# The P³ dataset: Pixels, Points and Polygons for Multimodal Building Vectorization

Raphael Sulzer¹,² Liuyun Duan¹ Nicolas Girard¹ Florent Lafarge²

¹LuxCarta Technology, Mouans-Sartoux, France

²Centre Inria d'Université Côte d'Azur, Sophia Antipolis, France

## Abstract

We present the P³ dataset, a large-scale multimodal benchmark for building vectorization, constructed from aerial LiDAR point clouds, high-resolution aerial imagery, and vectorized 2D building outlines, collected across three continents. The dataset contains over 10 billion LiDAR points with decimeter-level accuracy and RGB images at a ground sampling distance of 25 cm. While many existing datasets primarily focus on the image modality, P³ offers a complementary perspective by also incorporating dense 3D information. We demonstrate that LiDAR point clouds serve as a robust modality for predicting building polygons, both in hybrid and end-to-end learning frameworks. Moreover, fusing aerial LiDAR and imagery further improves accuracy and geometric quality of predicted polygons. The P³ dataset is publicly available, along with code and pretrained weights of three state-of-the-art models for building polygon prediction at https://github.com/raphaelsulzer/PixelsPointsPolygons.

## 1 Introduction

Cadastral maps that register the footprints of buildings as vector representations – typically 2D polygons – constitute an important source of information in numerous application fields, going from urban planning and navigation to environmental monitoring and disaster response through defense and intelligence. In the past decades, the construction and updates of these maps have been done mainly by human operators at some specific locations in the world only. Today, this tedious task is about to be replaced by automatic algorithms that learn to capture building outlines from satellite and aerial data, with the promise of vectorizing the several billion buildings in the world despite the strong variability of shape, density, and regularity of these objects.

Several scientific communities such as Computer Vision, Computer Graphics, Geoscience, Remote Sensing and Photogrammetry have actively worked on the building vectorization problem during the past years. For fully automatic building vectorization, deep networks are commonly trained on datasets that (i) exploit the image modality only, (ii) have little architectural and regional variability, as well as little variability in terms of acquisition characteristics [5, 16, 36, 37, 38], and (iii) use pixel masks instead of direct polygon annotations [29]. Unfortunately, these restrictions tend to make the efficiency of recent state-of-the-art (SOTA) methods [2, 41, 45] stagnant and, in the end, not ready to operate effectively, robustly and at large scale. (i) Using only overhead images can lead to false positive detections or missing building parts due to shadows and occlusions. Occlusions are particularly frequent in the form of trees hiding a building or part of it, or due to "leaning buildings" induced by image distortion. (ii) Small variability in the dataset can cause models to overfit to specific architectural styles of a country or region [29], to specific acquisition geometries, or even to a ground truth annotation source, which is often a (semi-)automatic extraction pipeline itself. Finally, (iii) using pixel-level supervision only can lead to noisy, overly complex and geometrically inconsistent polygons compared to official cadastral maps [41].
<figure><img src="image_1.png" /><figcaption>Figure 1: **Overview of P³**. We collect aerial images, aerial LiDAR point clouds and vectorized building outlines from the USA, Switzerland and New Zealand<fnref n="1" />. We harmonize and tile the data to create a large-scale benchmark dataset for building vectorization.</figcaption></figure>

To address these issues, we propose the P³ dataset, a dataset that provides two input modalities from different regions and precise vectorized building outline annotations. P³ includes the traditional image modality with aerial ortho- or near-nadir images, and an aerial LiDAR modality in the form of 3D point clouds. Aerial LiDAR point clouds become increasingly openly available from National Mapping Agencies (NMAs) at the scale of entire countries [3, 10, 20] and can thus constitute a complementary data source to imagery. In particular, aerial LiDAR point clouds provide direct height information with decimeter-level accuracy [10], and their acquisition is resilient to image distortion and meteorological and seasonal effects, as laser pulses can penetrate clouds and vegetation [34]. A second key specificity of our dataset is its scale and variability. The data cover a total area of 638km² across seven different regions on three different continents. Lastly, the dataset provides ground truth polygon annotations with geometric guarantees. In particular, polygons do not overlap with neighboring polygons and are either simple, or contain holes, e.g., to represent courtyards.

In addition to the P³ dataset, a second contribution of our work is a benchmark that analyzes the impact of the data modalities on the building vectorization problem. In particular, we propose a general pipeline to adapt the overpopulated image-based methods to the LiDAR modality and to the combination of image and LiDAR modalities. We conducted experiments with three recent SOTA methods: FFL [14], HiSup [41] and Pix2Poly [2]. Besides the traditional accuracy metrics used in

<footnote n="1">¹Licensed by Toitū Te Whenua Land Information New Zealand for re-use under CC-BY-4.0.</footnote>
the field, we also introduce a metric that measures the geometric quality of polygons in terms of symmetry and regularity. This aspect is often ignored in the commonly-used evaluation protocol, but is crucial for practitioners who want to exploit the potential of building maps.

Our dataset is designed to facilitate further research on multimodal building vectorization. It is available to download and can be used directly with a Python library that implements our benchmark with training, testing, and evaluation of the three building vectorization methods on our dataset.

# 2 Related work

Our review of previous work covers existing datasets for building detection and reconstruction, and methods for detecting and polygonizing building outlines.

## 2.1 Datasets

Datasets for building detection can be grouped into three categories, with either the exploitation of 2D data modality, 3D data modality or a combination of the two. Tab. 1 lists the existing datasets for each of these three categories and provides data and annotation specifications for each of them.

**2D** datasets that exploit the image modality constitute the dominant categories. Inria [29], CrowdAI [31], WHU [21] and Shanghai [9] are the most popular datasets used in the literature. Data are typically satellite or aerial images acquired at near-nadir with a ground sampling distance (GSD) between 5 and 80 cm. The Inria dataset [29] offers good urban diversity with a total area of 810km² covering different urban landscapes and countries, but requires a lossy conversion of the annotated pixel masks to polygons. Only the Microsoft [30] and Google [15] datasets exhibit higher diversity by covering millions of square kilometers. However, these two datasets provide building polygons with a low precision and without the original images. Other datasets such as WBD [32], RoofSat [5] and RoofVect [16] provide a more complete 2D roof wireframe description in the form of planar graphs. These datasets are however small and poorly diversified. Note that several datasets on this list have been artificially enriched by data augmentation, such as CrowdAI [31], RoofSat[5] or RoofVect [16]. In the case of the former, this enrichment strategy has been shown to cause biases in the results [1]. Note also that some datasets such as OpenCities [13] and SpaceNet2 [12] suffer from low-quality human annotations typically due to either the low resolution of the original data source or a lack of harmonization in between annotators.

**3D.** Building3D [39], City3D[18] and RoofN3D [40], which exploit 3D data, mostly target the 3D building reconstruction problem from LiDAR point clouds. Each point cloud represents a single building and not an urban scene or a part of it. Unfortunately, annotated 3D models that are created by automatic methods or human operators present strong geometric inconsistencies that prevent these datasets from being used effectively for the building footprint extraction task.

