CDBM: Complexity-Diversity Framework for Building Morphology Analysis

Evgenii Maslov; Alexandra Vabnits; Denis Karpov; Alexey Morozov; Anastasia Antsiferova; Art Prosvetov; Valentin Khrulkov

cs.CVOct 29, 2026

CDBM: Complexity-Diversity Framework for Building Morphology Analysis

Authors: Evgenii Maslov, Alexandra Vabnits, Denis Karpov, Alexey Morozov, Anastasia Antsiferova, Art Prosvetov, Valentin Khrulkov

Organizations: FusionBrain Lab, Artificial Intelligence Research Institute, 123112 Moscow, Russia · Independent Researcher

Abstract

We introduce Complexity-Diversity Building Metrics (CDBM), twelve interpretable descriptors for building massings represented as vertical extrusions. They measure how strongly geometric detail is expressed (complexity) and how unevenly it varies across one- and two-dimensional elements (diversity). Computed for 482,241,306 OpenStreetMap buildings and compared with 3D Building Metrics (3DBM) and the LION shape latent on task-specific samples, CDBM is tested on function, region, contextual relevance, real-generated discrimination, human preference and geometry-conditioned generation. With gradient boosting, CDBM best separates generated from mapped massings and best matches human preference; with logistic regression it matches 3DBM on realism. 3DBM leads on the other three tasks. As generation targets, the descriptors show that models struggle to produce strongly expressed and heterogeneous forms. CDBM complements existing indicators.

Figures & tables

Figure 1: Geometric interpretation of the twelve CDBM descriptors, organized by complexity versus diversity (columns) and linear versus planar properties (rows). Each descriptor is illustrated by massings with lower and higher values, arranged from top to bottom; the corresponding scores are shown.

Metric	Abbr.	Formula	Interpretation
Side length complexity	SLC	$\mu(R_{\mathrm{slc}})$	Shorter contour edges relative to building extent.
Side length diversity	SLD	$\sigma(R_{\mathrm{slc}})$	Greater variation in relative contour edge lengths.
Angle complexity	AC	$\mu(R_{\mathrm{ac}})$	Stronger departure from orthogonal geometry.
Angle diversity	AD	$\sigma(R_{\mathrm{ac}})$	Greater variation in angular departure from orthogonal geometry.
Extrusion height complexity	EHC	$\mu(R_{\mathrm{ehc}})$	Shorter extrusion heights relative to full building height.
Extrusion height diversity	EHD	$\sigma(R_{\mathrm{ehc}})$	Greater variation in relative extrusion heights.

Table 1: Building-level descriptor definitions. Interpretations describe higher metric values.

Figure 2: Geographic distribution of the twelve CDBM descriptors in the OSM-derived building dataset. Each occupied grid cell shows the mean descriptor value of its buildings. Colour scales are specific to each descriptor.

Group	#	Values
3D	18	hemisphericality, convexity, fractality, cuboidness, cubeness, proximity, spin, circumference, depth, girth, dispersion, range, equivalent cuboid, roughness; horizontal elongation; min/max vertical elongation ∗ ; form factor ∗
2D	14	the 2D analogues of these 14 indices, computed on the footprint
size	10	volume, surface area, footprint area and perimeter, bounding-box length and width; roof height: min, max, mean, std

Table 2: 3DBM values used as features. ∗ Recomputed by us, see deviations (i)–(ii).

Figure 3: A target (red) in Chicago with three contexts (grey, buildings within 100 m): (a) the true context; (b) a random false context, given away by a street grid turned by

38^{\circ}

; (c) an orientation-matched false context. Insets show the target at the same scale; dashed outlines mark the foreign site’s own building.

Group	Family	#	Features
LION	–	288	global latent (128) and pooled point latents (16)
3DBM	3D shape	36	the 18 3D indices of Table 2
	2D shape	28	the 14 2D indices
	size	20	the 10 size values
CoMa	orientation	5	orientation difference to the context mean and the nearest building; orientation density; two distribution distances (orientation; orientation, size and shape)
	shape	7	circularity, elongation, courtyard and stepback ratios; diversity of angles, extrusion heights and elevations

Table 3: Groups and families compared on contextual relevance. #: features; per-building descriptors count twice (Eq. 10 ).

Group	Regions / classes	Sampling	Total sites
Global8	Africa, Asia, Central America, Europe, North America, Oceania, Russia, South America	Location-capped (8,000 per region)	64,000
		Random (8,000 per region)	64,000
Urban8	Moscow, London, Paris, New York, Mexico City, Beijing, Shanghai, Delhi	Random (5,000 per urban area)	40,000
Europe15	France, Spain, Ukraine, Switzerland, Sweden, Italy, Portugal, Finland, Norway, Poland, the Netherlands, Czech Republic, the United Kingdom, Austria, Belgium	Territory-balanced (8,000 per country)	120,000
		Random (8,000 per country)	120,000

Table 4: Geographic classification tasks. Counts refer to complete datasets before the training/test split. Subregions are leaf-level locations in the OSM extract hierarchy.

