Probabilistic approximation to change and no change in multispectral remote sensing

Change assessment is a central and active area of inquiry in remote sensing. Broadly adopted probabilistic methods discriminate between change and no change based on image differencing, normalization and aggregation into a single band metric that is assumed to follow a Chi-square distribution. The adoption of the Chi-square distribution requires the application of band transformation to original data that is computer expensive and that operates under an untested assumption of multivariate distribution of pixel values in input bands. Despite the wide adoption of the Chi-square distribution, its appropriateness for discriminating between change and no change remains an open question. Here, we test the performance of the Chi-square distribution for change assessment compared to the use of the more-generic Gamma distribution. For this purpose, we implement an algorithm that iteratively removes observations labelled as change according to a pre-defined probabilistic distribution and a probability change threshold. We implement the algorithm in three study areas in tropical and subtropical regions representing contrasting ecological conditions and land cover types and changes. We also test whether input multispectral data meets the assumption of multivariate normality required for band transformation and for the use of the Chi-square distribution. We found that the Gamma distribution applied to untransformed data consistently performs more robustly to discriminate between change and no change compared to the application of band transformation and subsequent use of the Chi-square distribution. We also found that, in none of the evaluated cases, input multispectral data meet the assumption of multivariate normality required for band transformation. Our results suggest that assumptions about multivariate normality can affect the robustness of probabilistic change assessment in multispectral remote sensing. We encourage the remote sensing community to adopt the Gamma distribution applied to untransformed data as a probabilistic approach to differentiate between change and no change.