**2D and 3D.** Only a few datasets present 2D and 3D modalities, i.e. Roof3D [38], Potsdam, and Vaihingen [37]. These datasets are small and exhibit low urban diversity. They also do not offer vectorized annotations, but pixel masks only. For Roof3D and Potsdam, the complementary modality is a digital surface model (DSM) and provides 2.5D information only. In contrast, our dataset combines both images and 3D LiDAR at larger scale in various urban landscapes. In particular, it is 400 times larger than the Vaihingen dataset and provides 2D outline polygons as annotation.

## 2.2 Vectorization methods

Methods for detecting and polygonizing building outlines largely exploit the image modality. They generally fall into two main categories: hybrid methods and direct building polygon prediction.

**Hybrid methods** typically involve multiple stages, often combining segmentation or detection with polygon extraction and refinement steps. Many recent approaches in this category incorporate structured priors, semantics, or preexisting databases. For instance, semantically enriched point clouds can be used to validate and correct existing building databases of NMAs [35], and elevation information provides geometric primitive clues for building rectangles extraction [33]. ASIP [26]
<table><caption>Table 1: Specifications of existing Datasets. Modalities typically include satellite images (SI), aerial images (AI), drone images (DI), airborne LiDAR scans (ALS) and digital surface model (DSM). SI* specifies datasets that used satellite imagery for their annotation but the imagery itself is not included. Tiling specifies whether data is a single building (SB) only, an image tile adapted to deep learning frameworks (T) or a large georeferenced tile bigger than 1000×1000 px (T+). Diversity approximates the urban variability of the dataset with four categories: "- -" for a similar type of buildings from a single location, "-" for several types of buildings from a single location, "+" for several types of buildings from multiple locations in the world, and "++" if it covers at least 1% of the total urban scenes in the world. "H", "A" and "M" refers to the annotation origin, i.e., either from human operators, automatic algorithms or a mix of these two, respectively.</caption><thead><tr><th rowspan="2">Dataset</th><th colspan="5">Data specifications</th><th colspan="5">Annotation</th></tr><tr><th>Modality</th><th>Ground sampling</th><th>Area (km²)</th><th>Tiling</th><th>Diversity</th><th>Pixel label</th><th>2D outline polygon</th><th>2D roof wireframe</th><th>3D building wireframe</th><th>Origin</th></tr></thead><tbody><tr><td>Inria [29]</td><td>AI</td><td>0.3m</td><td>810</td><td>T+</td><td>+</td><td>✓</td><td></td><td></td><td></td><td>M</td></tr><tr><td>SemiCity [36]</td><td>SI</td><td>0.5m</td><td>50</td><td>T+</td><td>-</td><td>✓</td><td></td><td></td><td></td><td>H</td></tr><tr><td>WHU [21]</td><td>AI</td><td>0.075m</td><td>450</td><td>T</td><td>-</td><td>✓</td><td></td><td></td><td></td><td>H</td></tr><tr><td>CrowdAI [31]</td><td>SI</td><td>0.3m</td><td>2.3k</td><td>T</td><td>-</td><td></td><td>✓</td><td></td><td></td><td>H</td></tr><tr><td>OpenCities [13]</td><td>DI</td><td>0.4-0.8m</td><td>415</td><td>T</td><td>+</td><td></td><td>✓</td><td></td><td></td><td>H</td></tr><tr><td>Shanghai [9]</td><td>SI</td><td>0.3m</td><td>21</td><td>T</td><td>-</td><td></td><td>✓</td><td></td><td></td><td>H</td></tr><tr><td rowspan="7">2D</td><td>WHU 2[21]</td><td>SI</td><td>0.45m</td><td>550</td><td>T</td><td>+</td><td></td><td>✓</td><td></td><td></td><td>H</td></tr><tr><td>SpaceNet2 [12]</td><td>SI</td><td>0.3m</td><td>3k</td><td>T</td><td>+</td><td></td><td>✓</td><td></td><td></td><td>H</td></tr><tr><td>UBC [19]</td><td>SI</td><td>0.5-0.8m</td><td>66.1</td><td>T</td><td>+</td><td></td><td>✓</td><td></td><td></td><td>M</td></tr><tr><td>Microsoft [30]</td><td>SI*</td><td>0.3-1.0m</td><td>N/A</td><td>-</td><td>++</td><td></td><td>✓</td><td></td><td></td><td>A</td></tr><tr><td>Google [15]</td><td>SI*</td><td>0.5m</td><td>58M</td><td>-</td><td>++</td><td></td><td>✓</td><td></td><td></td><td>M</td></tr><tr><td>WBD [32]</td><td>SI</td><td>0.3m</td><td>32</td><td>SB</td><td>-</td><td></td><td></td><td>✓</td><td></td><td>H</td></tr><tr><td>RoofSat [5]</td><td>SI</td><td>0.3m</td><td>14.9</td><td>T</td><td>-</td><td></td><td></td><td>✓</td><td></td><td>H</td></tr><tr><td>RoofVect [16]</td><td>AI</td><td>0.1m</td><td>2</td><td>SB</td><td>-</td><td></td><td></td><td>✓</td><td></td><td>H</td></tr><tr><td rowspan="3">3D</td><td>Building3D [39]</td><td>ALS</td><td>30pts/m²</td><td>998</td><td>SB</td><td>+</td><td></td><td></td><td></td><td>✓</td><td>M</td></tr><tr><td>City3D [18]</td><td>ALS</td><td>4-50 pts/m²</td><td>N/A</td><td>SB</td><td>+</td><td></td><td></td><td></td><td>✓</td><td>A</td></tr><tr><td>RoofN3D [40]</td><td>ALS</td><td>4.7 pts/m²</td><td>1010</td><td>SB</td><td>-</td><td></td><td></td><td></td><td>✓</td><td>A</td></tr><tr><td rowspan="4">2D+3D</td><td>Roof3D [38]</td><td>AI+DSM</td><td>0.3m</td><td>22.4</td><td>T</td><td>-</td><td>✓</td><td></td><td></td><td></td><td>M</td></tr><tr><td>Potsdam [37]</td><td>AI+DSM</td><td>0.05m</td><td>3.4</td><td>T</td><td>-</td><td>✓</td><td></td><td></td><td></td><td>H</td></tr><tr><td>Vaihingen [37]</td><td>AI+ALS</td><td>0.08m, 4pts/m²</td><td>1.5</td><td>T</td><td>-</td><td>✓</td><td></td><td></td><td></td><td>H</td></tr><tr><td>P³ (ours)</td><td>AI+ALS</td><td>0.25m, 16pts/m²</td><td>638</td><td>T</td><td>+</td><td></td><td>✓</td><td></td><td></td><td>M</td></tr></tbody></table>

splits and merges cells of a polygonal partition according to a deep semantic segmentation map to generate compact polygons. Frame Field Learning [14] directly learns the directional fields that align with building boundaries, and obtains more regular polygons for urban scenes. HiSup [41] tackles this challenge by integrating directional fields, semantics, and geometry learning with hierarchical supervision to enhance the geometry precision. The sophisticated hierarchical design preserves a good balance between complexity and fidelity.

