Outline for lecture on shape
CSE/EE 576 May 3, 1995, SLT

1. Shape measures as global scalar features.
     convexity, roundness, aspect ratio, smoothness, 
     angularity, etc.

   Shape as description.
     resolution-independent descriptions of sets of points or
     of individual connected regions.

2. Region representation using Freeman codes and polygons

3. Scalar features.
    area, perimeter, moments
    Computing area from the image array (counting pixels).
      Easily done during bottom-up segmentation using a
      region adjacency graph.
    Computing area using boundary following (e.g., with
      the Freeman chain code.) keep adding or subtracting
      the y values reached along the boundary.  Add when
      moving right and subtract when moving left.
      Do nothing when moving up or down.
    Computing perimeter during segmentation: When merging
      two adjacent regions P = P1 + P2 - 2 P12.
      (Add the perimeters but subtract twice the length of
       the common boundary).
    Moments:
      The (p,q) th moment of a function g(x,y) is

                                p q
      m(p,q) = double integral x y g(x,y) dx dy

      If g(x,y) is the characteristic function of the region, then
      m(0,0) is the area of the region.
      The centroid is (m(1,0)/m(0,0), m(0,1)/m(0,0)).
      The set of all moments p,q = 0, 1, ...  form a complete
        description of g(x,y).

4. Polygonal approximation using Ramer's algorithm.