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BuildingNet: Learning to Label 3D Buildings

10/11/2021
by   Pratheba Selvaraju, et al.
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We introduce BuildingNet: (a) a large-scale dataset of 3D building models whose exteriors are consistently labeled, (b) a graph neural network that labels building meshes by analyzing spatial and structural relations of their geometric primitives. To create our dataset, we used crowdsourcing combined with expert guidance, resulting in 513K annotated mesh primitives, grouped into 292K semantic part components across 2K building models. The dataset covers several building categories, such as houses, churches, skyscrapers, town halls, libraries, and castles. We include a benchmark for evaluating mesh and point cloud labeling. Buildings have more challenging structural complexity compared to objects in existing benchmarks (e.g., ShapeNet, PartNet), thus, we hope that our dataset can nurture the development of algorithms that are able to cope with such large-scale geometric data for both vision and graphics tasks e.g., 3D semantic segmentation, part-based generative models, correspondences, texturing, and analysis of point cloud data acquired from real-world buildings. Finally, we show that our mesh-based graph neural network significantly improves performance over several baselines for labeling 3D meshes.

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1 Introduction

Architecture is a significant application area of 3D vision. There is a rich body of research on autonomous perception of buildings, led in large part by digital map developers seeking rich annotations and 3D viewing capabilities for building exteriors [15], as well as roboticists who design robots to operate in building interiors (e.g.  [46]). Recent advances in AR/VR also rely on computer-aided building analysis [7]. Early work on digital techniques for architectural design, including freeform design explorations as well as full-fledged constructions [16], led to the current ubiquity of computational design tools in architectural studios. In addition, computers can automate the processing of architectural data such as photographs, satellite images and building plans, for archival and analytical purposes (e.g.  [63, 33]).

Thus, there is significant incentive to apply modern data-driven geometry processing to the analysis of buildings. However, while buildings are bona fide geometric objects with well-established design principles and clear ontologies, their structural and stylistic complexity is typically greater than, or at least markedly different from, those of shapes in common 3D datasets like ShapeNet [6] and ScanNet [11]. This makes them challenging for standard shape analysis pipelines, both for discriminative tasks such as classification, segmentation and point correspondences, as well as for generative tasks like synthesis and style transfer. Further, data-driven methods demand data, and to the best of our knowledge there are no large-scale, consistently-annotated, public datasets of 3D building models.

In this paper, we present BuildingNet, the first publicly available large-scale dataset of annotated 3D building models whose exteriors and surroundings are consistently labeled. The dataset provides K annotated mesh primitives across K building models. We include a benchmark for mesh and point cloud labeling, and evaluate several mesh and point cloud labeling networks. These methods were developed primarily for smaller single objects or interior scenes and are less successful on architectural data.

In addition, we introduce a graph neural network (GNN) that labels building meshes by analyzing spatial and structural relations of their geometric primitives. Our GNN treats each subgroup as a node, and takes advantage of relations, such as adjacency and containment, between pairs of nodes. Neural message passing in the graph yields the final mesh labeling. Our experiments show that this approach yields significantly better results for 3D building data than prior methods. To summarize, our contributions are:

  • [noitemsep,topsep=0pt,parsep=0pt,partopsep=0pt,leftmargin=22pt]

  • The first large-scale, publicly available 3D building dataset with annotated parts covering several common categories, in addition to a benchmark.

  • A graph neural network that leverages pre-existing noisy subgroups in mesh files to achieve state-of-the-art results in labeling building meshes.

  • An annotation interface and crowdsourcing pipeline for collecting labeled parts of 3D meshes, which could also extend to other categories of 3D data.

Figure 2: Our interface for labeling 3D building models. The colors of annotated components follow the legend in the middle (we show here a subset of labels - the UI contained 16 more labels in a more extended layout). Any components that have not been labeled so far are shown in shades of light yellow/green (e.g., balcony components). The UI displays instructions on top and offers functionality to facilitate labeling, such as automatic detection of repeated components (“find similar”), automatic grouping/un-grouping of components (“expand”/“shrink”), and auto-focusing on unlabeled ones (“find unlabeled parts”).

2 Related Work

3D shape semantic segmentation datasets.

Existing datasets and benchmarks for 3D shape semantic segmentation are limited to objects with relatively simple structure and small number of parts [8, 22, 19, 59, 37, 62]. The earliest such benchmark [8, 22] had objects with few labeled parts per shape. More recently, Uy et al. [53] released a benchmark with 15K scanned objects but focuses on object classification, with part-level segmentations provided only for chairs. The most recent and largest semantic shape segmentation benchmark of PartNet [62] contains objects in categories, such as furniture, tools, and household items. However, even with PartNet’s fine-grained segmentation, its categories still have a few tens of labeled parts on average. Our paper introduces a dataset for part labeling of 3D buildings, pushing semantic segmentation to much larger-scale objects with more challenging structure and several tens to hundreds of parts per shape.

3D indoor scene datasets.

Another related line of work has introduced datasets with object-level annotations in real-world or synthetic 3D indoor environments  [20, 1, 40, 47, 5, 11, 29, 64, 14]. In contrast, our dataset focuses on building exteriors, a rather under-investigated domain with its own challenges. While an indoor scene is made of objects, which are often well-separated or have little contact with each other (excluding floors/walls), a building exterior is more like a coherent assembly of parts (windows, doors, roofs) i.e., a single large shape with multiple connected parts, including surroundings (e.g., landscape). Building exteriors share challenges of single-shape segmentation (i.e., segment parts with clean boundaries along contact areas) as well as scene segmentation (i.e., deal with the large-scale nature of 3D data). Buildings also come in a variety of sizes, part geometry and style [32], making this domain challenging for both shape analysis and synthesis.

3D urban datasets.

With the explosion of autonomous driving applications, large-scale 3D point cloud datasets capturing urban environments have appeared [39, 17, 44, 2, 49]. These datasets include labels such as roads, vehicles, and sidewalks. Buildings are labeled as a single, whole object. Our dataset contains annotations of building parts, which has its own challenges, as discussed above. The RueMonge14 dataset contains 3D building frontal facades captured from a street in Paris with labels related to buildings [43]. Our buildings are instead complete 3D models with significantly more challenging diversity in geometry, style, function, and with more fine-grained part labels.

Deep nets for 3D mesh understanding.

A few recent neural architectures have been proposed for processing meshes. Some network directly operate on the mesh geometric or topological features  [34, 18, 27, 45], spectral domain [3, 38, 61, 42], while others transfer representations learned by other networks operating, e.g., on mesh views or voxels  [21, 56, 26]

. Our method is complementary to these approaches. It is specifically designed to process meshes with pre-existing structure in the form of mesh components (groups of triangles), which are particularly common in 3D building models. CRFs and various grouping strategies with heuristic criteria have been proposed to aggregate such components into labeled parts

[56]. Our method instead uses a GNN to label components by encoding spatial and structural relations between them in an end-to-end manner. From this aspect, our method is also related to approaches that place objects in indoor scenes using GNNs operating on bounding box object representations with simple spatial relations, [65, 54], and GNN approaches for indoor scene parsing based on graphs defined over point clusters [28]. Our GNN instead aims to label mesh components represented by rich geometric features, and captures spatial and structural relations specific to building exteriors.

