Image Processing Reference
In-Depth Information
11. Compute the approximate vertices of the disk of radius 20 centered at
the point (−30,40) with the distance function {1,1,2} in 2-D integral
coordinate space. Find the maximum possible deviation of these coor-
dinate points from their true positions. Compute its area and perimeter
errors in percentage with respect to the Euclidean disk of the same ra-
dius.
12. Compute the volume of a digital sphere of radius 10 in the metric space
of the weighted distance function, where weights are given by {1,
2
,
3
}.
Show that the distance is the same as the 26-neighbor distance function
in 3-D.
13. Represent an m-neighbor distance in n-D as a weighted t-cost distance
function and compute the vertices of its hypersphere of radius r using
the Theorem 2.30.
14. Prove that the hypersphere of the inverse square root weighted t-cost
distance function encloses a Euclidean hypersphere of the same dimen-
sion and radius.
15. ∀n,n≥ 1, 1 ≤p < q ≤ n, and the following holds [69]: ∀(u) ∈ Σ
n
,
d
q
(u) ≤d
p
(u) ≤⌈q/p⌉d
q
(u).
16. Prove the following bounds for m-Neighbor distances in 3-D [68]:
d
1
(x) ≥ E
3
(x)
d
2
(x) > E
3
(x), iff x =
(±1, ±1, ±1)
= E
3
(x), iff x ∈
{(±k,0, 0), (0, ±k,0), (0, 0, ±k),
(±2, ±2, ±1),(±2, ±1, ±2), (±1, ±2, ±2)},k ≥ 0
< E
3
(x),
Otherwise
d
3
(x)
≤
E
3
(x)
