*2.1. Image Data*

An aerial image of 0.25 m Ground Sample Distance (GSD) of a rural scene in Ethiopia is used (Figure 2a,b). The local agricultural practice consists mostly of smallholder farming. The image was captured during the dry season around March. The crops within our study area consist mostly of millet, corn, and a local grain called teff. Since the crops are in the beginning of an agricultural cycle, they do not cover the visible cover parcel boundaries. The cadastral reference data cover 33 km2 containing 9,454 plots with a median size of 2500 m2. The cadastral reference data is derived through on-screen manual delineation from the aerial image. In case of uncertainty or invisible boundaries, the boundary is captured together with land owners in the field using high-resolution total stations. For a later assessment, in which we compare our approach to on-screen manual delineation, additional Unmanned Aerial Vehicle (UAV) data from Kenya and Rwanda is used (Figure 2c,d). The UAV data in Rwanda have a GSD of 0.02 m, and were captured with a rotary-wing Inspire 2 (SZ DJI Technology Co., Ltd., Shenzhen, Guangdong, People's Republic of China). The UAV data in Kenya have a GSD of 0.06 and were captured with a fixed-wing DT18 (Delair-Tech, Delair, Toulouse, France).

**Figure 2.** (**a**) Aerial image of 0.25 m Ground Sample Distance (GSD) for a rural scene in Ethiopia, divided into areas for training and testing our approach before comparing results to (**b**) the cadastral reference. Unmanned Aerial Vehicle (UAV) images for peri-urban scenes in (**c**) Rwanda (0.02 m GSD), and (**d**) Kenya (0.06 m GSD) to compare automated to manual delineation.

#### *2.2. Boundary Mapping Approach*

The boundary mapping approach refers to the one we previously described [22]. In the following, modifications and the data-dependent implementation of the three workflow steps are described. The source code is publically available [23].

Image segmentation is based on Multiresolution Combinatorial Grouping (MCG) [24], which delivers closed contours, capturing the outlines of visible objects. To run the original MCG implementation, the Ethiopian aerial image is tiled to 20 tiles of 8000 × 8000 pixels. The parameter k regulating over- and under-segmentation is set to produce over-segmentation (k = 0.1). This setting creates outlines around the majority of visible objects. Tests with parameters (k = 0.3 and k = 0.5) resulting in less over-segmentation show that visible object outlines are partly missed, while irrelevant lines around small objects are still produced. To reduce the number of irrelevant lines produced through over-segmentation, the lines are simplified through filtering (Figure 3): Lines around areas smaller than 30 m<sup>2</sup> are merged to the neighboring segments, which reduces the line count by 80% to 600,000 lines.

**Figure 3.** Multiresolution Combinatorial Grouping (MCG) image segmentation lines around visible objects (**a**) before and (**b**) after simplification reducing the line count by 80%.

According to our visual inspections, this post-processing removes artefacts in the segmentation results and keeps outlines of large objects being more relevant for cadastral mapping. For the high-resolution data from Rwanda and Kenya, we proceed similarly by tiling the data and setting k = 0.4 and k = 0.3, respectively.

Boundary classification is applied to the post-processed 600,000 MCG lines. We investigate two machine learning approaches to derive the boundary likelihood per MCG line: Random Forest (RF) and Convolutional Neural Networks (CNN). Both require the labeling of training data as 'boundary' and 'not boundary'. The training data for RF consist of lines, that for CNN of image tiles. For both approaches, the cadastral reference is buffered by a radius of 0.4 m. This size accounts for inaccuracies in the cadastral reference and the ortho-image, enlarges the number of 'boundary' samples, and is identical to the one applied to derive hand-crafted RF features. For both approaches, the ratio between training and testing data is set to 50%. The number of 'boundary' and 'not boundary' training samples is balanced to 1:1 by randomly under-sampling 'not boundary' tiles (Table 1). The areas for training and testing are randomly selected and large to minimize the number of lines at the borders of each area that are clipped and of limited use for further analysis (Figure 2). The boundary likelihood predicted by both approaches represents the probability (*y*ˆ) of a line being 'boundary':

$$boundary\,\,likelihood\,\,[0;1] = \mathcal{Y}\_{boundary}\tag{1}$$


**Table 1.** Distribution of training and testing data for boundary classification based on Random Forest (RF) and Convolutional Neural Networks (CNN).

RF classification is applied as shown in Figure 4 [22]. Instead of manually labeling lines for training, a line is now automatically labeled as 'boundary' when it overlaps with the cadastral reference buffer of 0.4 m by more than 50%. This value aligns with the threshold at which a CNN-derived result is labeled as 'boundary' or 'not boundary'. Since no DSM information is available for the study area, the feature dsm grad is not calculated.

**Figure 4.** Boundary line classification based on Random Forest (RF) to derive boundary likelihoods for MCG lines.

CNN classification is investigated by training state-of-the-art tile-based CNNs (Figure 5). We reformulate our problem of generating boundary likelihoods for MCG lines to be solvable by a tile-based CNN as follows: At first, image tiles of 224 × 224 pixels centered on an MCG line are cropped from the ortho-image. 224 × 224 × 3 is the standard size of images required by the used CNN. A tile is labeled as 'boundary' if the center pixel covering an MCG line overlaps with the cadastral reference buffer. A tile is created every 5 m along an MCG line. Decreasing this distance would increase the overlap, and thus the redundancy, of the image content per tile. Increasing this distance would reduce the number of tiles and thus the number of training data. With these settings, we generate 1.5 million tiles surrounding MCG pixels of which 5% are labeled as 'boundary' and 95% as 'not boundary'. After training, the CNN predicts boundary likelihoods for unseen testing areas (Figure 2a). The likelihoods of all tiles per MCG line are averaged based on the 97th percentile. This value aligns with the distribution of 'boundary' and 'not boundary' lines in the training data (Table 1). We use a pre-trained CNN architecture. We apply transfer learning by adding additional trainable layers: A global spatial average pooling layer, a fully connected layer with rectified linear unit (ReLU) activation, a dropout layer and a logistic layer with softmax activation. Only these last layers are trainable. We investigate using different pre-trained CNN architectures, including the Visual Geometry Group (VGG) [25], ResNet [26], Inception [27], Xception [28], MobileNet [29] and DenseNet [30], as well as different hyper-parameter settings on the learning optimizer, the depth of the fully connected layer and the dropout rate.

**Figure 5.** Boundary line classification based on Convolutional Neural Networks (CNNs) to derive boundary likelihoods for MCG lines.

Interactive delineation supports the creation of final cadastral boundaries. In comparison to our previous study [22], we now include more functionalities to delineate parcels (Table 2) and redesigned the Graphical User Interface (GUI). The interactive delineation is implemented in the open source geographic information system QGIS [31] as BoundaryDelineation plugin [32]:


**Table 2.** Delineation functionalities of BoundaryDelineation QGIS plugin.

**Figure 6.** Interactive delineation functionalities: (**a**) Connect lines surrounding a click, or (**b**) a selection of lines. (**c**) Close endpoints of selected lines to a polygon. (**d**) Connect lines along least-cost-path.