3D Building Mesh Segmentation and Labeling.

There has been relatively little work in this area. Early approaches for semantic segmentation of buildings relied on shallow pipelines with hand-engineered point descriptors and rules [50, 51]. A combinatorial algorithm that groups faces into non-labeled components spanning the mesh with high repetition was proposed in [12]. A user-assisted segmentation algorithm was proposed in [13]. Symmetry has been proposed as a useful cue to group architectural components [25, 36]. Our method instead aims to label 3D building meshes with a learning-based approach based on modern deep backbones for extracting point descriptors. It also incorporates repetitions as a cue for consistent labeling, along with several other geometric and structural cues.

3 Building Data Annotation

We first discuss the procedure we followed to annotate 3D building models. In contrast to 3D models of small and mid-scale objects, such as tools, furniture, and vehicles encountered in existing 3D shape segmentation benchmarks, such as ShapeNet [59, 60] and PartNet [37], buildings tend to contain much richer structure, as indicated by their mesh metadata. For example, one common type of metadata are groupings of polygon faces, commonly known as mesh subgroups [37], which correspond to geometric primitives and modeling operations used by modelers while designing shapes. These subgroups often correspond to “pieces” of semantic parts e.g., a window is made of subgroups representing individual horizontal and vertical frame pieces or glass parts. The average number of mesh subgroups per object at the last level of group hierarchy in the largest shape segmentation benchmark (PartNet [37]) is , and the median is . In our dataset, the average number of mesh subgroups per building is x larger ( subgroups), while the median is x larger ( subgroups). We note that these numbers include only building exteriors i.e., without considering building interiors (e.g, indoor furniture). PartNet relied on mesh subgroups for faster annotation i.e., the annotators were manually clicking and grouping them into parts. Selecting each individual mesh subgroup in our case would be too laborious in the case of a large-scale 3D building dataset. To this end, we developed a user interface (UI) that followed the PartNet’s principles of well-defined and consistent labelings, yet its primary focus was to deal with the annotation of a massive number of mesh subgroups per building. In particular, our UI offers annotators the option of label propagation to similar subgroups based on both geometric and mesh metadata to enable faster labeling. Another focus was to achieve consensus across several trained crowdworkers annotating in parallel. To this end, we employed a majority voting process. We focused on crowdsourcing annotations for common part labels encountered in buildings. In the rest of this section, we describe our user interface (UI) for interactive labeling of 3D buildings (Section 3.1), and the dataset collection process (Section 3.2).

3.1 Interface for labeling

Our interface is shown in Figure 2. On the left window, we display the building with a distinct color assigned to each mesh subgroup. When a subgroup is annotated, it changes color from the default palette (shades of light green and yellow) to a predetermined, different color according to its label. On the right, we display the textured version of the building so that crowdworkers also access color cues useful for labeling. The workers have full 3D control of viewpoint (pan, zoom, rotate). Changes on the viewpoint are reflected in both windows. On the top of the interface, we provide instructions and links with examples of parts from real-world buildings for each label. The workers are asked to label the mesh subgroups through a sequence of questions e.g., “label all walls”, then “label all windows”, and so on. Alternatively, they can skip the questions, and directly select a desired part label from the list appearing in the middle of the UI. To perform an assignment of a currently selected label to a mesh subgroup, the workers simply right-click on it and press enter. Alternatively, they can select multiple subgroups and annotate them altogether. All adjacent subgroups with the same label are automatically merged into a single labeled component to decrease the workload of manual merging. We note that we considered the possibility of incorporating mesh cutting tools to split large subgroups into smaller ones for assigning different labels, as done in PartNet [37]. However, such tools require reconstruction into watertight meshes, which could not be achieved for most building subgroups due to their non-manifold geometry, disconnected or overlapping faces, and open mesh boundaries. For the majority of buildings in our dataset, we observed that each subgroup can be assigned with a single part label without requiring further splits. Annotators were also instructed not to label any (rare) subgroups that contained parts with different labels.

Figure 3: Label propagation to repeated subgroups (top) or their parents (bottom). Initially selected subgroup is in white.

Clicking individual mesh subgroups for assigning part labels can be still cumbersome, since buildings have hundreds or thousands of them. Our UI takes advantage of the fact that buildings often have repeated mesh subgroups e.g., the same window mesh is re-used multiple times in a facade during 3D modeling. Thus, in a pre-processing step, we found all duplicate mesh subgroups by checking if they have the same mesh connectivity (mesh graph) and vertex locations match after factoring out rigid transformations. Details about duplicate detection are provided in the supplementary material (see Appendix A included after the references). Workers are then given the option to select all subgroup duplicates and propagate the same label to all of them at once, as shown in Figure 3(top). Another UI feature was to allow users to “expand” a mesh subgroup selection by taking advantage of any hierarchical grouping metadata. This expansion was performed by iteratively moving one level up in the mesh group hierarchy and finding all subgroups sharing the same parent with the initially selected subgroup, as shown in Figure 3(bottom). We refer readers to our supplementary video (see our project website) showing a tutorial with details of our UI operations.

Category  num#  avg#  med#  min#  max#  avg# un.
 models  subgrps  subgrps  subgrps  subgrps  subgrps
Residential 1,424 678.7 547 83 1989 167.1
 Commercial 153 723.4 606 90 1981 159.8
Religious 540 487.0 348 93 1981 139.9
Civic 67 628.8 480 118 1822 144.4
Castles 85 609.8 485 125 1786 193.0
Whole Set 2,000  623.6 497.5 83 1989 160.5
Table 1: Statistics per building category. From left to right: building category, total number of models, average/median/minimum/maximum number of mesh subgroups per model, average number of unique subgroups.

3.2 Dataset and Benchmark

To create our dataset, we mined building models from the 3D Warehouse repository [52]. Mining was driven by various quality checks e.g., excluding low-poly, incomplete, untextured meshes, and meshes with no or too few subgroups. We also categorized them into basic classes following the Wikipedia’s article on “list of building types” [58] and an Amazon MTurk questionnaire. Since we aimed to gather annotations of building exteriors, during a pre-processing step we removed interior structure from each building. This was done by performing exhaustive ray casting originating from mesh faces of each subgroup and checking if the rays were blocked. We also used ray casting to orient faces such that their normals are pointing outwards [48]

. Details about mining, classifying, and pre-processing of the 3D models are given in our supplement.

Part labels.

To determine a set of common labels required in our UI to annotate building exteriors, we launched an initial user study involving a small subset of buildings across all classes and participants with domain expertise (graduate students in civil engineering and architecture). For this study, we created a variant of our UI asking users to explicitly type tags for mesh subgroups. We selected a list of frequently entered tags to define our label set (see Table 2 and Appendix B of our supplement for details).

Annotation procedure.

