Change Detection in Spatial Data and Multivariate Statistics

Allan Aasbjerg Nielsen

Technical University of Denmark

Informatics and Mathematical Modelling

http://www.imm.dtu.dk/~aa

Abstract

Change detection is an important subject in many computer vision and remote sensing applications based on temporally dynamical data. Computer vision examples include industrial inspection and process control. Remote sensing application areas include for example agriculture, forestry, oceanography and environmental monitoring.

Simple change detection methods are often inadequate since they are typically sensitive to differences in calibration such as offset and gain in the measuring device used to record the data. Also, simple change detection methods applied to spatial data are typically non-spatial. This indicates a need for methods based on multivariate and spatial statistics.

Change detection methods typically include (in this notation X is a column vector of p variables recorded at each observation or pixel at one point in time, and Y is the same vector at the same geographical location at another point in time; a and b are column vectors of coefficients for calculating the linear combinations involved)

• Use of ad hoc transformations such as the normalized difference vegetation index (NDVI).

• Principal component analysis (PCA) on concatenated data: maximize the variance Var{a^T[X^T Y^T]^T}.

• Simple differencing: calculate X – Y.

• PCA on simple differences: maximize the variance Var{a^T(X – Y)}.

• Canonical correlation analysis (CCA) based multivariate alteration detection (MAD): maximize the variance Var{a^TX – b^TY}. CCA maximizes linear combinations a^TX of X and b^TY of Y, Corr{a^TX, b^TY}.

• MAF post-processing of MAD variables: maximize the correlation between a linear combination a^TX of X (after MAD transformation) and the same linear combination of the same data spatially shifted, Corr{a^TX(r), a^TX(r+D)}.

PCA, CCA, MAD and MAF transformations can all be found by eigenvalue decomposition. As opposed to simple differencing and derivatives thereof, MAD and MAF/MAD variables are invariant to linear and affine transformations, which means that they are insensitive to for example differences in offset and gain in a measuring device at the two points in time. MAF post-processing introduces a desired spatial element. Simultaneous inspection of spatial patterns and correlations with the original variables facilitates interpretation of MAD and MAF/MAD variables.