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Breaking Bad: A Dataset for Geometric Fracture and Reassembly

Silvia SellánYun-Chun ChenZiyi WuAnimesh GargAlec Jacobson

article2022NeurIPS56 citations

Introduces a large-scale benchmark of over one million physically simulated fractured shapes to advance geometric reassembly beyond traditional semantic part composition.

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Reassembling fractured objects into their original shapes is a critical capability across multiple domains, including cultural artifact preservation, digital heritage archiving, robotics, computer vision, and geometry processing. While machine learning offers promising avenues to automate this process, progress has been constrained by a lack of suitable training data. Existing shape assembly benchmarks focus predominantly on semantic part decomposition, reflecting how manufactured objects are constructed rather than how materials naturally fracture under physical impacts. In natural fractures, fragments lack distinct semantic identities, exhibit irregular and non-convex geometries, and vary widely in count and volume.

To address this gap, the article introduces Breaking Bad, a large-scale dataset designed to benchmark and advance geometric shape assembly. The primary objective is to model the physical destruction process across a diverse set of three-dimensional shapes and evaluate how modern deep learning architectures perform when reassembling physically realistic fragments. Using an efficient physics-based pre-fracture simulation framework, the authors generated over one million fractured objects derived from more than 10,000 base models. The dataset spans three main categories—everyday items, archaeological artifacts, and general 3D-printing geometries—providing roughly 100 distinct fracture patterns per base shape. To facilitate practical distribution, a lossless compression scheme reduces the raw storage requirement from over 1 terabyte to approximately 7.3 gigabytes.

Benchmarking state-of-the-art deep learning methods—specifically Global, Long Short-Term Memory, and Dynamic Graph Learning architectures—revealed several critical findings. First, existing models perform poorly on geometric fracture reassembly compared to semantic part assembly. Even the top-performing graph-based model achieved a part assembly accuracy of only 31.0% on everyday objects, largely because standard architectures rely on global shape priors rather than reasoning over fine-grained local fracture boundaries. Second, reassembly difficulty scales steeply with fragmentation: as the number of pieces increased from 20 up to 100, part accuracy dropped sharply below 8%. Third, pre-training models on everyday objects improved subsequent fine-tuning performance on archaeological artifacts, raising accuracy from 12.8% to 19.4%. Finally, generalization to entirely unseen object categories remains severely limited, with accuracy falling to single-digit percentages.

These findings indicate that fractured shape reassembly remains a largely unsolved challenge for current computer vision and machine learning frameworks. For decision-makers and researchers invested in automated restoration, heritage archiving, or robotic manipulation, the results demonstrate that deploying off-the-shelf assembly models carries high performance risk. Future investment should focus on developing purpose-built neural architectures that prioritize local geometric surface matching over global category priors, alongside sequential decision-making frameworks tailored for multi-part robotic assembly.

Readers should interpret these results within the scope of the underlying simulation assumptions. The dataset relies on brittle fracture models under isotropic, single-material conditions, meaning ductile deformations (such as bent metals or plastics) and progressive stress propagation are not captured. Despite these boundary conditions, the dataset provides a robust, high-confidence benchmark that establishes a standardized foundation for advancing automated geometric reassembly.

AdobeNVIDIAUniversity of TorontoVector Institutegeometric fracturegeometric shape assembly taskshape assembly datasets
arXiv: 2210.11463
Cover for Breaking Bad: A Dataset for Geometric Fracture and Reassembly

Abstract

We introduce Breaking Bad, a large-scale dataset of fractured objects. Our dataset consists of over one million fractured objects simulated from ten thousand base models. The fracture simulation is powered by a recent physically based algorithm that efficiently generates a variety of fracture modes of an object. Existing shape assembly datasets decompose objects according to semantically meaningful parts, effectively modeling the construction process. In contrast, Breaking Bad models the destruction process of how a geometric object naturally breaks into fragments. Our dataset serves as a benchmark that enables the study of fractured object reassembly and presents new challenges for geometric shape understanding. We analyze our dataset with several geometry measurements and benchmark three state-of-the-art shape assembly deep learning methods under various settings. Extensive experimental results demonstrate the difficulty of our dataset, calling on future research in model designs specifically for the geometric shape assembly task. We host our dataset at https://breaking-bad-dataset.github.io/.