One possibility to annotate building parts would be to hire “professionals” (e.g., architects). Finding tens or hundreds of such professionals would be extremely challenging and costly in terms of time and resources. In an early attempt to do so, we found that consistency was still hard to achieve without additional verification steps and majority voting. On the other hand, hiring non-skilled, non-trained crowdworkers would have the disadvantage of gathering erroneous annotations. We instead proceeded with a more selective approach, where we identified crowdworkers after verifying their ability to conduct the annotation task reliably based on our provided tutorial and instructions. During our worker qualification stage, we released our UI on MTurk accessible to any worker interested in performing the task. After a video tutorial, including a web page presenting real-world examples of parts per label, the workers were asked to label a building randomly selected from a predetermined pool of buildings with diverse structure and part labels. We then checked their labelings, and qualified those workers whose labeling was consistent with our instructions. We manually verified the quality of their annotations. Out of participants, workers qualified. After this stage, we released our dataset only to qualified MTurkers. We asked them to label as many parts as they can with a tiered compensation to encourage more labeled area (ranging from for labeling minimum of the building area to for labeling ). Out of the qualified MTurkers, accepted to perform the task in this phase. Each qualified MTurker annotated buildings and each annotation took min on average.

Dataset.

We gathered annotations for K buildings. Each building was annotated by different, qualified MTurkers (K annotations in total). We accepted a label for each subgroup if a majority of at least MTurkers out of agreed on it. The inlet figure shows a histogram displaying the distribution of buildings (vertical axis) for different bins of percentage of surface area labeled with achieved majority (horizontal axis). All buildings in our dataset have labeled area more than , and most have area labeled. In terms of annotator consistency, i.e., the percentage of times that the subgroup label selected by a qualified MTurker agreed with the majority, we found that it is , indicating that the workers were highly consistent. Our resulting 2K dataset has annotated mesh subgroups, and annotated components (after merging adjacent subgroups with the same label). The number of unique annotated subgroups and components are and respectively. Table 9 presents subgroup statistics for each basic building category. Table 2 shows labeled component statistics per part label. We include more statistics in the supplement.

Label # labeled # in training # in validation # in test
 comp. split (%) split (%) split (%)
Window 140,972 109,218 (47.8%) 15,740 (55.1%) 16,014 (46.0%)
Plant 26,735 20,974 (9.2%) 1,870 (6.5%) 3,891 (11.2%)
Wall 22,814 18,468 (8.1%) 2,270 (7.9%) 2,076 (6.0%)
Roof 12,881 10,342 (4.5%) 1,396 (4.9%) 1,143 (3.3%)
Banister 13,954 9,678 (4.2%) 1,467 (5.1%) 2,809 (8.1%)
Vehicle 8,491 7,421 (3.2%) 716 (2.5%) 354 (1.0%)
Door 9,417 7,363 (3.2%) 785 (2.7%) 1,269 (3.6%)
Fence 5,932 5,637 (2.5%) 88 (0.3%) 207 (0.6%)
Furniture 6,282 5,000 (2.2%) 575 (2.0%) 707 (2.0%)
Column 6,394 4,870 (2.1%) 623 (2.2%) 901 (2.6%)
Beam 6,391 4,814 (2.1%) 437 (1.5%) 1,140 (3.3%)
Tower 4,478 3,873 (1.7%) 286 (1.0%) 319 (0.9%)
Stairs 4,193 2,960 (1.3%) 472 (1.7%) 761 (2.2%)
Shutters 2,275 1,908 (0.8%) 77 (0.3%) 290 (0.8%)
Ground 2,057 1,572 (0.7%) 229 (0.8%) 256 (0.7%)
Garage 1,984 1,552 (0.7%) 182 (0.6%) 250 (0.7%)
Parapet 1,986 1,457 (0.6%) 153 (0.5%) 376 (1.1%)
Balcony 1,847 1,442 (0.6%) 199 (0.7%) 206 (0.6%)
Floor 1,670 1,257 (0.5%) 205 (0.7%) 208 (0.6%)
Buttress 1,590 1,230 (0.5%) 53 (0.2%) 307 (0.9%)
Dome 1,327 1,098 (0.5%) 114 (0.4%) 115 (0.3%)
Path 1,257 1,008 (0.4%) 113 (0.4%) 136 (0.4%)
Ceiling 1,193 903 (0.4%) 111 (0.4%) 179 (0.5%)
Chimney 1,090 800 (0.4%) 103 (0.4%) 187 (0.5%)
Gate 827 737 (0.3%) 65 (0.2%) 25 (0.1%)
Lighting 921 702 (0.3%) 51 (0.2%) 168 (0.5%)
Dormer 798 601 (0.3%) 48 (0.2%) 149 (0.4%)
Pool 742 544 (0.2%) 78 (0.3%) 120 (0.3%)
Road 590 444 (0.2%) 55 (0.2%) 91 (0.3%)
Arch 524 393 (0.2%) 11 (0.03%) 120 (0.3%)
Awning 386 295 (0.1%) 19 (0.1%) 72 (0.2%)
Total 291,998 228,561 28,591 34,846
Table 2: Number of labeled components per part label in our dataset, along with their number and frequency in the training split, hold-out validation, and test split.

Splits.

We split our dataset into buildings for training, for validation, for testing ( proportion). The dataset has no duplicate buildings. We created the splits such that (a) the distribution of building classes and parts is similar across the splits (Table 2 and supplementary) and (b) test buildings have high majority-labeled area () i.e., more complete labelings for evaluation.

Tracks.

We provide two tracks in our benchmark. In the first track, called “BuildingNet-Mesh”, algorithms can access the mesh data, including subgroups. In this aspect, they can take advantage of any pre-existing mesh structure common in 3D building models. The algorithms are evaluated in two conditions: when the RGB texture is available, and when it is not. In the second condition, algorithms must label the building using only geometric information. The second track, called “BuildingNet-Points”, is designed for large-scale point-based processing algorithms that must deal with unstructured point cloud data without access to mesh structure or subgroups, which is still challenging even in the noiseless setting. To this end, for each mesh, we sample points with Poisson disc sampling, to achieve a near-uniform sampling similarly to PartNet [37]. The point normals originate from triangles. There are also two evaluation conditions: with and without RGB color for points.

4 Building GNN

We now describe a graph neural network for labeling 3D meshes by taking advantage of pre-existing mesh structure in the form of subgroups. The main idea of the network is to take into account spatial and structural relations between subgroups to promote more coherent mesh labeling. The input to our network is a 3D building mesh with subgroups , where is the number of subgroups, and the output is a label per subgroup. In the next section, we describe how the graph representing a building is created, then we discuss our GNN architecture operating on this graph.

Graph Nodes.

For each 3D building model, we create a node for each mesh subgroup. Nodes carry an initial raw representation of the subgroup. Specifically, we first sample the mesh with 100K points (same point set used in the “BuildingNet-Points” track), then process them through the 3D sparse convolutional architecture of Minkowski network (MinkowskiUNet34 variant [9]). We also experimented using PointNet++ [41]. We extract per-point features from the last layer of these nets, then perform average pooling over the points originating from the faces of the subgroup to extract an initial node representation. We concatenate this representation with the 3D barycenter position of the subgroup, its mesh surface area, and the coordinates of the opposite corners of its Oriented Bounding Box (OBB) so that we capture its spatial dimensions explicitly. The combination of the above features in the resulting D node representation yielded better performance in our experiments.

Proximity edges.

