IR-MAD Iteratively Re-weighted Multivariate Alteration Detection

Transcription

1 IR-MAD Iteratively Re-weighted Multivariate Alteration Detection Nielsen, A. A., Conradsen, K., & Simpson, J. J. (1998). Multivariate Alteration Detection (MAD) and MAF Postprocessing in Multispectral, Bitemporal Image Data: New Approaches to Change Detection Studies. Remote Sensing of Environment, 64(1), Canty, M. J., Nielsen, A. A., & Schmidt, M. (2004). Automatic radiometric normalization of multitemporal satellite imagery. Remote Sensing of Environment, 91(3 4), Nielsen, A. A. (2007). The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data. IEEE Transactions on Image Processing, 16(2),

2 IR-MAD Iteratively Re-weighted Multivariate Alteration Detection Canty, M. J., & Nielsen, A. A. (2008). Automatic radiometric normalization of multitemporal satellite imagery with the iteratively re-weighted MAD transformation. Remote Sensing of Environment, 112(3), Effective at identifying areas of no-change, even when the fraction of invariant pixels is relatively small. Effective at identifying areas of significant change (radiometrically) No requirement for atmospheric correction (normalization) Code freely available Canty, M. J., & Nielsen, A. A. (2012). Linear and kernel methods for multivariate change detection. Computers & Geosciences, 38(1),

3 Two N-band multispectral images of the same scene acquired at different times. Ground reflectance changes have occurred at some locations, but not everywhere. Represent observations in the first N-band image by a random vector, FF = FF 1...., FF NN and create a scalar image, characterized by the random variable: UU = aa FF Then do the same for the second image: G= GG 1...., GG NN VV = bb GG Now consider the scalar difference image: UU VV This combines all of the change information into one image. Need for a and b to be specified in a suitable way. Nielsen et al. (1998) suggested Canonical Correlation Analysis (CCA)

4 Image 1: FF = FF 1...., FF NN linear combination: UU = aa FF Image 2: G= GG 1...., GG NN linear combination: VV = bb GG This leads to the coupled eigenvalue problem: Where ffgg gggg 11 gggg aa = ρρ 22 aa ggff ffff 11 bb = ρρ 22 bb ffff ffff gggg ΣΣ ffff and ΣΣ gggg are the covariance matrices of the two images ΣΣ ffff = ΣΣ gggg is the inter-image covariance matrix ρρ = vector of canonical correlations where ρρ ii = cccccccc UU ii, VV ii, are the square roots of the eigenvalues of the coupled eigenvalue problem. (1) The CVs are ordered by similarity (correlation).

5 Image 1: FF = FF 1...., FF NN linear combination: UU = aa FF Image 2: G= GG 1...., GG NN linear combination: VV = bb GG Solution of the coupled eigenvalue problems (Eq. 1) generates new multispectral images: UU = UU 1,, UU NN and VV = VV 1,, VV NN, the components of which are called the canonical variates (CVs), and are ordered by similarity (correlation). The canonical correlations ρρ ii = cccccccc UU ii, VV ii, i=1,, N, are the square roots of the eigenvalues of the coupled eigenvalue problem and the coefficients aa ii and bb ii, i=1,, N, are the eigenvectors which determine U and V from F and G. The pair UU 1, VV 1 is maximally correlated. The pair UU 2, VV 2 is maximally correlated subject to being orthogonal to (and uncorrelated with) both UU 1 and VV 1

6 The pair UU 11, VV 11 is maximally correlated. The pair UU 2, VV 2 is maximally correlated subject to being orthogonal to (and uncorrelated with) both UU 1 and VV 1 The MAD variates are generated as a sequence of transformed difference images: MM ii = UU NN ii+1 VV NN ii+1, i = 1,, N and have statistical properties which make them very useful for visualizing and analyzing change information. They : 1. are uncorrelated: cccccc MM ii, MM jj = 0 for i jj 2. have successively decreasing variances: vvvvvv MM ii = σσ 2 MMii = 2 1 ρρ NN ii+1 3. are ideally normally distributed (central limit theorem) 4. are invariant under affine transformation (Canty et al., 2004)

7 MAD variates: MM ii = UU NN ii+1 VV NN ii+1, i = 1,, N The first MAD variate: MM 1 = UU NN VV NN has the greatest variance and, ideally, describes the maximum change information. The second MAD variate: MM 2 = UU NN 1 VV NN 1 Has maximum variance subject to the condition that it is statistically uncorrelated with MM 1 The χχ 2 image represents the probability of change for each pixel. Each observation is weighted by a no-change probability given by Pr nnnnnnnnnnnnnnn = 1 PP χχ 2 ;pp zz. Pr (no change) is the probability that a sample z drawn from the chi-square distribution could be that large or larger. A small z implies a large probability of no change.

8 In the presence of genuine change, it should be possible to improve the sensitivity of the MAD transformation by placing emphasis on establishing an increasingly better background of no change against which to detect change. This can be done using an iteration scheme in which observations are weighted by the probability of no change, as determined by the preceding iteration, when estimating the sample means and covariance matrices which determine via CCA the MAD variates for the next iteration Iteration: After one transformation, the first principal axis only corresponds approximately to the (highly correlated) no-change pixels, since it is determined by both no-change and change observations. Weighting the observations inversely to their distance from the first principal axis and repeating the transformation improves the position of the principal axes relative to the no-change pixels and, correspondingly, enhances the change signal.

9 July 30, 2001 May 22, 2005 ASTER images near Esfahan, Iran

10 Mar 11, 2002 Apr 9, 2001 May 22, 2005 July 30, 2001 Sep 11, 2005 ASTER images near Esfahan, Iran

11 Mar 11, 2002 Apr 9, 2001 May 22, 2005 July 30, 2001 Sep 11, 2005 ASTER images near Esfahan, Iran

12 June 26, 2001 August 29, 2001 Landsat ETM+ images over Jülich, Germany

13 RGB color composite of MAD variates 4 (blue), 5 (green) and 6 (red) applied to the June 26, 2001 and August Jülich, Germany images Landsat ETM+ images over Jülich, Germany