**Direct building polygon prediction** approaches typically leverage advanced neural network architectures to process aerial or satellite imagery and directly output vectorized building polygons without intermediate raster representations. Popular methods such as PolyMapper [27]], PolyWorld[44], and Re-PolyWorld [45] directly extract vertices via convolutional or recurrent neural networks and apply a graph neural network to form polygons. PolyBuilding [17] shows promising performance by applying transformers that reduces the vertex redundancy in CNN-GCN paradigm. Based on the success of [42], the image-to-vertex sequence methods [2, 24, 43] represented by Pix2Poly employ a transformer to produce building vertex tokens as sequence, eliminating post-processing steps by using permutation matrices for connections. Other methods such as GAST [23] and PolyR-CNN [22]
<figure><img src="image_2.png" /><figcaption>**Figure 2: Example image/LiDAR tiles with polygon annotations.** In (a), we show an example tile of Jersey, NY, US. The image exhibits distortion which leads to the "leaning building" effect. The polygon annotation is nonetheless accurately placed on the base of the building. The LiDAR acquisition does not suffer from the "leaning building" effect. In (b), we show an example tile of Zurich, Switzerland. The depicted building has two interior cutouts. The polygon annotation has thus two interior rings which are connected to the exterior ring at their closest vertex.</figcaption></figure>

focus inside a region of interest. They thereby avoid complex designs but mainly handle relatively simple and small urban areas.

Most of the aforementioned methods are designed to work with images and do not leverage 3D information. We present a method to adapt existing neural networks in the field to exploit both image and LiDAR modalities, making them more accurate in complex urban environments.

## 3 Dataset

We collect data from nine cities across seven regions in three countries. Our dataset covers a total area of 638km² and includes approximately 10B pixels, 10B LiDAR points, and 224k individual building polygon annotations. Tab. A.1 and Tab. A.2 in the supplementary material (SM) provide detailed characteristics of the collected input data, including licensing, download links, region names, image resolution, etc. To optimize the raw remote sensing and cadastral data for deep learning frameworks, we resample, tile and harmonize images, point clouds and building polygons.

**Aerial images.** The raw input images are near-nadir acquisition with a GSD between 10 and 15 cm. The images are not orthorectified, resulting in some distortion in off-nadir image regions (see Fig. 2a). To standardize the images across all regions, we resample them to a GSD of 25 cm and clip them to non-overlapping tiles of 224×224 pixels, equivalent to 56 m×56 m on the ground. This process yields a total of 203k image tiles.

**Aerial LiDAR point clouds.** The LiDAR point clouds exhibit a density ranging from 6 to 21 points per square meter across different regions. The point clouds are georeferenced to the same coordinate system as the images. We clip them to equally sized non-overlapping tiles of 56 m×56 m. This results in 194k LiDAR tiles – slightly fewer than image tiles due to missing LiDAR data in certain areas, such as deep water. On average, the LiDAR tiles contain between 20k and 70k points. We preserve the original point cloud density without resampling. Additionally, we do not color the point clouds, as it would first require to orthorectify the images before projecting the image colors on them.

**Building outline polygon annotations.** Our dataset includes annotations as 2D polygons representing the orthogonal projections of the complete building perimeter onto the ground. For buildings without roof overhang, these polygons typically coincide with the building footprint – the 2D polygon where the building touches the ground. In off-nadir image regions, roof outlines may appear slightly offset from the building footprint due to image distortion (see Fig. 2a). We do not provide annotations for roof partitions or interior walls, as this information is only available for the Switzerland part of the dataset. Where two or more building outline polygons overlap in the input data we merge them into a single polygon. We clip the building polygons to match the same tile dimensions as the image and LiDAR tiles. Polygons spanning multiple tiles are split at the tile boundaries. We then convert the polygon annotations to the widely adapted MS-COCO format [28].
In the urban environment, larger buildings commonly feature interior cutouts such as courtyards, lightwells, air shafts, atriums, passageways, or alleys. The MS-COCO format does not directly support storing interior rings as polygons with holes in vector format. Additionally, most current deep learning based vectorization methods do not specifically address interior ring prediction. We thus adopt the convention established by Xu *et al* [41] to connect interior and exterior rings of a polygon at their closest vertex (see Fig. 2b). The upside of this approach is that it allows deep networks to predict interior rings without architecture modifications. However, it can create invalid geometry through self-intersection and complicate the explicit distinction between exterior and interior rings. To facilitate more robust solutions for future work, we include an additional attribute *hashole*, in the MS-COCO annotation, enabling distinction between interior and exterior rings.

# 4 Experiments

We now present the baseline methods used for comparison, as well as evaluation metrics used to assess their performance. We then present two experiments that introduce the characteristics of our dataset: an ablation study on input modalities on a subset of the dataset and a multimodal building outline prediction on the full dataset.

## 4.1 Baseline methods

We test the three following baseline methods on our dataset:

* **FFL** [14] employs a CNN-based decoder to predict per-pixel orientation (frame) fields and segmentation masks. Polygonization is performed by tracing the predicted frame fields to extract structured, direction-aligned polygon boundaries, followed by geometric regularization.
* **HiSup** [41] predicts (i) a point feature map for detecting convex and concave polygon vertices, (ii) an edge feature map in the form of attraction field maps, (iii) and a segmentation mask to represent the area enclosed by the polygon. These outputs are jointly processed and input into an optimization pipeline to reconstruct the final polygons.
* **Pix2Poly** [2] uses a transformer-based decoder to predict a sequence of vertex coordinates along with a permutation matrix ordering and grouping them to produce polygons. This enables direct, end-to-end polygon reconstruction without relying on intermediate per-pixel segmentations.

We reimplement all methods in a common library that we include in the publicly available repository. We use the following image encoder, point cloud encoder and fusion encoder for all methods.

* **Image encoder.** We use a standard Vision Transformer (ViT) [11] pretrained on ImageNet [8] with image input size of 224×224 pixels and a patch size of 8×8 pixels. The transformer extracts patch-level features without global pooling, thus producing a sequence of 784 patch embeddings. For processing these embeddings with the CNN-based decoders of Frame Field Learning (FFL) [14] and HiSup [41] we reshape and upsample the patches into a spatial map.
* **Point cloud encoder.** We design a novel point cloud encoder to process aerial LiDAR point clouds with a variable point count and density. We first scale the point cloud to a fixed height of 1 m. We then voxelize the point cloud into pillars that align with the 8×8 patches of the image encoder by choosing the pillar size to be 2×2×1 m (8 pixels on 25 cm imagery translates to 2 m). This results in 784 pillars, aligned with the 784 patch embeddings. We use a maximum number of points per voxel of 64. We then extract pillar features for each voxel [25] and process them with a small PointNet [6]. Finally, by replacing the patch embedding layer with the PointPillars encoder, we use the same ViT architecture as for the image encoder to further process the features. The output of the point cloud encoder is a sequence of 784 patch embeddings, which are then directly input to the Pix2Poly [2] decoder, or reshaped and upsampled to a spatial map for processing with the CNN-based decoders of FFL [14] and HiSup [41].