Driven by the observation that nearby subgroups tend to have the same label (e.g., adjacent pieces of glass or frame are labeled as “window”), or related labels (e.g., windows are often adjacent to walls), we create edges for pairs of subgroups that capture their degree of proximity. To avoid creating an overly dense graph, which would pose excessive memory overheads for the GNN, we created edges for pairs of subgroups whose distance was up to of the average of their OBB diagonals. Relaxing this bound did not improve results. To avoid a hard dependency on a single threshold, and to capture the degree of subgroup proximity at multiple scales, we computed the percentage of point samples of each subgroup whose distance to the other subgroup is less than , , , and of the average of their OBB diagonals. Given a pair of subgroups , this results in a edge raw representation , where each entry approximates the surface area percentage of proximal to at a different scale. Similarly, we compute a representation for the opposite edge direction.

Support edges.

Certain arrangements of labels are often expected along the upright axis of the building e.g., the roof is on top of walls. We create a “supporting” edge for each subgroup found to support another subgroup, and “supported-by” edges of opposite direction for each subgroup found to be supported by another subgroup. The edges are created by examining OBB spatial relations. Specifically, as in the case of proximity edges, we compute a multi-scale 4D edge raw representation measuring the area percentage of ’s bottom OBB face lying above the ’s top OBB face for different distances , , , of the average of the two OBB’s heights. We also compute a 4D edge raw representation corresponding to the the surface area percentage of ’s top OBB face lying beneath the ’s bottom OBB face.

Similarity edges.

Subgroups placed under a symmetric arrangement often share the same label (e.g., repeated windows along a facade). We create an edge per pair of subgroups capturing repetition. For each pair of subgroups, we compute the bidirectional Chamfer distance between their sample points after rigid alignment. To promote robustness to any minor misalignment, or small geometric differences between subgroups, we create similarity edges if the Chamfer distance is less than of the average of their OBB diagonals. Increasing this bound did not improve results. We normalize it within where corresponds to the above upper bound, and use as raw similarity edge representation. We also use the same representation for this opposite direction: .

Containment edges.

Driven by the observation that parts, such as doors or windows, are enclosed by, or contained within other larger parts, such as walls, we create edges for pairs of subgroups capturing their degree of containment. For each pair of subgroups, we measure the amount of ’s volume contained within the ’s OBB and also their volume Intersection over Union as a 2D edge representation (and similarly for the opposite edge direction).

Figure 4: Architecture of the message passing layer. The door representation (blue node) is updated from a support edge (yellow edge) to a roof component (red node) and a proximity edge (orange edge) to a window (purple node).

Network architecture.

The network updates node and edge representations at each layer inspired by neural message passing [24]. Figure 4 shows one such layer of message passing. Below we explain our architecture at test time.

Initialization.

Given a pair of subgroups and , we first concatenate their edge representations across all types:

We note that some of the edge types might not be present between two subgroups based on our graph construction. The entries of our edge representations indicate degree of proximity, support, containment, or similarity, and are normalized between by definition. Zero values for an edge representation of a particular type indicate non-existence for this type. Each raw edge representation is initially processed by a MLP to output a learned representation , where are learned MLP parameters. The initial node representation is .

Node and edge updates.

Each of the following layers process the node and edge representations of the previous layer through MLPs and mean aggregation respectively:

where are learned MLP parameters. We use

layers of node/edge updates. Finally, the last GNN layer processes the node representations of the third layer, and decodes them to a probability per label using a MLP and softmax. Details about the architecture are in the supplement.

Training loss.

Since some parts are more rare than others, as shown in Table 2, we use a weighted softmax loss to train our network, where weights are higher for rarer parts to promote correct labeling for them (i.e., higher mean Part IoU). For each building, the loss is , where is the set of all annotated subgroups in the building,

is the ground-truth one-hot label vector for subgroup

, is its predicted label probabilities, and is the weight for the label empirically set to be the log of inverse label frequency (i.e., a smoothed version of inverse frequency weights similarly to [35]). We use the same loss to train the MinkowskiNet used in our node representation: the loss is simply applied to points instead of subgroups. We experimented with other losses, such as the focal loss [30] and the class-balanced loss [10], but we did not find significant improvements in our dataset (see supplementary material).

Implementation details.

Training of the BuildingGNN is done through the Adam optimizer [23] with learning rate , beta coefficients are and weight decay is set to . We pick the best model and hyper-parameters based on the performance in the holdout validation split.

5 Results

Figure 5: Comparisons with other methods. Despite a few errors (red text), the BuildingGNN is closer to human annotations.

We now discuss our evaluation protocol, then show qualitative and quantitative results for our benchmark tracks.

Evaluation protocol.

Since most part classes are commonly encountered across different building categories (e.g., walls, doors, windows), all evaluated methods are trained across all five building categories (i.e., no category-specific training). Methods must also deal with the part class imbalance of our dataset. For evaluation in the point cloud track (“BuildingNet-Points”), we use the metrics of mean shape IoU and part IoU, as in PartNet [37]. We also report the per-point classification accuracy. For the mesh track (“BuildingNet-Mesh”), the same measures are applied on triangles. However, since triangles may differ in area, we propose the following IoU variations, where the contribution of each triangle is weighted by its face area. Given all the annotated triangles across all buildings of the test dataset , the part IoU for a label is measured as:

where is the majority-annotated (ground-truth) label for a triangle , is the predicted label for it, and evaluates the above binary expressions. The shape IoU for a shape with a set of annotated triangles is measured as:

where is the set of all labels present in the annotations or predictions for that shape. We also report the per-triangle classification accuracy weighted by face area [22].

“BuildingNet-Points” track.

As an initial seed for the leaderboard of this track, we evaluated three popular nets able to handle our point sets: PointNet++ [41], MID-FC [55], and MinkowskiUNet34 [9]. We also tried other point-based networks e.g., DGCNN [57], but were unable to handle large point clouds due to excessive memory requirements (see our supplementary material for more discussion). All networks were trained under the same augmentation scheme (12 global rotations per building and small random translations). For all networks, we experimented with SGD, Adam [23], with and without warm restarts [31]

, and selected the best scheduler and hyperparameters for each of them based on the validation split. We did not use any form of pre-training. Table

3 reports the results. We observe that the MinkowskiNet offers the best performance. We also observe that the inclusion of color tends to improve performance e.g., we observe a increase in Part IoU for MinkowskiNet. Another observation is that compared to PartNet classes, where the Part IoU ranges between for PointNet++, the performance in our dataset is much lower: PointNet++ has Part IoU. Even for the best performing method (MinkowskiNet), the part IoU is still relatively low (), indicating that our building dataset is substantially more challenging.

Method ? ? Part IoU Shape IoU Class acc.
PointNet++ 8.8% 12.2% 52.7%
MID-FC(nopre) 20.9% 19.0% 59.4%
MinkNet 26.9% 22.2% 62.2%
PointNet++ 14.1% 16.7% 59.5%
MID-FC(nopre) 25.0% 22.3% 63.2%
MinkNet 29.9% 24.3% 65.5%
Table 3: “BuildingNet-Point” track results. The column ‘?’ means whether networks use point normals, and the column ‘?’ means whether they use RGB color as input.

“BuildingNet-Mesh” track.

