18 sec, the defect is better defined with respect to the surroundings, and by t = 23 sec the
defect has risen substantially higher than the surroundings.
0.25-----
0.2 def > ATnorm(per avg) + 2_ -. -
0.15 -
0.1 ATnorm(per avg) 2
-0.05 -------------- ---
-0.05 -- I- -
-0.15
0 1 2 3 4 5 6 7 8
Square Root of Time (secl2)
Figure 6-61. Determining point at which defect is detected in ATdef plots
The second method that was investigated involves computing a two-dimensional
cross-correlation coefficient for each defect area at each time step. The two-dimensional
cross-correlation coefficient, R, is defined as follows (Matlab User's Guide 2002):
ZZ A(t) -mean(A(t))] [B -mean(B)]}
R(t) m n (6-11)
-0 [A(t) mean(A(t))]2 [Bm mean(B)]2
m n m n
R(t) = 2-D correlation coefficient at time = t
A(t) = mxn matrix of defect area pixels at time = t
B = mxn matrix of defect area pixels @ time = 60
R provides an indication of similarity between two matrices. The matrix B in
Equation 5-11 is populated with the pixel values of the rectangle defining the defect area
at t = 60 sec. This matrix represents the "best" image available for the defect of interest.
The two-dimensional correlation coefficient is computed at each time step by applying
Equation 5-11 to the matrix for the defect area at time t (A(t)) and B. The general