*2.3. Accuracy Assessment*

The accuracy assessment investigates multiple aspects of our workflow, each requiring a different analysis:

CNN Architecture: This analysis aims to optimize the CNN architecture by considering loss and accuracy for training and validation data per epoch. The curves for training loss and validation loss, as well as for training accuracy and validation accuracy, are expected to converge with incremental epochs. Loss is the summation of errors made for each example in training, and should be minimized. We use cross-entropy loss that increases as the predicted probability (*y*ˆ*i*) diverges from the actual label (*yi*):

$$cross-entropy\ loss = -(y\_i \log(\mathfrak{H}\_i) + (1 - y\_i)\log(1 - \mathfrak{H}\_i))\tag{2}$$

All predictions < 0.5 are considered as 'not boundary', those ≥ 0.5 as 'boundary'. This results in a confusion matrix showing the number of tiles being False Positive (FP), True Positive (TP), False Negative (FN) and True Negative (TN). From this matrix, the accuracy is derived as the sum of correctly classified tiles divided by all tiles:

$$accuracy\,\,[0;1] = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{FP} + \text{FN} + \text{TN}} \tag{3}$$

RF vs. CNN Classification: This analysis compares the boundary likelihood obtained through RF and CNN to the percentage to which an MCG line overlaps with the cadastral reference. Both are buffered with a radius of 0.4 m. The area of their overlap in relation to the entire MCG buffer area represents the percentage of overlap:

$$\text{overlap}\,\,[0;1] \,\,=\frac{\text{area}\_{\text{MCG}-\text{buffer}} \cap \,\,\text{area}\_{\text{cadastral}-\text{buffer}}}{\text{area}\_{\text{MCG}-\text{buffer}}}\tag{4}$$

We investigate whether lines that should get a boundary likelihood > 0, i.e., those that fall within the cadastral reference buffer, are assigned a boundary likelihood > 0:

$$\text{recall} \,\, [0; 1] = \frac{\text{TP}}{\text{TP} + \text{FN}} \tag{5}$$

Then, we check whether the assigned boundary likelihood is valid, i.e., whether it is equal to the line's overlap with the cadastral reference buffer. This is indicated by the precision that captures the ratio of lines having a boundary likelihood that aligns with overlap to the sum of lines having a correct or too positive boundary likelihood:

$$precision\ \left[0;1\right] = \frac{\text{TP}}{\text{TP} + \text{FP}} \tag{6}$$

Since the boundary likelihood captures the probability of a line being a 'boundary' line, a high boundary likelihood should go along with a high overlap between the MCG and cadastral reference buffer:

$$\text{overlap}\begin{bmatrix} 0;1\end{bmatrix} \\ \text{boundary likeilhod } \begin{bmatrix} 0;1\end{bmatrix} \tag{7}$$

Both values are not expected to be identical, which can be influenced by altering the buffer size. Our focus is on comparing RF to CNN, and secondarily on the boundary likelihood itself. Results are considered only in areas for testing in which we have cadastral reference data (Figure 2).

Manual vs. Automated Delineation: This analysis compares the time and number of clicks required to delineate visible boundaries, once manually, and once with the automated approach. Manual delineation refers to delineating parcels based on the ortho-image without further guidance. Automated delineation refers to our approach, including RF or CNN classification depending on which approach shows superior results in this study. All delineations should fall within the cadastral reference buffer of the 0.4 m radius. The buffer size represents the local accepted accuracy for cadastral delineation and falls within the 2.4 m proposed for rural areas by the International Association of Assessing Officers (IAAO) [33].

The comparison is conducted for a rural area in Ethiopia and two peri-urban areas in Rwanda and Kenya (Figure 2). No urban area is selected, as indirect surveying relies on the existence of visible boundaries, which are rare in densely populated areas. Furthermore, indirect surveying in urban areas saves less logistics for field surveys, due to smaller parcel sizes. Only parcels for which all boundaries are visible, and thus detectable from the ortho-image, are kept for this analysis. Since no digital up-to-date cadastral reference exists for our areas in Kenya and Rwanda, cadastral reference data are created based on local knowledge in alignment with visible boundaries.
