Change detection, in the Remote Sensing discipline, is the analytical process that aims to detect changes -- over time and space -- of the land cover or/and land use.
PCA as a change detection technique
Among the most common and successful change detection practices, is the application of Principal Components Analysis (PCA) on bi- or multi-temporal multi-dimensional data (Lu et al., 2003).
What is PCA?
Principal Components Analysis (PCA) is a multi-dimensional linear transformation algorithm. It reconstructs a multivariate data set in a way that the first variables, called principal components (PCs), contain most of the original data variance. Thus, PCA provides the potential to describe or represent reliably a multi-dimensional data set by using fewer dimensions than the ones that compose the initial data set (Jolliffe, 2002).
How does it work?
PCA redirects the highest variances of the original data set, which mainly resemble unchanged landscape characteristics, in the first components. It is the user's responsibility to then extract changes by means of advanced digital image processing operations, i.e. image (segmentation and) classification.
PCA-based change detection using (G)FOSS
PCA is implemented in GRASS-GIS (i.pca module), R (princomp() and prcomp() functions), OrfeoToolbox, SAGA-GIS and probably more (Free &) Open Source Applications.
An example in-depth work, from which most of the above text has been extracted, demonstrates how to map burned areas -- which is essentially a change detection analysis -- based on PCA and GFOSS. Please, refer to this work for an extensive list of references upon the subject.
On the use of GRASS-GIS and R to perform PCA, there is a dedicated GRASS-wiki page titled Principal Components Analysis.
Jolliffe, I. T. (2002). Principal Component Analysis. Springer, 2nd edition. 28 illustrations.
Lu, D., Mausel, P., Brondizio, E., and Moran, E. (2003). Change detection techniques. International Journal of Remote Sensing, 25(12):2365.