Keywords

geometric fracturegeometric shape assembly taskshape assembly datasetsfracture simulationbrittle fracturedynamic fractureprocedural fracturesemantic part assembly methodsobject decomposition

Table of Contents

  • 1 Introduction
  • 2 Related Work
  • 3 Background: Fracture Modes for Fast Simulation
  • 4 The Breaking Bad Dataset
  • 4.1 Fracture Simulation
  • 4.2 Dataset Analysis
  • 4.3 Dataset Access and Storage
  • 4.4 Licensing
  • 5 Case Study Application: 3D Geometric Shape Assembly
  • 6 Case Study Evaluation
  • 6.1 Task Performance
  • 6.2 Ablation Study: Number of Fractured Pieces
  • 6.3 Analysis of Model Pre-training and Fine-tuning
  • 6.4 Generalization to Unseen Objects
  • 7 Limitations & Future Work
  • Acknowledgments
  • References
  • Checklist

Knowls

  1. Knowl 1 — Breaking Bad Dataset Composition and Structure

    definition

    The Breaking Bad dataset is a large-scale collection of physically simulated fractured 3D objects designed for geometric shape understanding and fracture reassembly. The dataset contains 1,047,400 fractured shapes generated from 10,474 base 3D models (yielding 100 distinct breakdown patterns per base model) with an average of 8.06 fractured pieces per pattern.

    The base models are divided into three subsets:

    1. Everyday Objects Subset: 542 models across 20 PartNet categories (BeerBottle, Bottle, Bowl, Cup, Cookie, DrinkBottle, DrinkingUtensil, Mirror, Mug, PillBottle, Plate, Ring, Spoon, Statue, Teacup, Teapot, ToyFigure, Vase, WineBottle, WineGlass).
    2. Artifacts Subset: 204 models from Thingi10K tagged with sculpture or scan, representing archeological and cultural heritage fragments.
    3. Others Subset: 9,475 diverse geometric models from Thingi10K representing gaming assets, fabrication shapes, and general 3D models.

    Unlike semantic assembly datasets (such as PartNet, AutoMate, and JoinABLe) where decomposition aligns with human-defined part semantics, or procedural datasets where trimming relies on arbitrary analytic level sets, Breaking Bad models realistic physical destruction resulting in irregular, non-convex fragment geometries.

  2. Knowl 2 — Physics-Based Fracture Simulation and Dataset Generation Algorithm

    algorithm

    The fracture generation pipeline constructs 100 physically plausible fracture configurations for any input 3D surface mesh by computing discontinuous vibrational fracture modes on an enclosing cage and projecting randomized impact vectors onto these modes.

    Input: Watertight triangular base surface mesh MM
    Output: Set of 100 distinct fractured mesh configurations {Fj}j=1100\{F_j\}_{j=1}^{100}
    Normalize MM to fit into a unit-length bounding box [−0.5,0.5]3[-0.5, 0.5]^3
    Construct a coarse triangular cage mesh CC (4,000 faces) enclosing MM using Simple Nested Cages at grid resolution 100
    Tetrahedralize the cage CC into tetrahedral mesh Ω\Omega with mm tetrahedra using TetGen
    Compute the first k=20k=20 discontinuous fracture modes U~=[u~1,…,u~k]∈R12m×k\tilde{U} = [\tilde{u}_1, \dots, \tilde{u}_k] \in \mathbb{R}^{12m \times k} by solving:
        argmin⁡U~TM~U~=I12∑r=1ktrace⁡(U~TQ~U~)+ω∑r=1kED(u~r)\operatorname{argmin}_{\tilde{U}^T \tilde{M} \tilde{U} = I} \frac{1}{2} \sum_{r=1}^k \operatorname{trace}(\tilde{U}^T \tilde{Q} \tilde{U}) + \omega \sum_{r=1}^k E_D(\tilde{u}_r)
        where Q~,M~∈R12m×12m\tilde{Q}, \tilde{M} \in \mathbb{R}^{12m \times 12m} are per-tetrahedron-corner elastic stiffness and mass operators, EDE_D measures discontinuity, and ω=0.001\omega = 0.001
    Transfer the fracture modes from Ω\Omega to the input mesh MM by intersecting mode-induced fracture faults with MM
    Set the first 20 fracture patterns {F1,…,F20}\{F_1, \dots, F_{20}\} as the 20 raw fracture modes
    pattern_count = 20
    while pattern_count < 100 do
        Sample a random impact location and force vector w∈R12mw \in \mathbb{R}^{12m} on the surface of CC
        Sample a discontinuity threshold τ∼U(τmin⁡,τmax⁡)\tau \sim \mathcal{U}(\tau_{\min}, \tau_{\max})
        Compute fractured displacement w∗=U~U~TM~ww^* = \tilde{U} \tilde{U}^T \tilde{M} w
        Extract disconnected fragments from MM where displacement discontinuity across faults exceeds τ\tau
        if fragment count NN satisfies 2≤N≤1002 \le N \le 100 then
            pattern_count = pattern_count + 1
            Fpattern_count=extracted fragmentsF_{\text{pattern\_count}} = \text{extracted fragments}
        end if
    end while
    return {Fj}j=1100\{F_j\}_{j=1}^{100}

