For example, as people get jobs their happiness is raised. A research may reach this conclusion after surveying people about their work status, and their happiness level. A relationship can be measured using correlation analysis. Now, the correlation analysis may show a significant association between these two variables. Yet, we cannot claim that because people have jobs, they are happy. Even though, it makes sense that when people have a job, their happiness increases. The causation conclusion would require much work to prove, yet correlation can be sufficient to confirm your point, which says there is association between having a job and one’s happiness.
Examining the denominator of ( 2 ),
the length of the feature vector can be precomputed
in approximately 3 N 2 operations
(small compared to the cost of the cross-correlation),
and in fact the feature can be pre-normalized to length one.
The problematic quantities are those in the expression
The image mean and local (RMS) energy must be computed at each u , v , . at ( M - N +1) 2 locations,
resulting in almost
3 N 2 ( M - N +1) 2 operations (counting add, subtract, multiply as one operation each).
This computation is more than is required for the direct computation of ( 3 )
and it may considerably outweight the computation indicated by ( 4 )
when the transform method is applicable.
A more efficient means of computing the image mean and energy under the feature is desired.
These quantities can be efficiently computed from tables
containing the integral (running sum)
of the image and image square over the search area, .,