# RSB: Robust Successive Binarization for Change Detection in Bitemporal Hyperspectral Images
## 1 Introduction  
The task of change detection (CD) refers to those algorithms and methods that, given as input a collection of remotely sensed images, taken at different times of the same area, provide as output binary images where the white pixels denote the changed regions, while black pixels denote the unchanged parts; see [1] for a comprehensive survey. The CD task is especially useful in the Earth's surface observation programs, which aim at monitoring any relevant change in the environment due, for example, to natural disasters [2, 3], urban expansions, agricultural habits and so on; see [4] and references therein for a broad overview. Hyperspectral (HS) sensors remotely acquire data observations at high spectral and spatial resolution. In particular, every HS image can be thought of as a three-mode tensor, where, in the first and second mode, the spatial information is stored, while, in the third mode, the spectral information is registered at specific, predetermined wavelengths of the light. Hence, for every pixel, a hundred regularly spaced narrow bands are stored, allowing for a great abundance of information. For this reason, a common denominator of many CD methods is the use either of matrix or tensor factorizations [5, 6, 7, 8], or autoencoder architectures; see, e.g., [9, 10], which can provide a reasonable representation in suitable subspaces of reduced dimensions, allowing one to eliminate redundancies while keeping the relevant features. Another strong motivation for using matrix or tensor decompositions is to remove the noise affecting the original HSI or to restore the missing information; see, e.g., [11, 12, 13, 14] for recent advances regarding this topic. Taking care of the preprocessing phase has been proven to significantly improve the final CD results; see [15]. In this work, however, since most of the publicly available datasets for CD are already preprocessed, this step is not implemented. A second common component in many CD algorithms is the use of specific similarity or dissimilarity functions (sometimes called error functions) that, hence, produce several types of scenarios. Most algorithms do not provide an automatic selection of the best output, but all of the produced outputs are analyzed and the optimal results are selectedvia post-analysis, i.e., after the evaluation, the best binary change map is the one with the higher computed accuracy. On the one hand, in certain cases, very accurate results can be achieved with a specific configuration--see, e.g., [16]--but on the other hand, such approaches are still limited in real applications when the reference binary change map, i.e., the ground-truth image, is not available to provide a post-analysis evaluation. In this work, a new method is proposed that does not use any initial projection and that computes a suitable mean image given 6 types of error functions. This strategy is therefore _robust_ with respect to the chosen function and it is automatic, i.e., the best choice is not obtained via any post-analysis. After the similarity or dissimilarity phase, usually, a binarization technique is applied, either by using clustering [17; 18] or via automatic thresholding techniques [19; 20]. Here, a novel thresholding method is also proposed. In particular, three _binarization_ procedures are formulated and applied _successively_. In the first one, for every error function, a collection of 5 different binary images are produced and a suitable mean image is computed. Then, this mean image is again binarized by setting to 0 any pixel value below 1 and setting to 1 any pixel value originally greater than 1. Lastly, the newly produced mean images for every error function are summed together and binarized again according to a new threshold value. This type of successive binarization is compared against the most commonly adopted thresholding techniques.