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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184 Digital Geometry in Image Processing
Let us define p, p
′
, q, q
′
such that a
l
= f
a
(x
p
′
, p
′
, b
u
), b
l
= f
b
(p, y
p
, a
u
),
b
u
= f
b
(q′, y
q′
+ 1, a
l
), and a
u
= f
a
(x
q
+ 1, q, b
l
).
Corollary 5.5. D(f
lu
) or D(f
ul
) differs from D
o
only at point(s) like (q
′
, y
q
′
+
1) or (x
q
+ 1, q), which define b
u
and a
u
.
From the above corollary, we can say that f
lu
or f
ul
are ver y close approx-
imations of the original curve re presented by the function f. If we assume one
more property about the curve, then we can prove
(i) that the Domain of D
o
in the a − b plane is contained in the recta ngle
R
ul
whose diagonally opposite vertices are (a
l
, b
u
) and (a
u
, b
l
); and
(ii) that R
ul
is the smallest ...
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