* **Fusion encoder.** We use a fusion encoder that concatenates the image and point cloud features along the channel dimension. The resulting feature map is then processed with a small 2D CNN to reduce the channel dimension, and again fed into the same ViT architecture as before. We use a fusion encoder that concatenates the image and point cloud features along the channel dimension. The resulting feature map is then processed with a small 2D CNN to reduce the channel dimension, and again fed into the same ViT architecture as before.
<table><caption>Table 2: Modality ablation. We compare baseline models trained and tested on different modalities of the Switzerland subset. For each metric, we highlight the best and second best scores.</caption><thead><tr><th rowspan="2">Model</th><th rowspan="2">Modality</th><th colspan="6">Boundary</th><th colspan="2">Area</th><th colspan="2">Complexity</th><th colspan="2">Efficiency</th></tr><tr><th>POLIS [m] ↓</th><th>CD [m] ↓</th><th>HD [m] ↓</th><th>MTA [°] ↓</th><th>AP ↑</th><th>AR ↑</th><th>IoU ↑</th><th>NR=1</th><th>Time [s] ↓</th><th>Params ↓</th></tr></thead><tbody><tr><td rowspan="3">ViT [11] +<br>FFL [14]</td><td>Image</td><td>3</td><td>2.7</td><td>12</td><td>41</td><td>0.275</td><td>0.46</td><td>0.839</td><td>0.847</td><td>0.532</td><td>23.7M</td></tr><tr><td>LiDAR</td><td>2.35</td><td>1.94</td><td>9.66</td><td>44.8</td><td>0.359</td><td>0.545</td><td>0.87</td><td>0.829</td><td>0.582</td><td>23.7M</td></tr><tr><td>Fusion</td><td>2.14</td><td>1.88</td><td>8.9</td><td>39.7</td><td>0.376</td><td>0.569</td><td>0.877</td><td>0.874</td><td>0.58</td><td>26.4M</td></tr><tr><td rowspan="3">ViT [11] +<br>HiSup [41]</td><td>Image</td><td>2.46</td><td>2.48</td><td>11.4</td><td>35.2</td><td>0.287</td><td>0.493</td><td>0.85</td><td>0.885</td><td>0.124</td><td>30.8M</td></tr><tr><td>LiDAR</td><td>2.05</td><td>2.01</td><td>9.58</td><td>37</td><td>0.347</td><td>0.54</td><td>0.87</td><td>0.882</td><td>0.165</td><td>30.8M</td></tr><tr><td>Fusion</td><td>1.91</td><td>1.9</td><td>8.94</td><td>35.2</td><td>0.355</td><td>0.568</td><td>0.872</td><td>0.89</td><td>0.129</td><td>33.5M</td></tr><tr><td rowspan="3">ViT [11] +<br>Pix2Poly [2]</td><td>Image</td><td>2.46</td><td>2.5</td><td>10.8</td><td>34.3</td><td>0.317</td><td>0.492</td><td>0.845</td><td>0.906</td><td>1.44</td><td>31.9M</td></tr><tr><td>LiDAR</td><td>1.88</td><td>1.9</td><td>8.5</td><td>34.1</td><td>0.379</td><td>0.552</td><td>0.869</td><td>0.913</td><td>1.15</td><td>31.9M</td></tr><tr><td>Fusion</td><td>1.8</td><td>1.82</td><td>8.16</td><td>33.4</td><td>0.398</td><td>0.578</td><td>0.87</td><td>0.915</td><td>1.15</td><td>34.6M</td></tr></tbody></table>

## 4.2 Metrics

We use three different types of metrics to evaluate the performance of the baseline methods: (i) boundary- and area-based accuracy and completeness metrics, (ii) complexity metrics, and (iii) efficiency metrics, i.e. average prediction time and the number of trainable parameters of the models. All metrics are computed per tile and then averaged over all tiles. Formal definitions of the metrics can be found in Sec. A.2 in the SM.

**Boundary- and area-based metrics.** (i) The intersection over union (IoU) metric provides a combined measure of accuracy and completeness of the predicted polygons. However, it does not provide a good measure of the boundary distance between the predicted and ground truth polygons, as it is mainly influenced by the polygon area [7]. (ii) Average Precision (AP) and average recall (AR) computed over different IoU thresholds measure the accuracy and completeness of the predicted polygon sets [28]. (iii) The POLIS metric [4] measures the symmetric distance between each predicted polygon vertex and its closest point on the ground truth polygon boundary, and vice versa. (iv, v) The Hausdorff and Chamfer distance (HD and CD) measure the average and maximum boundary distance of predicted and ground truth polygons, irrespective of vertex locations. (vi) Finally, the maximum tangent angle (MTA) [14] measures the maximum angular error between the predicted and ground truth polygon edges. POLIS, HD, CD and MTA are computed for ground truth and predicted polygon pairs with a minimum IoU of 0.5. They are important measures for practitioners because they correlate with a high visual similarity of predicted and ground truth polygons.

**Complexity metrics.** (i) NR measures the relative difference of the number of predicted and ground truth vertices. (ii) C-IoU, defined as the product of NR and IoU measures the similarity between predicted and ground truth polygons in terms of both shape and complexity. And finally, (iii) the normalized degree of freedom (DoF) measure the regularity and symmetry of polygon edges [5]. A lower DoF score indicates that the predicted polygons are simpler and more regular, while a higher DoF score indicates that the predicted polygons are more complex and less regular.