For our mesh track, we first include a number of baselines which rely on networks trained on the point cloud track, then transferring their results to meshes. One strategy for this transfer is to build correspondences between mesh faces and nearest points. Specifically, for each point we find its nearest triangle. Since some triangles might not be associated with any points, we also build the reverse mapping: for each triangle, we find its closest point. In this manner, every triangle has a set of points assigned to it with the above bi-directional mapping. Then we perform average pooling of the point probabilities per triangle: where and are point and triangle probabilities respectively. We report results of these baselines in Table 4

. We note that we tried max pooling, yet average pooling had better performance (see supplement). Another strategy is to aggregate predictions based on mesh subgroups instead of triangles i.e., average probabilities of points belonging to each subgroup. This strategy takes advantage of mesh structure and improves results. Another baseline is Graph Cuts (GC) on the mesh, which has been used in mesh segmentation

[22] (see supplement for the GC energy). Finally, we report results from our GNN (“BuildingGNN”), using PointNet++ or MinkowskiNet node features. The BuildingGNN significantly improves the respective baselines e.g., with color as input, BuildingGNN with PointNet++ features improves Part IoU by over the best PointNet++ variant, while BuildingGNN with MinkowskiNet features improves Part IoU by over the best MinkowskiNet variant. The BuildingGNN with MinkowskiNet features performs the best with or without color. Our supplement includes an ablation study showing that each edge type in the BuildingGNN improves performance over using node features alone, while the best model is the one with all edges.

Method ? ?  Part IoU Shape IoU Class acc.
 PointNet++2Triangle 8.8% 13.1% 54.7%
MidFC2Triangle 23.1% 22.1% 42.9%
MinkNet2Triangle 28.8% 26.7% 64.8%
PointNet++2Sub 9.5% 16.0% 57.9%
MidFC2Sub 26.4% 28.4% 46.2%
MinkNet2Sub 33.1% 36.0% 69.9%
MinkNet-GC 29.9% 28.3% 66.0%
BuildingGNN-PointNet++ 29.0% 33.5% 67.9%
BuildingGNN-MinkNet 40.0% 44.0% 74.5%
PointNet2Triangle 14.0% 18.0% 60.7%
MidFC2Triangle 27.3% 26.2% 45.6%
MinkNet2Triangle 32.8% 29.2% 68.1%
PointNet2Sub 16.1% 23.5% 64.8%
MidFC2Sub 30.3% 33.1% 48.6%
MinkNet2Sub 37.0% 39.1% 73.2%
MinkNet-GC 33.8% 31.1% 68.9%
BuildingGNN-PointNet++ 31.5% 35.9% 73.9%
BuildingGNN-MinkNet 42.6% 46.8% 77.8%
Table 4: “BuildingNet-Mesh” results. PointNet++2Triangle means triangle-pooling with PointNet++ (similarly for others). PointNet2Sub means subgroup-pooling. MinkNet-GC means graph cuts with MinkowskiUNet34 unary terms.

Qualitative results.

Figure 5 shows comparisons of BuildingGNN with other methods. We observe that its predictions are closer to human annotations compared to others. Figure 1 presents more results from BuildingGNN.

6 Discussion

We presented the first large-scale dataset for labeling 3D buildings and a GNN that takes advantage of mesh structure to improve labeling. A future avenue of research is to automatically discover segments in point clouds and embed them into a GNN like ours. Currently, edges are extracted heuristically. Learning edges and features in an end-to-end manner may improve results. Finally, mesh cutting and hierarchical labeling can lead to richer future dataset versions.

Acknowledgements.

We thank Rajendra Adiga, George Artopoulos, Anastasia Mattheou, Demetris Nicolaou for their help. Our work was funded by Adobe, NSF (CHS-1617333), the ERDF and the Republic of Cyprus through the RIF (Project EXCELLENCE/1216/0352), and the EU H2020 Research and Innovation Programme and the Republic of Cyprus through the Deputy Ministry of Research, Innovation and Digital Policy (Grant Agreement 739578).

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– Supplementary Material –

Appendix A: Building collection

Mining building models.

We used the Trimble 3D Warehouse repository [52] to mine 3D building models. Specifically, we used keywords denoting various building categories, following a snapshot from Wikipedia’s article on “list of building types” [58]. The article contained common building types, such as “house”, “hotel”, “skyscraper”, “church”, “mosque”, “city hall”, “castle”, “office building”, and so on, organized into basic categories, such as residential, commercial, industrial, agricultural, military, religious, educational, and governmental buildings. For each keyword, we retrieved the first models. Since some keyword searches returned much fewer buildings, and since identical models were retrieved across different searches (e.g., a building can have both tags “house” and “villa”), we ended up with models. The models were stored in the COLLADA file format.

Mesh-based filtering.

Low-poly meshes often represent low-quality or incomplete buildings, and they often cause problems in rendering and geometry processing. Thus, we removed models with less than faces and also removed models with extremely large number of faces (more than faces) that tend to significantly slow down mesh processing and rendering for interactive segmentation (total models removed). Since our UI relies on labeling mesh subgroups (submeshes) stored in the leaf nodes of the COLLADA hierarchy, we excluded under-segmented models with less than mesh subgroups, and over-segmented models with more than mesh subgroups, which would be more challenging to label (total models removed). As a result, the filtered dataset contained models.

Crowdworker-based filtering.

The above keyword searches can be affected by noisy metadata, such as erroneous and irrelevant tags not describing the actual shape class. As a result, most of the retrieved models did not represent buildings. Some models also contained entire neighborhoods or multiple buildings. Thus, our next step was to filter 3D models that did not represent single buildings. We resorted to crowdworkers from Amazon Mechanical Turk (MTurk) to verify whether each model is a single building or not, and also classify it into basic categories following Wikipedia’s categorization. To this end, we created web questionnaires showing each model from four viewpoints with elevation degrees from the ground plane, and azimuth difference degrees. We asked MTurk participants (MTurkers) to select a category that best describe the model (see Figure 6 for an example of rendered views, and basic categories we used). We instructed them to answer “can’t tell” if the displayed model did not represent a single building, or when they could not recognize it.

Each participant was asked to complete a questionnaire with queries randomly picked from our filtered set of models. Each query showed one model (Figure 6). Queries were shown in a random order. Each query was repeated twice in the questionnaire in a random order to detect unreliable participants providing inconsistent answers (i.e., we had unique queries per questionnaire). We filtered out unreliable MTurk participants who gave two inconsistent answers to more than out of the unique queries in the questionnaire. Each participant was allowed to answer one questionnaire at most to ensure participant diversity. We had total different, reliable MTurk participants in this study. For each of the models, we gathered consistent votes from different MTurk participants. We accepted a building category for a model, if it was voted by at least out of MTurkers. We note that this majority is statistically significant: given categories, the probability of a model getting out of votes given random answers is negligible according to a binomial test (). We removed models lacking majority votes (i.e., they were not buildings, or the category could not be determined with high agreement).

The categories “agricultural”, “industrial”, “stadium” had less than buildings, thus, we decided to exclude them since their part variability and corresponding labels, would not be sufficiently represented in training, validation, and test splits of the segmentation dataset. We also decided to merge the “educational” and “governmental” buildings into a single broader category, called “civic” buildings commonly used to characterize both types of buildings, since we observed that the exterior of a governmental building (e.g., town hall) is often similar to the exterior of an educational one (e.g., public library or college). The remaining number of models characterized as buildings from our study was . We note that all models in our dataset are stored as COLLADA files, and have hierarchy tree depth (excl. the root). We refer the reader to Table 5 for statistics per basic category in our dataset and its splits.

