Image Processing Reference
In-Depth Information
particular straight string of length n. It is most interesting to note that the
domain is in general a quadrilateral with vertices at LPT(PR), LPT(QR),
LPT(QS), and LPT(PS) where P,R and Q,S are the points in the primal
plane as discussed earlier. The domains for n = 3 and 4 are shown in Figs.
3.5(a) and 3.5(b).
FIGURE 3.5: (a) Domains of all DSLSs of length 3. (b) Domains of all
DSLSs of length 4.
3.2 Iterative Refinement: An Algebraic Characterization
In this section, we have considered that a CSLS l : y = mx + c,0 ≤ m <
1,0 ≤ c < 1 is digitized using OBQ from x = 0 to x = n to obtain a DSLS
D(l) = D. D(L) is mathematically defined as follows.
D = D(L) = {(i,y i )|i is an integer and y i = ⌊(mi + c)⌋,0 ≤i ≤ n}
In an alternative notation, we list (n + 1) y values in increasing values of
x from 0 to n, i.e., alternatively we represent D as {y i |0 ≤i ≤ n}.
3.2.1 Gradient and Intercept Estimation
The inequalities derived from the definition of the floor function and the
n + 1 equations y i = ⌊m o i + c o ⌋ for i = 0 to n obtained from D o can be used
to obtain an algorithm called I R that refines the upper and lower bounds of
m and c iteratively. We present the algorithm in the following theorem [38].
Search WWH ::




Custom Search