## 4.3 Results

**Modality ablation.** We first conduct an ablation study on a subset of our dataset containing only data from Switzerland. This subset is less challenging than the full dataset because it exhibits lower variability. We use it to evaluate the impact of different input modalities on the polygon prediction task. We train each baseline method with a point, an image, and a fusion encoder. Tab. 2 demonstrates that models utilizing LiDAR data consistently predict more complete (~0.55 AR) and accurate polygons (0.35-0.38 AP) compared to models using only images (0.46-0.49 AR, 0.28-0.32 AP). The fusion encoder efficiently integrates the strengths of both input modalities to achieve the best performance for all models. Interestingly, for angular error MTA and vertex ratio NR, FFL and HiSup perform better for image-predicted polygons. This can be attributed to the presence of more prominent corner and edge features in the images compared to LiDAR point clouds. The recently proposed end-to-end polygon prediction approach, Pix2Poly, exhibits significantly slower runtime compared to hybrid methods. Fig. 3, confirms the higher accuracy and geometry simplicity of LiDAR- and multimodal-predicted polygons compared to those predicted from images alone.
<figure><img src="image_3.png" /><figcaption>**Figure 3: Modality ablation.** We present a sample tile displaying predicted and ground truth building polygons from the Switzerland subset. The first column shows ground truth polygons, while subsequent columns show predicted polygons from baseline models trained on different input modalities, i.e. images only (first row), LiDAR only (second row), and the fusion of image and LiDAR data (third row). Note, in the bottom right corner, where a tree obscuring a building corner adversely affects the image-only prediction, while LiDAR-only and multimodal polygon predictions remain unaffected by this occlusion. Across all models, polygons predicted using multimodal inputs demonstrate superior simplicity and accuracy, especially with Pix2Poly.</figcaption></figure>

**Multimodal building outline prediction.** We now evaluate the performance of the baseline methods on the full dataset. Each model is trained with a fusion encoder using both images and LiDAR point clouds as input. Evaluation metrics for the full dataset are shown in Tab. 3.

The full dataset is more challenging due to its greater variability, leading to a drop in all metrics. For example, the mean IoU decreases by about 3 percentage points compared to the Switzerland subset. Pix2Poly produces the best polygons in terms of complexity and accuracy, exhibiting the best or second best results for all metrics. Fig. 4 shows examples of Pix2Poly's more compact and accurate polygon predictions compared to other methods. However, the figure also shows that Pix2Poly still has some shortcomings. The prediction in the first row shows how an incorrect connection in the building outline leads to a significant boundary error. The second row reveals entirely missing building outlines for the Pix2Poly prediction, and the third row shows a missing interior cutout. Notably, the HiSup-prepredicted polygon is the only one that accurately captures the hole present in the polygon outline. A common limitation of the CNN-based methods is their tendency to produce excessive vertices for building polygons, falling to fully address the regularity and symmetry present in urban areas. In terms of relative performance, our results align with those reported on other datasets [9, 13, 29]. However, using identical encoders across all methods results in smaller performance gaps between the tested methods.

More ablation studies and additional results can be found in Sec. A.4 and Sec. A.5 in the SM.
<figure><img src="image_4.png" /><figcaption>Figure 4: **Multimodal polygon prediction.** We show ground truth and predicted building outlines from our full dataset, from top to bottom for Switzerland, New Zealand¹ and the USA, with input LiDAR point clouds superimposed on aerial images. The first column shows the ground truth reference polygons, while the second to fourth column present predicted polygons generated by FFL [14], HiSup [41] and Pix2Poly [2] utilizing both input modalities.</figcaption></figure>

<table><caption>Table 3: **Multimodal polygon prediction** of baseline models with fusion encoder on the full dataset.</caption><thead><tr><th rowspan="2">Model</th><th colspan="3">Boundary</th><th colspan="2">Area</th><th colspan="4">Complexity</th></tr><tr><th>POLIS [m] ↓</th><th>CD [m] ↓</th><th>HD [m] ↓</th><th>MTA [°] ↓</th><th>AP ↑</th><th>AR ↑</th><th>IoU ↑</th><th>C-IoU ↑</th><th>NR=1</th><th>DoF ↓</th></tr></thead><tbody><tr><td>ViT [11] + FFL [14]</td><td>2.41</td><td>2.11</td><td>9.34</td><td>40.4</td><td>0.286</td><td>0.43</td><td>0.832</td><td>0.763</td><td>0.848</td><td>0.808</td></tr><tr><td>ViT [11] + HiSup [41]</td><td>2.07</td><td>2.03</td><td>9.1</td><td>36.5</td><td>0.309</td><td>0.474</td><td>0.844</td><td>0.789</td><td>0.881</td><td>0.758</td></tr><tr><td>ViT [11] + Pix2Poly [2]</td><td>1.91</td><td>1.92</td><td>8.17</td><td>34.4</td><td>0.347</td><td>0.49</td><td>0.842</td><td>0.801</td><td>0.901</td><td>0.741</td></tr></tbody></table>

## 5 Conclusion, Limitations and Future Work

We present a new dataset and benchmark for building vectorization from high resolution aerial images and LiDAR point clouds. Because such high resolution data is expensive to gather, it is mainly available from developed countries. Currently, our dataset is limited to data from Switzerland, the USA and New Zealand. We plan to expand it to other countries in the future if new data becomes available. Therefore, our dataset is not representative of the entire world. For example, the dataset does not include informal or improvised buildings found in both rural and urban areas of underdeveloped countries. Furthermore, the dataset only includes building outlines, and does not provide annotations for roof partitions, building heights or other 3D annotations. Creating 3D annotations in a reliable manner is a challenge that we plan to tackle in the future to increase the application spectrum of our dataset.

We also present a benchmark of state-of-the-art methods for building vectorization. Equipped with recent image and LiDAR encoders all tested methods produce accurate and complete building polygons. We show that (i) LiDAR point clouds are a valuable source for building outline prediction, that (ii) the combination of image and LiDAR point clouds leads to the best predictions, and that (iii) our dataset is challenging enough to require multimodal approaches.
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# A Supplementary Material

In this supplementary material, we provide additional details about the dataset (Sec. A.1) and formal definitions of the evaluation metrics (Sec. A.2). We then describe our experimental setup (Sec. A.3) and present additional ablation studies (Sec. A.4) and additional results (Sec. A.5). Finally, we discuss potential negative societal impacts of our work (Sec. A.6).

## A.1 Data source and details

In Tab. A.1 and Table A.2 we provide further details about the data we collect. We download the data from national or regional mapping agencies. All data is publicly available and free to download, re-use, modify and redistribute. Only the data from New Zealand requires an attribution under the CC-BY-4.0 license.

The downloaded data is in different formats and resolutions and we harmonize the data to the common $P^3$ specifications explained in the main text.

