April 2016
Intermediate to advanced
318 pages
9h 47m
English
book
Digital Geometry in Image Processing
by Jayanta Mukhopadhyay, Partha Pratim Das, Samiran Chattopadhyay, Partha Bhowmick, Biswa Nath Chatterji
Content preview from Digital Geometry in Image Processing
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52 Digital Geometry in Image Processing
Theorem 2.11. d
Knight
is a metric over Z
2
.
Theorem 2.12. ∀u, v ∈ Z
2
, d
Knight
(u, v) is the length of a shortest Knight’s
path from u to v as defined by N(Knight).
Proof. Adopt Algorithm 2 for N (Knight) and proceed as in d
n
m
.
The Knight’s move is non-proximal and somewhat atypical in digital geom-
etry. Yet, it has been extended in [72] as a Super-Knight’ s Distance with a
class of neighborhood sets N(Super −Knight) = {(±p, ±q), (±p, ±q)} where
p, q ∈ P and p ≥ q ≥ 1. d
Super−Knight
is a metric under ce rtain conditions
(see Ex ercise 3) on N(Super − Knight) [72].
2.4 Path-Dependent Neighborhoods and Distances
In the ...
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