Transform:
           Example:
               1. Movie (13K)

By Huseyin Tek and Benjamin B. Kimia