<table><caption>Table A.1: **Data sources.** We collect data from nine different cities in three countries, ranging from urban to rural areas, and including a variety of building types. The dataset is split into training (77%), validation (1%), and test sets (22%). The image GSD varies between 12.5 and 15 cm, while the average LiDAR point density varies between 6 and 21 points per square meter. Note that, we downsample the images to a GSD of 25 cm for the benchmark dataset. The annotations are either semi-automatically extracted from orthorectified images or constitute cadasteral data.</caption><thead><tr><th>Country</th><th>Split</th><th>Modality</th><th>License</th><th>Restrictions</th><th>Link</th></tr></thead><tbody><tr><td rowspan="4">United States</td><td>train, val, test</td><td>Images</td><td>Custom</td><td>None</td><td>data.gis.ny.gov</td></tr><tr><td>train, val, test</td><td>LiDAR</td><td>None</td><td>None</td><td>data.gis.ny.gov</td></tr><tr><td>train, test</td><td>Buildings</td><td>Custom</td><td>None</td><td>nycmaps-nyc.hub.arcgis.com</td></tr><tr><td>val</td><td>Buildings</td><td>Custom</td><td>None</td><td>data.gis.ny.gov</td></tr><tr><td rowspan="4">Switzerland</td><td>train, val, test</td><td>Images</td><td>None</td><td>None</td><td>swisstopo.admin.ch</td></tr><tr><td>train, val, test</td><td>LiDAR</td><td>None</td><td>None</td><td>swisstopo.admin.ch</td></tr><tr><td>train, val, test</td><td>Buildings</td><td>None</td><td>None</td><td>swisstopo.admin.ch</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">New Zealand</td><td>train, val, test</td><td>Images</td><td>CC-BY-4.0</td><td>Attribution required</td><td>data.linz.govt.nz</td></tr><tr><td>train, val, test</td><td>LiDAR</td><td>CC-BY-4.0</td><td>Attribution required</td><td>data.linz.govt.nz</td></tr><tr><td>train, val, test</td><td>Buildings</td><td>CC-BY-4.0</td><td>Attribution required</td><td>data.linz.govt.nz</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><thead><tr><th colspan="3">Region</th><th colspan="2">Image</th><th colspan="2">LiDAR</th><th colspan="2">Building Annotations</th></tr><tr><th>Country</th><th>City</th><th>Type</th><th>Split</th><th>GSD [cm]</th><th>Density [pts/m²]</th><th>Source</th><th>Type</th><th>Count</th></tr></thead><tbody><tr><td rowspan="3">United States</td><td>New York City</td><td>city</td><td>train</td><td rowspan="3">15</td><td>21</td><td rowspan="3">semi-automatic<br>image extraction</td><td rowspan="3">2D outline<br>polygon</td><td>88k</td></tr><tr><td>Albany</td><td>residential</td><td>val</td><td>6</td><td>1.3k</td></tr><tr><td>Yonkers</td><td>industrial</td><td>test</td><td>6</td><td>31k</td></tr><tr><td rowspan="3">Switzerland</td><td>Zurich</td><td>city</td><td>train</td><td rowspan="3">10</td><td>17</td><td rowspan="3">manual<br>image extraction</td><td rowspan="3">2D roof<br>wireframe</td><td>43k</td></tr><tr><td>Basel</td><td>city</td><td>val</td><td>11</td><td>0.3k</td></tr><tr><td>Jouxtens-Mézery</td><td>residential</td><td>test</td><td>13</td><td>11k</td></tr><tr><td rowspan="3">New Zealand</td><td>Twyford</td><td>rural</td><td>train</td><td rowspan="3">12.5</td><td>16</td><td rowspan="3">semi-automatic<br>image extraction</td><td rowspan="3">2D outline<br>polygon</td><td>31k</td></tr><tr><td>Waipukurau</td><td>rural</td><td>val</td><td>19</td><td>1.6k</td></tr><tr><td>Gisborne</td><td>city</td><td>test</td><td>19</td><td>16k</td></tr></tbody></table>

Table A.2: **Data details.** We collect data from nine different cities in three countries, ranging from urban to rural areas, and including a variety of building types. The dataset is split into training (77%), validation (1%), and test sets (22%). The image GSD varies between 10 and 15 cm, while the average LiDAR point density varies between 6 and 21 points per square meter. Note that, we downsample the images to a GSD of 25 cm for the benchmark dataset. The annotations are either semi-automatically extracted from orthorectified images or constitute cadasteral data.

## A.2 Evaluation metrics

The evaluation metrics used in our benchmark are defined as follows.

**Intersection over union (IoU)** The IoU metric is defined as the ratio between the intersection and the union of the predicted and ground truth polygons. Let $P^g$ be the set of ground truth polygons and $P^d$ the set of predicted polygons of a single tile, then the IoU is defined as:

$$ \text{IoU}(P^g, P^d) = \frac{|P^g \cap P^d|}{|P^g \cup P^d|} \qquad (1) $$

**Average precision (AP) and recall (AR)** The average precision (AP) and average recall (AR) metrics are computed using the IoU metric averaged over different thresholds [28]. For a fixed IoU threshold $\tau$, a predicted polygon $p^d$ is considered a true positive (TP) if it matches a ground truth polygon $p^g$ with IoU $\ge \tau$. Otherwise, it is a false positive (FP). Ground truth polygons not matched by any prediction are counted as false negatives (FN). Then, precision and recall are defined as

$$ \text{Precision} = \frac{\text{TP}}{\text{TP} + \text{FP}} \qquad (2) $$

and

$$ \text{Recall} = \frac{\text{TP}}{\text{TP} + \text{FN}} \qquad (3) $$

AP and AR are computed and averaged over 10 IoU thresholds $\tau \in \{0.50, 0.55, ..., 0.95\}$ as

$$ \text{AP} = \frac{1}{10} \sum_{\tau} \text{Precision}_{\tau} \qquad (4) $$

and

$$ \text{AR} = \frac{1}{10} \sum_{\tau} \text{Recall}_{\tau}. \qquad (5) $$

**POLIS** The POLIS metric [4] is computed for ground truth and predicted polygons $p^g$ and $p^d$ matched with a minimum IoU threshold of 0.5. Let $V$ be the vertices of a polygon $p$. Then, the POLIS metric is defined as the symmetric average distance between each predicted vertex $v^d \in p^d$ and its closest point $x^g$ on boundary of the matched ground truth polygon $\partial p^g$, and vice versa, i.e.

$$ \text{POLIS}(p^g, p^d) = \frac{1}{2|v^g|} \sum_{v^g \in p^g} \min_{a \in \partial p^d} ||v^g - a|| + \frac{1}{2|v^d|} \sum_{v^d \in p_d} \min_{b \in \partial p^g} ||v^d - b||. \qquad (6) $$
**Chamfer distance (CD)** The Chamfer distance (CD) is defined similarly to the POLIS distance. However, instead of using the polygon vertices, we sample points on the polygon boundaries to approximate the boundary distance of $\partial p^g$ and $\partial p^d$. Let $S_g$ and $S_d$ be 2D point sets sampled with a maximum spacing of 10 cm on the polygon boundaries $\partial p^g$ and $\partial p^d$ for all polygons $p^g \in P^g$ and $p^d \in P^d$ of a tile. Then, the CD is defined as:

$$ CD(S^g, S^d) = \frac{1}{2|S^g|} \sum_{s^g \in S^g} \min_{s^d \in S^d} ||s^g - s^d||_2 + \frac{1}{2|S^d|} \sum_{s^d \in S^d} \min_{s^g \in S^g} ||s^d - s^g||_2. \quad (7) $$

**Hausdorff distance (HD)** The Hausdorff distance (HD) is defined as the maximum distance between the predicted and ground truth polygon boundaries. Using the same sampled points on the polygon boundaries as before, the HD is defined as

$$ HD(S^g, S^d) = \max_{s^g \in S^g} \min_{s^d \in S^d} ||s^g - s^d||_2 + \max_{s^d \in S^d} \min_{s^g \in S^g} ||s^d - s^g||_2. \quad (8) $$