Source	Sampling	Total sites
Moscow	All eligible	10,567
Moscow	Random	1,800
Urban8	All eligible	23,322
Urban8	Class-balanced	4,900
Calgary	Random	1,800
Shanghai	Random	1,800

Table 5: Building-function classification tasks. Counts refer to complete datasets before the training/test split. The Moscow “all eligible” sample contains 8,000 apartment buildings and 2,567 buildings from the other six classes.

Features	Logistic Regression	CatBoost
LION	0.810	0.837
3DBM	0.861	0.931
CDBM (ours)	0.862	0.972

Table 6: Real–generated classification performance (ROC–AUC) for each feature representation. Best results for each classifier are shown in bold.

Figure 4: Association between classifier realism scores and human preference scores, evaluated separately for each generator. (a) Spearman and (b) Pearson correlations for logistic regression; (c) Spearman and (d) Pearson correlations for CatBoost.

Figure 5: ROC-AUC of descriptor sets, averaged over the eight main settings; feature counts in brackets. Groups are bold and shaded, their families lighter. Dots on the left show which groups a set contains (filled: the whole group; ring: part of it). The axis is broken between the sets with and without CoMa’s orientation features. Teal marks sets with our descriptors.

Figure 6: What each group adds to sets with CoMa’s orientation features, with random (hollow) and orientation-matched (filled) negatives, each averaged over its four main settings. (a, b) Gain in ROC-AUC on two base sets; bars are 95% bootstrap intervals. (c) Share of the base sets (number on the right) on which adding our descriptors gains more than adding the group.

Task	Model	Base	CDBM (ours)		LION		3DBM
			Only	+ base	Only	+ base	Only	+ base
Global8, location cap	CatBoost	0.7918	0.6860	0.8365	0.6608	0.8069	0.8317	0.8739
Global8, location cap	LR	0.7121	0.6339	0.7323	0.6329	0.7366	0.7232	0.7750
Global8, random sampling	CatBoost	0.7669	0.6825	0.8152	0.6654	0.7913	0.8087	0.8458
Global8, random sampling	LR	0.6911	0.6357	0.7297	0.6374	0.7360	0.7168	0.7743
Urban8	CatBoost	0.9042	0.7862	0.9456	0.7729	0.9231	0.9420	0.9594

Table 7: Geographic classification: test macro-averaged one-vs-rest ROC–AUC. “Only” denotes the feature representation without base features; “+ base” includes them. The highest score among all seven feature sets in each row is bold, and the second-highest is underlined.

Task	Model	Base	CDBM (ours)		LION		3DBM
			Only	+ base	Only	+ base	Only	+ base
Moscow, all eligible	CatBoost	0.8857	0.8250	0.9357	0.8956	0.9221	0.9432	0.9422
Moscow, all eligible	LR	0.8546	0.7693	0.9056	0.8840	0.9010	0.9246	0.9262
Urban8, all eligible	CatBoost	0.8487	0.8087	0.8990	0.8330	0.8660	0.9069	0.9085
Urban8, all eligible	LR	0.7773	0.7474	0.8239	0.8016	0.8245	0.8585	0.8587
Urban8, class balancing	CatBoost	0.8546	0.8253	0.8939	0.8435	0.8619	0.9020	0.9005

Table 8: Building-function classification: test macro-averaged one-vs-rest ROC–AUC. “Only” denotes the feature representation without base features; “+ base” includes them. Urban-area information is available to all variants in the two Urban8 tasks. The highest score among all seven feature sets in each row is bold, and the second-highest is underlined.

Figure 7: Geometry-conditioned generation performance across the twelve CDBM descriptors: a) aggregate target-match scores $s$ , displayed as $-\log(1-s)$ , b) target-match scores as a function of the requested descriptor value. Colours identify the four evaluated generative models; higher scores indicate closer agreement with the target.

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CoMa: Contextual Massing Generation with Vision-Language Models

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FusionBrain Lab, Artificial Intelligence Research Institute, 123112 Moscow, Russia · Research Center of the Artificial Intelligence Institute, Innopolis University, 420500 Innopolis, Russia · ITMO University, Institute of Design and Urban Studies, 197101 Saint Petersburg, Russia+2

Vision-Language Models Multimodal Generation 3D Shape Generation

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Context-aware building massing is an important early-stage design task: given a site for buildings, a generated massing should not only fit the target parcel, but also relate to the scale, density, and morphology of its surrounding urban fabric. This task is naturally multimodal, since the target output should remain structured and editable, while the surrounding context, including other buildings or roads, can be represented as vector geometry, map imagery, or three-dimensional views. In this paper, we study contextual massing generation using vision-language models (VLMs) and analyze their performance on this task across different context modalities during training and inference. We assemble an experimental dataset of 12,845 Melbourne massings with parcel contours, structured 3D geometry, neighboring buildings, top-down views, and multi-view 3D context images. We also introduce a learned contextual relevance metric for evaluating whether generated massings are morphologically compatible with their surrounding context. Using Qwen3-VL models, we compare no-context, unimodal-context, and multimodal-context training regimes and evaluate inference performance under controlled combinations of modalities and amounts of context. The results show that model size strongly affects generation quality, multimodal training improves the use of individual modalities, and multimodal inference provides a stronger contextual signal than isolated context inputs.

Abstract

Morphological Analysis

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