Category  #orig.  #label.   # train. #  val.  # test
 build.  build. (%) (%) (%)
Residential 1424 1266 1007 (62.9%) 133 (66.5%) 126 (63.0)%
Commercial 153 131 104 (6.5%) 16 (8.0%) 11 (5.5%)
Religious 540 469 386 (24.1%) 38 (19.0%) 45 (22.5%)
Civic 67 61 45 (2.8%) 8 (4.0%) 8 (4.0%)
Castles 85 73 58 (3.6%) 5 (2.5%) 10 (5.0%)
Total: 2286 2,000 1600 (80%) 200 (10%) 200 (10%)
Table 5: From left to right: number of models per basic building category after filtering (original buildings), number of buildings whose parts were labeled by crowdworkers in our dataset (labeled buildings), number and percentage of training, hold-out validation and test buildings

Mesh pre-processing.

The meshes in the above dataset were pre-processed to (a) detect and remove interior structure for each building (since we aimed to gather annotations of building exteriors), (b) detect exact duplicates of subgroups useful for label propagation, as discussed in Section 3.1 (interface for labeling) in our main paper. To detect whether a subgroup is interior, we sample points per each triangle in the subgroup and shoot rays to external viewpoints from all these sample points. If a single ray escapes from the subgroup, it is marked as external, otherwise it is internal. We remove all subgroups marked as internal. For duplicate detection, we process all-pairs of subgroups in a building. Specifically, for each pair of subgroups, we exhaustively search for upright axis rotations minimizing Chamfer distance. The optimal translation is computed from the difference of the vertex location barycenters. After factoring out the rigid transformation, we compute one-to-one vertex correspondences based on closest pairs in Euclidean space. If all closest pairs have distance less than of the average OBB diagonals of the subgroups, we also check if their mesh connectivity matches i.e., the subgroup mesh adjacency matrix is the same given the corresponding vertices. If they match, the pair is marked as duplicate. Finally, all such pairs are merged into sets containing subgroups found to be duplicates of each other.

Appendix B: Part labels

To determine a set of common labels used to identify parts in buildings, we created a variant of our UI that asked users to explicitly type tags for selected components instead of selecting labels from a predefined list. We gathered tags from people who have domain expertise in the fields of building construction or design. Specifically, we asked graduate students in civil engineering and architecture to tag components in a set of

buildings uniformly distributed across the different categories. Each student labeled

- different buildings. We selected tags that appeared at least in of the labeled components to filter out uncommon tags. We concatenated the remaining tags with the most frequent tags appearing in the COLLADA leaf nodes (appearing at least in of subgroups). We merged synonyms and similar tags.

The resulting list had tags. During the main phase of annotation of our 2K buildings, tags were used very sparsely: less than subgroups throughout the dataset were annotated with these tags: “ramp”, “canopy”, “tympanum”, “crepidoma”, “entablature”, “pediment”, “bridge”, and “deck”. We decided them to exclude them from our dataset since the number of train or test subgroups with these labels would be too low (less than , or they existed in only one building). Any subgroups annotated with these tags were considered as “unlabeled” (undetermined) ones.

Category  avg. #  med. #  avg. #  med. #
faces faces  vertices  vertices
Residential 58,522.7 32,295.5 18,830.6 10,684.0
Commercial 49,248.5 28,862.0 16,722.6 10,041.0
Religious 51,882.7 25,979.0 16,687.4 8,654.0
Civic 40,380.1 20,512.0 13,910.2 7,281.0
Castles 70,731.2 26,493.0 21,050.0 8,822.0
Whole Set 56,250.4 29,741.5 18,120.9 9,845.0
Table 6: Statistics regarding mesh resolution in our dataset. From left to right: building category, average/median number of faces and vertices.

Appendix C: Additional dataset statistics

As discussed in our main paper, we gathered annotations from qualified MTurkers for buildings ( annotations per building). Table 6 shows statistics on the polygon resolution of the meshes in our 2K dataset. Table 7 reports the worker consistency per part label, which is measured as the percentage of times that a subgroup label selected by a qualified MTurker agrees wit the majority. Table 8 reports the worker consistency per building category for the training, hold-out validation, and test split. We observe that the worker consistency remains similar across all splits and building categories.

Table 9 reports statistics on the number of subgroups per building category, unique subgroups (counting repeated subgroups with exactly the same mesh geometry as one unique subgroup), and number of annotated subgroups. We note that there were often subgroups that represented tiny, obscure pieces (e.g., subgroups with a few triangles covering a tiny area of a wall, beam, or frame), and these were often not labeled by annotators. As we explained in the main paper, most of the buildings had more than of their area labeled (and all had labeled area). Table 10 presents more statistics on the labeled components (merged, adjacent subgroups with the same label) of the building dataset per each basic category.

Label Worker consistency
Window 93.4%
Plant 98.7%
Wall 88.2%
Roof 88.7%
Banister 86.5%
Vehicle 99.2%
Door 84.9%
Fence 85.9%
Furniture 95.1%
Column 87.2%
Beam 76.3%
Tower 81.4%
Stairs 92.0%
Shutters 79.3%
Ground 84.8%
Garage 86.9%
Parapet 82.6%
Balcony 75.9%
Floor 79.1%
Buttress 85.0%
Dome 83.5%
Corridor 70.6%
Ceiling 78.4%
Chimney 93.3%
Gate 90.8%
Lighting 90.9%
Dormer 70.4%
Pool 86.8%
Road 73.8%
Arch 72.1%
Awning 59.5%
Table 7: Worker consistency for each different part label.
Worker Consistency
Category train. val. test all
Residential 92.2% 93.3% 91.5% 92.2%
Commercial 87.7% 89.4% 95.1% 88.6%
Religious 91.4% 91.7% 91.7% 91.5%
Civic 93.6% 98.8% 98.0% 94.9%
Castles 94.1% 88.8% 88.3% 92.9%
Average: 91.8% 92.4% 92.9% 92.0%
Table 8: Worker consistency in the training, hold-out validation, test split, and our whole dataset per category.
Category  num#  avg#  med#  min#  max#  avg# un.  med# un.  min# un.  max# un.  avg# un.  med# un.  min# un.  max# un.
 models  subgrps  subgrps  subgrps  subgrps  subgrps  subgrps  subgrps  subgrps  l.subgrps  l.subgrps  l.subgrps  l.subgrps
Residential 1,424 678.7 547 83 1989 167.1 144 61 920 61.4 50.0 7 613
 Commercial 153 723.4 606 90 1981 159.8 139 70 907 49.4 44.0 3 223
Religious 540 487.0 348 93 1981 139.9 129 65 667 47.2 45.0 7 139
Civic 67 628.8 480 118 1822 144.4 123 75 618 43.0 43.0 8 106
Castles 85 609.8 485 125 1786 193.0 166 76 590 38.6 37 2 92
Whole Set 2,000  623.6 497.5 83 1989 160.5 140 61 920 55.9 47.0 2 613
Table 9: Statistics for each building category. From left to right: building category, total number of models, average/median/minimum/maximum number of mesh subgroups over the category’s models (leaf nodes of the COLLADA metadata of the building models), average/median/minimum/maximum number of unique (non-duplicate) subgroups, average/median/minimum/maximum number of annotated unique mesh subgroups.
Category  num#  avg#  med#  min#  max#  avg# un.  med# un.  min# un.  max# un.
 models  l.comp.  l.comp.  l.comp.  l.comp.  l.comp.  l.comp.  l.comp.  l.comp.
Residential 1,424 321.8 243.0 13 1970 46.1 42.0 8 371
 Commercial 153 408.0 296.0 4 1680 44.6 39.0 3 247
Religious 540 272.2 184.0 18 1469 37.7 35.0 6 135
Civic 67 378.4 263.0 36 1667 39.3 33.0 7 252
Castles 85 295.3 210.0 40 1200 30.5 28.0 2 107
Whole Set 2,000  316.6 231.0 4 1970 43.2 39.0 2  371
Table 10: Statistics per building category regarding components (merged adjacent mesh subgroups). From left to right: building category, total number of models, average/median/minimum/maximum number of annotated components per model, average/median/minimum/maximum number of annotated unique (non-duplicate) components per model.

