## Materials and Methods
### Module Description
#### 2.3.4 Image Co-Registration  
Although orthorectification compensates for geometric distortions due to relief and imaging geometry, if done without GCPs, as described above, the process provides an absolute accuracy that may not suffice for certain applications. Mapping crops in smallholder fields with VHSR images is such an application, as the risk of spatial misalignment between images is high. Significant accuracy of georeferencing can be achieved by bias correction of the RPC parameters prior to orthorectification to eliminate systematic effects [38]. However, this requires the selection of GCPs per image, which is unsuitable for automated applications. Several image matching algorithms have been established to automatically detect candidate GCP points, used mainly in pattern recognition, such as in the Scale-Invariant Feature Transform (SIFT) algorithm introduced in [39; 40] and the Speeded Up Robust Features (SURF) of [41].  
An application of these methods to VHSR images provided shifts greater than the pixel size of the image and were disregarded. Instead, an algorithm that implements feature extraction with  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistical Attribute** & **Image Provider** & **Orthorectified** & **Co-Registered** \\ \hline \(\text{Mean}_{\text{X}}\) of absolute residual values (m) & 5.288 & 11.375 & 1.319 \\ Standard deviation\({}_{\text{X}}\) of absolute residual values (m) & 4.026 & 1.888 & 0.82 \\ Meany of absolute residual values (m) & 1.875 & 1.511 & 0.324 \\ Standard deviation of absolute residual values (m) & 0.205 & 0.169 & 0.162 \\ \(\text{Min}  
automatic scale detection [42] based on the identification of objects was developed in-house. The overall idea is based on GCP extraction from an image time series, which is a well-known problem due to the temporal variability of the position of the candidate objects [43]. Roads (excluding bridges and elevated roads) may provide reliable GCPs, and these have been used as GCPs in several studies [12; 44]. However, low-income countries typically feature a sparse paved road network, and concrete roads are regularly absent from the image scene. In our approach, tree crowns are characterized by a bell-shaped intensity surface [45] and corrected for parallax. Their centroids are extracted as tie points, and the strongest candidates are used as GCPs. For every study area, one image is declared as the master image on the basis of the longest visible shadow of the trees, as calculated from the positions of the sun and the satellite from the image metadata [46].  
The level of georeferencing accuracy does not only associate with the image's spatial resolution but also with the intended application. Generally, however, a high accuracy is important in the analysis of large data volumes because of easier integration with Geographical Information System applications and post-processing [29]. In their algorithmic development of the automated extraction of GCPs from the road network [12], the authors report a higher accuracy of coregistration of RapidEye images in comparison to DG images. They attribute this to the improvements of their initial algorithm for RapidEye, which extracts the road centerline from an image with a pixel resolution of one to three pixels of the width of the road. As the spatial resolution increases, the number of pixels required to cover the road width also increases, and, therefore, the centerline is no longer pronounced; instead finer road features become discernible. This methodology suggests that GCPs derived from the road network are dependent on the correspondence of the spatial resolution of the road width and the pixel resolution. In our approach, however, the higher the spatial resolution, the higher the accuracy.