**Maximum tangent angle (MTA)** The MTA [14] is also computed for ground truth and predicted polygons matched with a minimum IoU threshold of 0.5. We sample an ordered sequence of points $T^d$ on the predicted polygons boundary and project it to the matched ground truth polygons, i.e. for each $t^d$ we find the closest point $x^g$ on the ground truth polygons boundary. For both sequences of points $T^d$ and $X^g$, omitting the superscript, corresponding normed tangent directions are computed as

$$ \text{Tangent}(t_i) = \frac{t_{i+1} - t_i}{\|t_{i+1} - t_i\|} \quad \text{and} \quad \text{Tangent}(x_i) = \frac{x_{i+1} - x_i}{\|x_{i+1} - x_i\|}. \quad (9) $$

The angle differences between the two are computed from the scalar product

$$ \Delta\theta_i = \cos^{-1}(\langle \text{Tangent}(t_i), \text{Tangent}(x_i) \rangle). \quad (10) $$

Before computing the maximum angle error MTA, we filter out tangents whose projection is stretched more than a factor of 2, e.g., due to mismatches between ground truth and predicted segments. We keep all $\Delta\theta_j, \forall j \in A$ where $A = \{j | j \in [1..n], \frac{1}{2} < \frac{\|x_{i+1} - x_i\|}{\|t_{i+1} - t_i\|} < 2\}$. The final maximum tangent angle error is then computed as

$$ \text{MTA} = \max_{j \in A} \Delta\theta_j. \quad (11) $$

**Vertex number ration (NR)** The relative difference of predicted and ground truth number of vertices $|V^d|$ and $|V^g|$ per tile is defined as

$$ \text{NR} = \frac{||V^d| - |V^g||}{|V^d| + |V^g|} \quad (12) $$

**Complexity IoU (C-IoU)** The complexity IoU (C-IoU) is defined as the product of the IoU and the vertex ratio (NR):

$$ \text{C-IoU} = \text{IoU} \cdot \text{NR}. \quad (13) $$

**Line degree of freedom (DoF)** The line-degree of freedom score (DoF) [5] is defined as the ratio of the degree of freedom $k_L$ of a configuration of line segments $L$ to twice the number of lines $|L|$ in the configuration.

$$ \text{DoF}(L) = \frac{k_L}{2|L|} \quad (14) $$

The degree of freedom $k_L$ is computed via the counting of the number of line-segments in different regularization groups, i.e. for parallelism, orthogonality and co-linearity as regularities, the degree of
<table><caption>Table A.3: **Ground sampling distance ablation.** We compare a ViT [11] + FFL [14] model trained and tested on aerial images with a GSD of 15 and 25 cm. For each metric, we highlight the best and second best scores.</caption><thead><tr><th rowspan="2">GSD [cm]</th><th colspan="5">Boundary</th><th colspan="2">Area</th><th colspan="3">Complexity</th></tr><tr><th>POLIS [m] ↓</th><th>CD [m] ↓</th><th>HD [m] ↓</th><th>MTA [°] ↓</th><th>AP ↑</th><th>AR ↑</th><th>IoU ↑</th><th>C-IoU ↑</th><th>NR=1</th><th>DoF ↓</th></tr></thead><tbody><tr><td>15</td><td>3.98</td><td>3.48</td><td>15.9</td><td>44.5</td><td>0.279</td><td>0.475</td><td>0.862</td><td>0.764</td><td>0.823</td><td>0.842</td></tr><tr><td>25</td><td>3</td><td>2.7</td><td>12</td><td>41</td><td>0.275</td><td>0.46</td><td>0.839</td><td>0.759</td><td>0.847</td><td>0.826</td></tr></tbody></table>

freedom is given by

$$k_L = 2|L| - \sum_{i=1}^{K^{\parallel, \perp}} (k_i^{\parallel, \perp} + 1) - \sum_{i=1}^{K^{\parallel}} (k_i^{\parallel} + 1) - \sum_{i=1}^{K^{--}} (k_i^{--} + 1) \quad (15)$$

where $K^{\parallel, \perp}$, $K^{\parallel}$ and $K^{--}$ correspond to the number of parallel groups which are also mutually orthogonal, the number of parallel groups which are not orthogonal to other groups, and the number of co-linear sub-groups inside all the parallel groups respectively. $k_i^{\parallel, \perp}$ is the number of line segments in the $i^{th}$ group of $K^{\parallel, \perp}$, $k_i^{\parallel}$ the number of line segments in the $i^{th}$ group of $K^{\parallel}$, and $k_i^{--}$ the number of line segments in the $i^{th}$ group of $K^{--}$.

Having a DoF score of 1 means that all line segments of the configuration are independent and not subject to regularity constraints. Note that a DoF score of 0 is not possible as, even in the case where all the line segments were mutually co-linear, at least one of the line-segment must be described by two parameters. In such a case, the minimal score would be $1/|L|$.

We compute the DoF score with a threshold of 0.5° for the predicted polygons. We filter out polygon edges on the tile boundary as they are not subject to regularity constraints of a polygon.

## A.3 Experimental setup

We perform data augmentation on the images and point clouds in the form of random horizontal and vertical flips, and random 90° rotations. We also apply random color jitter, brightness and contrast changes to the images. We train all models with a batch size of 16 and an initial learning rate of 0.0001. We use the Adam optimizer with a weight decay of 0.01 and a cosine annealing learning rate scheduler. We train on four NVIDIA V100 GPUs with 32GB VRAM each. Training takes between 20 and 30 hours for 200 epochs.

## A.4 Additional ablation studies

We conduct two more ablation studies on the Switzerland subset that investigate the impact of the GSD of the input images and the point density of the LiDAR point clouds on the performance of a FFL model.

**Image ground sampling distance** The original Switzerland data contains images with a GSD of 10 cm. We prepare a subset of the data with a GSD of 15 cm and compare the results with a model trained on images with a GSD of 25 cm. The GSD of 25 cm is the one used in our benchmark dataset. We train a FFL model with an image encoder and input images with a GSD of 15 and 25 cm. Tab. A.3 shows the results of the ablation study. The model trained on images with a GSD of 15 cm achieves better results on the area-based metrics while the one trained on images with 25 cm GSD achieves better results on all other metrics. We attribute this to the fact that the model trained on 15 cm GSD images has access to a smaller context window (see Sec. A.1).

