Learning OpenCV, 2nd Edition

is convenient to talk about the covariance matrix , whose components include all of the covariances

between the variables as well as the variances of the variables individually. As can be seen from the

formula above, the covariance matrix is symmetric, i.e.,

.

In a much earlier chapter, we encountered a function which could be used when dealing with individual

vectors of data (as opposed to whole arrays of individual vectors). That function was

cv::calcCovarMatrix(), which will allow us to provide

N

vectors of dimension

d

and it will spit out

the

d

-by-

d

covariance matrix. Our problem now, however, is that we would like to compute such a matrix

for every point in an array (or at least, in the case of a 3-dimensional RGB image, we would like to

compute the 6 unique entries in that matrix).

In practice, the best way to do this is simply to compute the variances using the code we already developed,

and to compute the three new objects (the off-diagonal elements of

) separately. Looking at the

formula for the covariance, we see that cv::accumulateSquare() will not quite work here, as we

need to accumulate the

terms (i.e., the product of two different channel values from a particular

pixel in each image).

The function which does this for us in OpenCV is cv::accumulateProduct().

void accumulateProduct(

cv::InputArray src1, // Input, 1 or 3 channels, U8 or F32

cv::InputArray src2,