###### Abstract
\begin{table}
\begin{tabular}{c c} \hline
**Stage 1** & **Before Significant Functionalization of Rivers (<18 th-19 th century)** \\ \hline \multicolumn{2}{c}{Channel lengthening/shortening} \\ High-energy rivers (\(\omega\) \(>\) 30 W/m\({}^{2}\)) & ++ \\ Low-energy rivers (\(\omega\) \(<\) 30 W/m\({}^{2}\)) & - \\ \hline
**Stage 2** & **Before Embankment Removal Associated to River Restoration** \\ \hline \multicolumn{2}{c}{Channel lengthening/shortening} \\ High-energy rivers (\(\omega\) \(>\) 30 W/m\({}^{2}\)) & _Natural context (not constricted)_ & _Artificialized context (channelized)_ \\ High-energy rivers (\(\omega\) \(>\) 30 W/m\({}^{2}\)) & ++ & o \\ Low-energy rivers (\(\omega\) \(<\) 30 W/m\({}^{2}\)) & - & o \\ \hline
**Stage 3** & **After Embankment Removal Accompanying River Restoration** \\ \hline \multicolumn{2}{c}{Channel lengthening/shortening} \\ High-energy rivers (\(\omega\) \(>\) 30 W/m\({}^{2}\)) & _Natural context (not constricted)_ & _Artificialized context (channelized)_ \\ High-energy rivers (\(\omega\) \(>\) 30 W/m\({}^{2}\)) & ++ & _+/++_ \\ Low-energy rivers (\(\omega\) \(<\) 30 W/m\({}^{2}\)) & - & - \\ \hline \end{tabular}
\end{table} 
Table 1: Recent geomorphological change of rivers subdivided in three stages. (++) high; (+) moderate; (\(-\)) low; (o) zero. Figure 2: Some examples of modern braided-river metamorphoses, which have been expressed, after channelization works, by shortening (Stage 2A) or lengthening (Stage 2B) their watercourse. River-restoration works in Europe since the 2000s (WDF) lead to finding the initial conditions of braided rivers (Stage 3A) or to achieving an intermediate fluvial style (e.g., wandering pattern) between braided and single channel (Stage 3B). stream power [35; 36; 37]: (S1) rivers with sufficient energy (\(\omega>30\) W/m\({}^{2}\)) allow moderate (30 W/m\({}^{2}\)\(<\)\(\omega<\) 100 W/m\({}^{2}\)) or significant (\(\omega>\) 100 W/m\({}^{2}\)) geomorphological adjustments. (S2) rivers that have low energy (\(\omega<\) 30 W/m\({}^{2}\)) allow nothing (\(\omega<\) 10 W/m\({}^{2}\)) or not much (10 W/m\({}^{2}\)\(<\)\(\omega<\) 30 W/m\({}^{2}\)) in terms of geomorphological readjustments. We can cite in this regard the work of [28] on the Yerres River, a right-bank tributary of the Seine River upstream from Paris, which demonstrated during the 100-year R.I. flood (June 2016) that the river (\(\omega<\) 30 W/m\({}^{2}\)) experienced no longitudinal and lateral change, with barely a few minor traces of weak incision in the channel bottom. The correlation of these two situations (S1, S2) with the new context of (i) embankment removal of rivers and (ii) the monitoring of the geomorphological impact of rivers restoration leads to improving the mapping method of fluvial beds, the subject of this paper. The methods commonly used to analyze the temporal evolution of river channels from imagery, such as aerial photos and satellite images (2D variability), or even DTMs (e.g., BD Alti in France) and LIDAR surveys (3D variability), are based on transects (cross-sections) or channel-area calculation [38]. These cross-sections must meet two conditions: (i) they must always be perpendicular to the flow axis of the river; (ii) they must be equidistant,  
Figure 3: Mismatch of equidistant cross-sections. Diachronic monitoring of the watercourse development using cross-sections (A–G) surveyed perpendicular to the flow axis and equidistant and considering a river passing from meandering pattern (Stage 1) to straight pattern (Stage 2). The number of sections varies from one watercourse to another if the cross-section’s equidistance is respected. This method based on the comparison of equidistant cross-sections does not work as long as the channel varies in length over time. In any case, it is not possible to draw up cross-sections in the same place when the channel deforms laterally and longitudinally. and this equidistance must not be modified to be reproducible, i.e., the measurements from one image to another must always be made at the same place.