  3. Knowl 3 — Super-Segmentation Lossless Compression for Fractured Shape Datasets

    model/method

    Because simulated impact projections w∗=U~U~TM~ww^* = \tilde{U}\tilde{U}^T \tilde{M} w only create discontinuities along the fault surfaces pre-spanned by the k=20k=20 precomputed fracture modes U~\tilde{U}, every fracture pattern of a given base mesh is a subset of a single common partition.

    The base mesh is pre-partitioned into a master "super-segmentation" mesh comprising all possible atomic sub-pieces formed by the intersection of the 20 fracture modes. Instead of storing 100 full 3D mesh files per base object, storage requires only:

    1. The single geometry of the super-segmented mesh.
    2. A binary/categorical index list for each of the 100 impact simulations indicating which super-segments remain bonded or separate into distinct fragments.

    Decompression reconstitutes any individual fracture pattern by merging adjacent super-segments that share connected labels. This strategy reduces the dataset's disk footprint from over 1 TB in raw .OBJ format to 10 GB uncompressed (and 7.3 GB zipped), providing an approximate 100-fold lossless compression.

  4. Knowl 4 — Geometric Characteristics and Non-Convexity Statistics of Breaking Bad Subsets

    data/table

    Geometric distributions across the dataset subsets (Everyday, Artifacts, Others, and All) are quantified at the 25th, 50th, and 75th percentiles across key attributes: number of fractured pieces per object (FP/O), number of vertices per fractured piece (V/FP), number of faces per fractured piece (F/FP), normalized piece volume (V/FP, ×10−4\times 10^{-4}), and piece convexity rank (PCR, ×10−2\times 10^{-2}) computed via line-of-sight weak convex decomposition.

    Category #O #FP / #O #V / #FP #F / #FP V / #FP (×10−4\times 10^{-4}) PCR (×10−2\times 10^{-2})
    Percentile 25th 50th 75th 25th 50th 75th 25th 50th 75th 25th 50th 75th 25th 50th 75th
    Everyday 542 2 3 6 98 279 949 216 742 3,162 2.47 9.32 71.13 6.19 16.63 44.00
    Artifacts 204 3 8 19 90 307 757 208 872 2,310 0.64 3.96 23.75 9.13 19.78 45.44
    Others 9,475 3 6 13 70 331 1,119 146 832 3,222 0.51 6.17 39.36 5.58 11.17 16.00
    All 10,221 3 10 13 92 286 1,345 22 286 2,552 0.05 2.70 31.89 6.38 13.99 28.90

    The low PCR values across percentiles establish that fragments possess complex concave boundaries, differing from procedural Voronoi fracture algorithms that generate exclusively convex pieces.

  5. Knowl 5 — Vision-Based Multi-Part Fracture Reassembly Problem Formulation and Evaluation Protocol

    experimental setup

    In the multi-part geometric fracture reassembly task, a model receives an unordered set of NN point clouds P={Pi}i=1N\mathcal{P} = \{P_i\}_{i=1}^N sampled from the fragmented pieces of a broken object, where Pi∈R1000×3P_i \in \mathbb{R}^{1000 \times 3} contains 1,000 points sampled uniformly from the surface of piece FiF_i. Each input point cloud PiP_i is zero-centered and rotated by a random rotation matrix to simulate unoriented fragments.

    The objective is to predict canonical SE(3)\mathrm{SE}(3) transformation parameters qi=(Ri,Ti)q_i = (R_i, T_i) for each fragment i∈{1,…,N}i \in \{1, \dots, N\}, with predicted rotation matrix Ri∈SO(3)R_i \in \mathrm{SO}(3) and translation vector Ti∈R3T_i \in \mathbb{R}^3, such that the assembled point cloud S=⋃i=1N(RiPi+Ti)\mathcal{S} = \bigcup_{i=1}^N (R_i P_i + T_i) reconstructs the original object geometry.

