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.