###### Abstract
In this paper, we focused on one type of river restoration, which concerns actions that can help to give more lateral space to rivers (Figure 2) by removing longitudinal structures (gabions, walls, dikes, embankments or other riverbank protections) along the channels (for an exhaustive and complete review on river restoration, see [29, 30, 31]). Allowing rivers to obtain more lateral migration capacity amounts to working on the 'river space of good functioning' [32], i.e., the space that the river needs to regulate erosion processes at the watershed scale as well as low-waters and floods thanks to the reactivation of the margins of the active channel. Most of the time, river channelization has resulted in the simplification and shortening of streams, reduction of channel sinuosity and increase in the hydraulic slope and bed shear stress. This was the case for the braided rivers, which were channelized (Figure 2, Stage 2A). Sometimes, the channel pattern of the rivers has been modified from braided to meandering channel (Figure 2, Stage 2B), which has led to lengthening the watercourse and reducing the energy slope and specific stream power. From this operating model, we can distinguish three stages in the recent history of rivers (Table 1):  
* Stage 1: before significant functionalization of rivers. This stage can be assimilated to the free-flowing state of rivers (generally, before the eighteenth-nineteenth century, but sometimes before the Modern Times or Middle Ages). Lengthening or shortening of active channels by variations of fluvial style due to allocyclic and/or autocyclic processes is (i) common in high-energy rivers, (ii) much less in low-energy rivers. * Stage 2: before embankment removal associated with river restoration. (i) In the natural context (not constricted), high-energy rivers show a good ability to lengthen/shorten their multiple or single channels. In low-energy rivers, channel lengthening/shortening is possible but limited. (ii) In the artificialized context (channelized), no significant channel lengthening/shortening is possible either in high-energy rivers or in low-energy rivers. * Stage 3 (since 2000 with the emergence of environmental policies such as WFD in Europe that encourages restoration works [27, 33, 34]: current embankment removal accompanying river restoration. (i) In a natural context (not constricted), high-energy rivers are able to lengthen/shorten their multiple or single channels. Low-energy rivers can also be characterized by small channel lengthening/shortening when this occurs. (ii) In an artificialized context (channelized), high-energy rivers are exposed to a possible lengthening/shortening of their multiple or single channels. Low-energy rivers encounter high difficulty in lengthening/shortening their channel, and morphological adjustments are only locally visible. This evolution, which tends towards a possible increase in the rate of lengthening/shortening of rivers in Stage 3, raises questions about how to take into account the longitudinal deformation of the multiple and single channels in the high-frequency monitoring of river beds from imagery. Surprisingly, the critical analysis of the literature concludes that the problem of longitudinal deformation of river beds (Figure 3) has not been taken into account in the story that is told from diachronic image processing. In addition, if current trend is towards embankment removal, rivers are confronted with two situations (S), depending on their degree of energy expressed as \(\omega\) = specific