    Performance is measured with four metrics:

    1. Root Mean Square Error of Rotation (RMSE(RR)): Angular error in degrees between predicted and ground-truth Euler rotations.
    2. Root Mean Square Error of Translation (RMSE(TT)): Euclidean distance between predicted and ground-truth piece centers (imes10−2 imes 10^{-2}).
    3. Shape Chamfer Distance (CD): Chamfer distance between the assembled point cloud S\mathcal{S} and ground truth assembled point cloud S∗\mathcal{S}^* (imes10−3 imes 10^{-3}).
    4. Part Accuracy (PA): Percentage of predicted fragments whose transformed point clouds fall within a Chamfer distance threshold of their ground-truth placement.

  6. Knowl 6 — Baseline Performance Comparison on Geometric Fracture Reassembly

    empirical result

    Three learning-based shape assembly methods—Global (encoder-decoder), LSTM (sequential assembly), and Dynamic Graph Learning (DGL, graph neural network)—were benchmarked on fractured shapes from the Everyday subset containing 2 to 20 pieces. Models were trained per category and averaged over all 20 categories.

    Method RMSE (RR) ↓\downarrow (degree) RMSE (TT) ↓\downarrow (×10−2\times 10^{-2}) CD ↓\downarrow (×10−3\times 10^{-3}) PA ↑\uparrow (%)
    Global 80.7 15.1 14.6 24.6
    LSTM 84.2 16.2 15.8 22.7
    DGL 79.4 15.0 14.3 31.0

    DGL outperforms Global and LSTM across all metrics due to relational reasoning between fragment pairs in graph message passing. However, all models demonstrate substantially lower accuracy compared to their reported performance on semantic part assembly benchmarks. Because semantic priors are absent in fractured geometry, PointNet-based global feature representations fail to provide the localized surface mating cues required for geometric alignment.

  7. Knowl 7 — Impact of Fragment Count on Assembly Performance

    empirical result

    An ablation study evaluated the DGL model trained on different piece count ranges (2–20, 2–50, and 2–100 pieces) and tested across three piece count intervals (2–20, 21–50, and 51–100 pieces) on the Everyday object subset.

    Test set (pieces) RMSE (RR) ↓\downarrow (degree) RMSE (TT) ↓\downarrow (×10−2\times 10^{-2}) CD ↓\downarrow (×10−3\times 10^{-3}) PA ↑\uparrow (%)
    Results of training on fractured objects with 2 to 20 fracture pieces
    2–20 79.4 15.0 14.3 31.0
    21–50 84.4 20.1 15.0 7.5
    51–100 85.1 21.3 23.0 4.8
    Results of training on fractured objects with 2 to 50 fracture pieces
    2–20 79.9 14.8 14.0 29.9
    21–50 84.5 19.6 14.0 7.7
    51–100 84.8 20.5 18.1 4.7
    Results of training on fractured objects with 2 to 100 fracture pieces
    2–20 79.8 14.4 14.0 29.4
    21–50 84.3 19.2 14.5 7.4
    51–100 85.3 20.0 13.9 4.8

    As the number of fracture pieces grows, the combinatorial complexity causes part accuracy to decline sharply from ~30% for 2–20 pieces down to ~7.5% for 21–50 pieces and ~4.8% for 51–100 pieces. Training with larger piece counts (2–100 pieces) reduces Chamfer distance on the 51–100 test set from 23.0 to 13.9 ×10−3\times 10^{-3}.

  8. Knowl 8 — Effect of Pre-Training and Fine-Tuning on Artifact Reassembly

    empirical result

    The effectiveness of transferring representations learned on everyday objects to archaeological shapes was assessed by comparing baseline models trained from scratch on the Artifacts subset versus models pre-trained on Everyday objects and fine-tuned on Artifacts (tested on ≤20\le 20 pieces).

    Method RMSE (RR) ↓\downarrow (degree) RMSE (TT) ↓\downarrow (×10−2\times 10^{-2}) CD ↓\downarrow (×10−3\times 10^{-3}) PA ↑\uparrow (%)
    Results of training the model from scratch
    Global 84.8 16.7 19.0 12.7
    LSTM 85.2 17.2 23.5 6.6
    DGL 85.8 16.8 19.4 12.8
    Results of fine-tuning from Everyday object pre-training
    Global 83.8 16.6 19.0 13.3
    LSTM 84.6 16.8 21.5 11.7
    DGL 81.7 16.6 17.3 19.4

    Fine-tuning improves reassembly accuracy across all architectures. For DGL, fine-tuning improves Part Accuracy by 6.6 percentage points (from 12.8% to 19.4%), reduces rotation error from 85.8° to 81.7°, and decreases Chamfer distance from 19.4 to 17.3 ×10−3\times 10^{-3}.