**LiDAR point density** The point clouds from Switzerland have an average density between 11 and 17 pts/m². However, locally, the density can be much higher, e.g., on vertical features such as building walls. We train a FFL model with a LiDAR point encoder and input 1, 4, 16, 32, 64 and 128 pts/m². We achieve this by adapting the maximum number of points during the voxelization step in our point cloud encoder. Voxels with fewer points are upsampled to the maximum number of points, while voxels with more points are downsampled [25].
<figure><img src="image_5.png" /><figcaption>Figure A.1: **Ground sampling distance ablation.** We present a sample tile displaying predicted and ground truth building polygons from the Switzerland subset with different point densities. The models are trained on images with a GSD of 15 and 25 cm which leads to different input tiles and predictions.</figcaption></figure>

<table><caption>Table A.4: **Density ablation.** We compare a ViT [11] + FFL [14] model trained and tested on increasingly dense LiDAR point clouds. In the experiments in the main text, we use 16 pts/m² as the default density.</caption><thead><tr><th rowspan="2">Density [pts/m²]</th><th colspan="4">Boundary</th><th colspan="3">Area</th><th colspan="2">Complexity</th></tr><tr><th>POLIS [m] ↓</th><th>CD [m] ↓</th><th>HD [m] ↓</th><th>MTA [°] ↓</th><th>AP ↑</th><th>AR ↑</th><th>IoU ↑</th><th>C-IoU ↑</th><th>NR=1</th><th>DoF ↓</th></tr></thead><tbody><tr><td>1</td><td>2.77</td><td>2.24</td><td>11.2</td><td>48.2</td><td>0.293</td><td>0.487</td><td>0.847</td><td>0.714</td><td>0.78</td><td>0.868</td></tr><tr><td>4</td><td>2.55</td><td>2.03</td><td>10.1</td><td>46.5</td><td>0.34</td><td>0.519</td><td>0.865</td><td>0.746</td><td>0.812</td><td>0.869</td></tr><tr><td>16</td><td>2.35</td><td>1.94</td><td>9.66</td><td>44.8</td><td>0.359</td><td>0.545</td><td>0.87</td><td>0.765</td><td>0.829</td><td>0.866</td></tr><tr><td>32</td><td>2.23</td><td>1.85</td><td>9.2</td><td>43.1</td><td>0.363</td><td>0.553</td><td>0.874</td><td>0.774</td><td>0.838</td><td>0.859</td></tr><tr><td>64</td><td>2.17</td><td>1.83</td><td>9.07</td><td>41.9</td><td>0.373</td><td>0.56</td><td>0.877</td><td>0.785</td><td>0.849</td><td>0.859</td></tr><tr><td>128</td><td>2.21</td><td>1.9</td><td>9.24</td><td>41</td><td>0.362</td><td>0.56</td><td>0.876</td><td>0.783</td><td>0.846</td><td>0.842</td></tr></tbody></table>

Tab. A.4 shows that even a model trained with 1 pt/m² leads to a high mean IoU of 84.7%. This shows that even the sparse 3D information is sufficient to detect most buildings in our dataset. Increasing the point density until 64 pts/m² improves all metrics, i.e. it allows the model to predict more complete and accurate, but also simpler polygons, with a more accurate number of vertices compared to the ground truth. At 128 pts/m², the model performance starts to decline again for some of the metrics. We attribute this to the fact that only very few voxels have a density of 128 pts/m². Our point cloud encoder thus upsamples most voxels to this point density by duplicating existing points. This may lead to a slower convergence of the model and a less accurate prediction. Fig. A.2 visualizes the point clouds and predictions with different point densities. The model trained with 1 pt/m² is able to predict the building outlines, but the polygons are less accurate and more complex than the ones predicted with higher point densities. Higher point densities lead to more accurate and simpler polygons.

## A.5 Additional example predictions

**Failure case** We show a failure case of our dataset and baseline method in Fig. A.3. Here, the image and LiDAR data have a temporal mismatch. The image shows two newly constructed buildings, while

<figure><img src="image_6.png" /><figcaption>Figure A.2: **LiDAR density ablation.** We present a sample tile displaying predicted and ground truth building polygons from the Switzerland subset with different point densities. Only LiDAR points are used for the prediction.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure A.3: **Failure case.** We show a failure case of our dataset and baseline methods. Here, the image and LiDAR data have a temporal mismatch. The image shows two newly constructed buildings, while the LiDAR data is from a previous flight that shows buildings that are most likely demolished. The ground truth polygons align with the LiDAR data and not with the image. The predicted polygons from both LiDAR and image data are not accurate and do not match the ground truth.</figcaption></figure>

the LiDAR data is from a previous flight that shows buildings that are most likely demolished. The ground truth polygons align with the LiDAR data and not with the image. The predicted polygons from both LiDAR and image data are not accurate and do not match the ground truth. While this case is rare in our dataset, it shows that the models are not able to handle temporal mismatches between the image and LiDAR data.

**Modality ablation** We present additional example predictions for the modality ablation with the baseline methods on the Switzerland subset in Fig. A.4 and Fig. A.5.

**Multimodal building outline prediction** We present additional example predictions of the baseline methods on the full dataset in Fig. A.6 and Fig. A.7.

## A.6 Potential negative societal impacts

The limited availability of high resolution data across the globe introduces a bias in our dataset towards developed countries. Models trained on such data might not perform as well on underdevelopped, vulnerable or marginalized communities potentially leading them being overlooked in disaster response or aid distribution.

A potential misuse of models trained on such dataset is the surveillance and monitoring of certain areas and communities as well as planning of malicious activities.
<figure><img src="image_8.png" /><figcaption>Figure A.4: **Modality ablation 2.** We show an example tile of predicted and ground truth building polygons from the Switzerland subset. The first column shows ground truth polygons, and following columns show predicted polygons of the baseline models trained on different modalities, i.e. images only (first row), LiDAR only (second row), and both image and LiDAR data (third row). The tile shows a complex building due to a cutout and open roof structure. FFL and HiSup struggle to predict the building outline, while Pix2Poly is able to predict the building outline almost perfectly using image and LiDAR data.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure A.5: **Modality ablation 3.** We show an example tile of predicted and ground truth building polygons from the Switzerland subset. The first column shows ground truth polygons, and following columns show predicted polygons of the baseline models trained on different modalities, i.e. images only (first row), LiDAR only (second row), and both image and LiDAR data (third row). All models produce the best polygon predictions when trained on both modalities.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure A.6: **Multimodal polygon prediction 2.** We show ground truth and predicted building outlines from our full dataset, from Switzerland, New Zealand¹ and the USA (from top to bottom). Shown are input LiDAR point clouds on top of input aerial images. The first column shows the ground truth reference polygon. The second to fourth column show the predicted polygons from FFL [14], HiSup [41] and Pix2Poly [2] using both modalities.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure A.7: **Multimodal polygon prediction 3.** We show ground truth and predicted building outlines from our full dataset, from Switzerland, New Zealand¹ and the USA (from top to bottom). Shown are input LiDAR point clouds on top of input aerial images. The first column shows the ground truth reference polygon. The second to fourth column show the predicted polygons from FFL [14], HiSup [41] and Pix2Poly [2] using both modalities.</figcaption></figure>