Appendix D: Network and experiments details

BuildingGNN.

We provide more details about the structure of the BuildingGNN network architecture in Table 11. Table 12 presents statistics on the number of edges per type used in BuildingGNN for our training set.

Layers Output
Edge (MLP(1141, layer=1)))
Node (6D(OBB)+1D(SA)+3D(C)+31D(MN)
Input ( + + )
Encoder (MLP(Input256, layer=1)))
GN(LeakyReLU(0.2)))
(MLP(64*3128, layer=3)))
GN(LeakyReLU(0.2)))
(MLP(64*3128, layer=5)))
GN(LeakyReLU(0.2)))
Decoder (MLP(12864, layer=1)))
softmax
Table 11: BuildingGNN architecture: The Node representation combines the OBB - (Object Oriented Bounding Box) , SA - (Surface area), C - (centroid) and MN - (MinkowskiNet pre-trained features) for each sub group. The GNN is composed of (a) an encoder block made of three MLPs having 1, 3 and 5 hidden layers respectively, and (b) a decoder block with one MLP having 1 hidden layer followed by softmax. We refer to the code for more details.
Label max # min # mean # # median
 edges edges edges edges
Proximity 16317 81 778.0 489.0
Similarity 762156 5 26452.1 4875.5
Containment 26354 71 2,054.5 1,390.0
Support 7234 7 687.5 492.0
All 772878 259 29972.1 7818.0
Table 12: Statistics for the number of BuildingGNN edges per type present in the graphs of the training buildings.

MinkNet-GC.

As mentioned in the experiments section of our main paper, we implemented a simple graph-cuts variant, called MinkNet-GC, that incorporates label probabilities from MinkowskiUNet34 as unary terms, and a pairwise term that depends on angles between triangles, inspired by [22]. Specifically, we use the following energy that we minimize using [4]:

(1)

where are the label assignments we wish to compute by minimizing the above energy, is the set of faces in a mesh, and are the adjacent faces of each face . The unary term is expressed as follows: , where

is the probability distribution over part labels associated with the face

produced through average pooling of probabilities computed from MinkowskiUNet34 on the triangle’s associated points. The pairwise term uses angles between face normals, , for , where is the angle between the normals of faces . The term results in zero cost for right angles between normals indicating a strong edge. The parameter is adjusted with grid search in the hold-out validation set.

Average vs max pooling.

As discussed in our experiments section of our main paper, one possibility to aggregate probabilities of points associated per triangle or component is average pooling: where and are point and triangle probabilities respectively. An alternative is to use max pooling (i.e., replace sum with max above). We experimented with average vs max pooling also per component. As shown in Table 13, average pooling works better for both triangle- and component-based pooling (we experimented with MinkowskiNet per-point probabilities).

Method Pool. ? ? Part IoU Shape IoU Class acc.
MinkNet2Triangle Avg 28.8% 26.7% 64.8%
Max 28.6% 26.1% 64.4%
Avg 32.8% 29.2% 68.1%
Max 31.5% 28.1% 66.8%
MinkNet2Sub Avg 33.1% 36.0% 69.9%
Max 30.4% 32.4% 65.6%
Avg 37.0% 39.1% 73.2%
Max 32.7% 34.8% 67.4%
Table 13: “BuildingNet-Mesh” results using average and max pooling aggregation over triangles and components (weighted cross-entropy loss was used for all these experiments).

Experiments with different losses.

We experimented with different losses for our MinkowskiNet variants for the “BuildingNet-Point” and “BuildingNet-Mesh” tracks. Specifically, we experimented with the Weighted Cross-Entropy Loss (WCE) described in our main paper, Cross-Entropy Loss (CE) without label weights, the Focal Loss (FL) [30], -balanced Focal Loss (-FL) [30], and Class-Balanced Cross Entropy Loss (CB) [10]. Table 14 and Table 15 show results for the “BuildingNet-Point” and “BuildingNet-Mesh” tracks respectively. We observe that (a) in the case that color is not available, WCE is slightly better than alternatives according to all measures for both tracks (b) when color is available, CB is a bit better in terms of Part IoU, but worse in terms of Shape IoU than WCE in the case of the point cloud track. For the mesh track, CB is slightly better according to all measures. In general, WCE and CB behave the best on average, yet their difference is small. For the rest of our experiments, we use WCE.

Performance for each part label.

Our main paper reports mean Part IoU performance in the experiments section. Table 18 reports the BuildingGNN-PointNet++ and BuildingGNN-MinkNet part IoU performance for each label. We also report the performance of MinkowskiNet and PointNet++ for the point cloud track. We observe that networks do better for common part labels, such as window, wall, roof, plant, vehicle, while the performance degrades for rare parts (e.g., awning, arch), or parts whose shape can easily be confused with other more dominant parts (e.g., garage is often confused with door, wall, or window).

Method Loss ? ? Part IoU Shape IoU Class acc.
MinkNet WCE 26.9% 22.2% 62.2%
CE 24.5% 21.2% 61.3%
FL 26.1% 21.8% 61.2%
-FL 22.3% 19.8% 61.5%
CB 26.4% 20.9% 61.4%
MinkNet WCE 29.9% 24.3% 65.5%
CE 28.5% 24.5% 65.3%
FL 28.7% 24.9% 65.2%
-FL 30.1% 25.3% 65.2%
CB 30.4% 24.0% 65.5%
Table 14: “BuildingNet-Point” track results using the Weighted Cross-Entropy Loss (WCE), Cross-Entropy Loss (CE), Focal Loss (FL), -balanced Focal Loss (-FL) and finally Class-Balanced Cross Entropy Loss (CB). All these were used to train the MinkowskiUNet34 architecture. For the FL and -FL experiments the hyper-parameter was set to and for the -FL the same weights were used as the weighted cross entropy loss (see Section 4.3 in our main paper). For the CB experiments we set .
Method Loss ? ? Part IoU Shape IoU Class acc.
MinkNet2Sub WCE 33.1% 36.0% 69.9%
CE 30.7% 32.7% 68.8%
FL 31.0% 33.4% 67.9%
-FL 27.2% 28.3% 66.7%
CB 32.9% 34.3% 69.1%
MinkNet2Sub WCE 37.0% 39.1% 73.2%
CE 35.6% 39.2% 73.5%
FL 35.1% 38.4% 73.2%
-FL 36.0% 38.2% 72.4%
CB 38.0% 39.7% 73.9%
Table 15:

