. Which point-to-point distance metric produces diamond-shaped equal-distance contours?
Manhattan distance (|dx| + |dy|) forms diamonds; chessboard forms squares; Euclidean forms circles.
. Why does the plain Freeman chain-code estimate L = N_e + sqrt(2)*N_o systematically overestimate a smooth curve's true length?
A digitized circle's boundary alternates through many short zig-zag steps, which sum to more length than the smooth true arc.
. What is the key computational advantage of the chamfer distance transform over an exact Euclidean distance transform?
The chamfer transform propagates local distances in two raster-scan passes, a fast approximation to the more expensive exact Euclidean distance transform.
. What does the chessboard distance D8 correspond to physically?
D8 = max(|dx|, |dy|) is the shortest path length when diagonal (8-connected) moves are allowed, like a chess king.