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Davies: Computer Vision, 5th edition: Solutions to selected problems 16
(b) Shrinking once will eliminate the short spurs, but then expanding once will be
necessary to try to restore the remaining parts of objects to their former sizes and shapes.
(c) The (r, ) graph method for describing shapes is bookwork (see the main text in
Chapter 9): a circle is represented by a constant line at r = a. A 3-element 1-D median
filter will eliminate single element notches in the (r, ) graph. A 5-element 1-D median
9.4
(a) The (r, ) graph is a polar plot of the object boundary relative to the centroid. It
converts a complex 2-D problem to a simpler 1-D problem. However, any occlusion
(b) The simple algorithm for approximating a convex hull is:
This algorithm produces a crude octagonal approximation. If it is desired to produce a
smooth analogue approximation, why not try using the (r, ) representation. However, the
mismatch produced by a straight line becoming a sec curve prevents this from being
Davies: Computer Vision, 5th edition: Solutions to selected problems 17
9.5
A one-pixel rotation of the square, i.e., an angle of arctan(1/20), gives a sudden increase
– 1), when the actual increase in boundary length
should be 4/20 = 1/5. Thus there is gross distortion in the measurement, and this also
