### Multivariate Alteration Detection (MAD) and MAF Post-Processing in Multispectral, Bi-temporal Image Data: New Approaches to Change Detection Studies

### ¹Department of Mathematical Modelling, Technical University of Denmark,

²Digital Image Analysis Laboratory, Scripps Institution of Oceanography

Accurate and quantitative change detection in a temporal sequence
of satellite scenes is an important requirement for many
climate and global change studies.
This paper introduces the
Multivariate Alteration Detection (MAD) transformation
and describes the Minimum/Maximum Autocorrelation Factor (MAF)
transformation,
and it combines these two
multivariate statistical transformations to
quantitatively and accurately detect changes in sequences of
satellite data.
As opposed to
the popular Principal Component (PC) transformation
both the MAD and the MAF transformations are invariant to affine transformations
which means that they are both insensitive to for instance
1) changes in offset and gain in a measuring device such as an imaging
spectrometer, and 2) simple multiplicative atmospheric corrections.
Both Landsat Multispectral Scanner System (MSS)
data and Advanced Very High Resolution Radiometer (AVHRR) data,
together with the above cited analysis methods, are used to
quantify case studies of urbanization and
ENSO-related (El Niño-Southern Oscillation) alteration of ocean thermal
structure.
Change is also computed by applying
the PC transformation to simple difference images.
These latter analyses are compared with those derived using the MAF/MAD
analyses.
Results show that the combination of MAF/MAD analysis
is superior to the PC analysis for accurate detection of
patterns of spatial change in multivariate satellite scenes.
Moreover, the MAF/MAD analysis is less effected by noise in the
data than is the PC analysis and the MAF/MAD analysis also is
more effective than PC analysis for the detection of outliers in
data.
MAF/MAD analysis, coupled with simple spectral
differencing of properly intercalibrated images, is an effective
combination to 1) compute accurate rates of change, and 2)
place these rates in a statistically meaningful spatial context
(i.e., a natural image context).
This combination can be achieved
by assigning significance to the simple differenced values only
in regions where the cross-correlation between the simple
differences and the MAF/MADs is high.