2.2.2. Change Detection

The second processing block is the change detection, where some of the features extracted from the Sentinel images are jointly analyzed using the Pruned Exact Linear Time (PELT) [43]. The method is a well-known changepoint detection method that provides an exact segmentation of the time series with a linear time complexity.

Given a time series *s* = (*<sup>s</sup>*1, ... , *sk*), the number *n* and time position *t*1:*n* = (*<sup>t</sup>*1, ... , *tn*) of the changepoints are obtained by solving the following penalized minimization problem:

$$Q\_n(s\_{1:k'} \, p) = \min\_{n, t\_{1:n}} \left\{ \sum\_{i=1}^{n+1} \left[ \mathcal{C} \left( s\_{(t\_{i-1}+1):t\_i} \right) \right] + p \right\} \tag{7}$$

where *C* is the segment-specific cost function

$$\mathcal{C}(s\_{a:b}) = \sum\_{i=a+1}^{b} \|s\_i - \overline{s}\_{a:b}\|\_2^2 \tag{8}$$

and *p* = *log*(*k*) a penalty term to control overfitting.

In a preliminary study that we carried out on 22 test sites [44], we showed that the combined use of the Sentinel-1 sigma0VH and Sentinel-2 NDVI returns more accurate change detection results than those of the single features. Figure 5 shows an example of the changepoints detected on an RDS where a building was demolished between summer 2017 and summer 2018, and some vegetation grew between summer 2018 and summer 2019. As can be seen, the combined use of Sentinel-1 and Sentinel-2 detection successfully returned the two dates. After the optimization phase of the change detection process, during which we performed several tests on an extended dataset using different combinations of features, the NDVI feature was replaced by NDWI2.

**Figure 5.** Changepoint analysis for the RDS "Service voirie d'Angleur" in Liège showing (**a**) Sentinel-1 image (left: July 2017; center: July 2018; right: July 2019); (**b**) Sentinel-2 images (left: July 2017; center: July 2018; right: July 2019); (**c**) orthophotos ground truth (left: summer 2017; center: summer 2018; right: summer 2019); (**d**) bi-dimensional time series sigma0VH (Sentinel-1); (**e**) bi-dimensional time series NDVI (Sentinel-2).

The overall process returns either a list of changepoints dates (one or multiple) or no changepoints. When one or multiple changepoints are detected, these become the input of the next block—the change classification. When no changepoints are detected, this information is reported directly in the final report, "Results per RDS".