“BuildingNet-Mesh” results using different loss functions

Variant ? ?  Part IoU  Shape IoU   Class acc.
Node-OBB 10.0% 17.1% 56.5%
Node-PointNet++ 14.0% 19.1% 52.2%
Node-OBB+PointNet++ 24.4% 27.8% 71.7%
w/ support edges 26.7% 29.2% 71.5%
w/ containment edges 27.9% 30.6% 72.6%
w/ proximity edges 26.4% 29.4% 71.4%
w/ similarity edges 23.1% 28.5% 69.8%
BuildingGNN-PointNet++ 31.5% 35.9% 73.9%
Table 16: BuildingGNN ablation study based on PointNet++ node features
Variant ? ?  Part IoU  Shape IoU   Class acc.
Node-OBB 10.0% 17.1% 56.5%
Node-MinkNet 35.6% 35.9% 67.7%
Node-OBB+MinkNet 40.0% 40.6% 75.8%
w/ support edges 42.0% 43.5% 77.8%
w/ containment edges 41.1% 42.0% 76.8%
w/ proximity edges 39.9% 40.6% 75.6%
w/ similarity edges 41.2% 43.0% 75.8%
BuildingGNN-MinkNet 42.6% 46.8% 77.8%
Table 17: BuildingGNN ablation study based on MinkowskiNet node features
Label   BuildingGNN  BuildingGNN   MinkNet  PointNet++   BuildingGNN  BuildingGNN   MinkNet  PointNet++
 MinkNet(n+c) PointNet++(n+c) (n+c) (n+c)  MinkNet(n)   PointNet++(n) (n) (n)
Window 70.5% 71.1% 44.1% 34.8% 70.4% 68.3% 35.6% 0.0%
Plant 81.0% 69.8% 79.6% 70.3% 79.8% 69.8% 79.7% 48.4%
Vehicle 83.7% 77.3% 77.1% 29.7% 82.7% 72.4% 75.8% 19.2%
Wall 78.1% 77.5% 64.5% 57.9% 76.0% 74.4% 63.2% 54.4%
Banister 50.0% 19.9% 44.9% 0.0% 56.5% 22.0% 45.6% 0.0%
Furniture 59.7% 37.0% 56.0% 0.0% 58.3% 43.5% 54.9% 0.0%
Fence 55.5% 34.7% 71.3% 16.5% 64.1% 19.7% 49.5% 9.6%
Roof 78.9% 72.1% 65.3% 58.2% 70.2% 69.0% 67.0% 56.4%
Door 41.7% 37.6% 21.7% 0.0% 39.2% 37.7% 23.8% 0.0%
Tower 53.4% 41.2% 46.5% 2.3% 50.8% 37.5% 43.4% 4.8%
Column 61.5% 27.6% 49.5% 0.6% 53.6% 34.7% 42.9% 1.1%
Beam 24.9% 22.4% 13.8% 0.02% 30.3% 21.5% 17.2% 0.0%
Stairs 38.6% 25.6% 26.9% 0.0% 41.0% 24.1% 27.8% 0.0%
Shutters 1.0% 1.3% 0.0% 0.0% 1.7% 0.0% 0.0% 0.0%
Garage 9.0% 10.6% 3.6% 0.0% 10.6% 8.4% 6.8% 0.0%
Parapet 24.9% 3.9% 11.6% 0.0% 28.6% 2.5% 21.0% 0.0%
Gate 14.0% 16.5% 6.4% 0.0% 7.9% 12.3% 7.9% 0.0%
Dome 53.8% 10.1% 48.0% 1.9% 54.3% 14.2% 54.5% 16.3%
Floor 51.5% 37.7% 47.8% 36.9% 51.2% 30.9% 46.8% 30.0%
Ground 75.0% 65.1% 77.4% 64.1% 61.8% 55.5% 60.8% 42.6%
Buttress 23.8% 9.6% 15.6% 0.0% 38.7% 12.3% 6.1% 0.0%
Balcony 19.6% 9.5% 15.0% 0.0% 15.5% 15.6% 17.3% 0.0%
Chimney 70.0% 50.9% 57.9% 0.0% 53.6% 49.5% 60.1% 0.0%
Lighting 6.4% 9.1% 16.8% 0.0% 24.9% 3.5% 23.3% 0.0%
Corridor 16.3% 10.5% 15.9% 4.2% 7.2% 4.1% 7.2% 0.0%
Ceiling 28.0% 23.8% 22.1% 4.6% 28.0% 20.5% 17.4% 4.6%
Pool 70.8% 53.0% 78.7% 77.8% 38.1% 33.0% 43.0% 0.0%
Dormer 27.3% 20.4% 9.6% 0.0% 22.1% 23.3% 6.8% 0.0%
Road 46.2% 24.1% 53.5% 40.0% 1.9% 16.3% 21.5% 0.0%
Arch 8.4% 5.2% 0.9% 0.0% 3.2% 2.9% 0.8% 0.0%
Awning 1.5% 0% 3.8% 0.0% 1.6% 0.0% 0.0% 0.0%
Table 18: Part IOU performance for each label. BuildingGNN-MinkNet and BuildingGNN-PointNet++ are tested on the mesh track, while MinkNet and PointNet++ are tested on the point cloud track. The left half of the table reports performance when color is available (“n+c”), while the right half reports performance when it is not available (“n”).

Appendix E: BuildingGNN ablation study

We conducted an ablation study involving different node features, and also experimenting with different types of edges in our BuildingGNN. Table 16 present the results for different experimental conditions of our BuildingGNN based on PointNet++ as node features. We first experimented using no edges and processing node features alone through our MLP structure. We experimented with using only OBB-based features (“Node-OBB”), using features from PointNet++ alone (“Node-PointNet++”), and finally using both node features concatenated (“Node-OBB+PointNet++”). We observe that using all combinations of node features yields better performance compared to using either node feature type alone. Then we started experimented with adding each type of edges individually to our network (e.g., “w/ support edges” in Table 16 means that we use node features with support edges only). Adding each type of edge individually further boosts performance compared to using node features alone. Using all edges (“BuildingGNN-PointNet”) yields a noticeable Part IoU increase and Shape IoU increase compared to using node features alone. Table 17 shows the same experiments using MinkowskiNet-based features. We observe that combined node features perform better than using either node feature type alone. Adding each type of edges helps, except for proximity edges that seem to have no improvement when used alone. Using all edges still yields a noticeable Part IoU increase and Shape IoU increase compared to using node features alone.

We also experimented with DGCNN [57] as a backbone in our GNN for extracting node features. Unfortunately, DGCNN could not directly handle our large points clouds (100K points). It runs out of memory even with batch size on a 48GB GPU card. We tried to downsample the point clouds (10K points) to pass them to DGCNN, then propagated the node features back to the K points using nearest neighbor upsampling. The part IoU was in the mesh track with color input and using all edges (i.e., the performance is comparable to BuildingGNN-PointNet++, but much lower than BuildingGNN-MinkNet). Still, since other methods were able to handle the original resolution without downsampling, this comparison is not necessarily fair, thus we excluded it from the tables showing the track results in our main paper.

Appendix F: Additional Material

We refer readers to our project page www.buildingnet.org for the dataset, source code, and other supplementary material.