Learning OpenCV, 2nd Edition

the axes of the new basis can be ordered by their importance

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. These basis vectors will turn out to be the

eigenvectors of the covariance matrix for the distribution as a whole, and the corresponding eigenvalues

will tell us about the extent of the distribution in that dimension.

We are now in a position to explain why PCA is handled by one of these function objects. Given a

distribution once, the PCA object can compute and retain this new basis. The big advantage of the new

basis is that the basis vectors that correspond to the large eigenvalues carry most of the information about

the objects in the distribution. Thus, without losing much accuracy, we can throw away the less informative

dimensions. This dimension reduction is called a KLT Transform.

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Once you have loaded a sample

distribution and the principal components are computed, you might want to use that information to do

various things, such as applying the KLT transform to new vectors. By making the PCA functionality a

function object, it can “remember” what it needs to know about the distribution you gave it, and thereafter

use that information to provide the “service” of transforming new vectors on demand.

Figure 3-4. (a) Input data is characterized by a Gaussian approximation; (b) the data is projected into the

space implied by the eigenvectors ...