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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Modeling of a Voxelated Surface 245
Algorithm 16: Algo rithm DCS.
Algorithm DCS (int r)
1. int i ← 0, j ← r, s ← 0, w ← r − 1
2. int l ← 2w
3. while (j > i) do
4. include
8 sym points (i, j)
5. s ← s + i
6. i ← i + 1
7. s ← s + i while (s 6 w)
8. w ← w + l
9. l ← l − 2
10. j ← j − 1
Lemma 7.4. The number of perfect squares in a closed interval [v, w] is at
most one more than the number of perfect squares in the preceding closed
interval [u, v − 1] of equal length, where the intervals are taken from the non-
negative integer axis.
Now, from Lemma 7.3 it is obvious that the length of the interval contain-
ing the squares of abscissae (of grid points of C
Z
1
(o, ...
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