  9. Knowl 9 — Cross-Category Generalization to Unseen Fractured Objects

    empirical result

    Generalization was tested by deploying models trained on Everyday objects (and models fine-tuned on Artifacts) directly on the unseen 'Others' subset ({N≤20}\{N \le 20\} pieces).

    Method RMSE (RR) ↓\downarrow (degree) RMSE (TT) ↓\downarrow (×10−2\times 10^{-2}) CD ↓\downarrow (×10−3\times 10^{-3}) PA ↑\uparrow (%)
    Results of testing models trained only on Everyday objects
    Global 86.4 19.4 42.2 6.0
    LSTM 84.9 18.7 45.3 4.8
    DGL 86.6 20.1 38.5 7.5
    Results of testing models fine-tuned on Artifact objects
    Global 83.9 18.8 39.2 6.7
    LSTM 82.9 17.9 40.3 5.5
    DGL 81.3 17.2 36.6 8.3

    Performance degrades substantially on unseen out-of-distribution geometries, with Chamfer distance increasing to 36.6–45.3 ×10−3\times 10^{-3} and Part Accuracy falling to 4.8–8.3%. However, models exposed to larger, more diverse pre-training data (the fine-tuned models) consistently achieve lower errors across all evaluation metrics.

  10. Knowl 10 — Physical and Numerical Assumptions in Dataset Generation

    limitation

    The fracture generation framework incorporates several physical and numerical assumptions that constrain fracture behavior:

    1. Brittle Material Assumption: Objects are modeled strictly as linear elastic brittle materials experiencing sudden impacts; ductile deformation, bending, tearing, and plastic distortion are not represented.
    2. Instantaneous Fracture Propagation: Discontinuities are formed instantaneously across precomputed modal boundaries rather than through time-stepped dynamic stress relief waves. Consequently, real-world crack characteristics (such as fracture faults intersecting strictly at right angles) are not enforced.
    3. Tetrahedral Mesh Boundary Confinement: Fracture surfaces strictly follow the faces of the coarse tetrahedral cage mesh Ω\Omega, leaving post-processing surface smoothing as an optional step.
    4. Material Homogeneity and Isotropy: Each 3D object is treated as a single, isotropic material with uniform density and stiffness, neglecting internal compositional variations, structural grain, or directional anisotropy.

Coverage note — None was omitted. All principal contributions—including dataset design, simulation pipeline, super-segmentation compression, geometric statistics, evaluation setup, baseline comparisons, ablations on fragment count, pre-training/fine-tuning analyses, generalization experiments, and simulation limitations—are fully covered.

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Citation

MLA
Sellán, S., et al. “Breaking Bad: A Dataset for Geometric Fracture and Reassembly”. arXiv, 2022, http://arxiv.org/abs/2210.11463v1.
APA
Sellán, S., Chen, Y.-C., Wu, Z., Garg, A., & Jacobson, A. (2022). Breaking Bad: A Dataset for Geometric Fracture and Reassembly. arXiv. http://arxiv.org/abs/2210.11463v1
Chicago
Sellán, S., Y.-C. Chen, Z. Wu, A. Garg, and A. Jacobson. 2022. “Breaking Bad: A Dataset for Geometric Fracture and Reassembly”. arXiv. http://arxiv.org/abs/2210.11463v1.
Harvard
Sellán, S. et al. (2022) “Breaking Bad: A Dataset for Geometric Fracture and Reassembly”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2210.11463v1.
Vancouver
1. Sellán S, Chen Y-C, Wu Z, Garg A, Jacobson A (2022) Breaking Bad: A Dataset for Geometric Fracture and Reassembly. arXiv

BibTeX

@article{sellan2022breaking,
  title = {Breaking Bad: A Dataset for Geometric Fracture and Reassembly},
  author = {Sellán, Silvia and Chen, Yun-Chun and Wu, Ziyi and Garg, Animesh and Jacobson, Alec},
  year = {2022},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2210.11463v1},
  eprint = {2210.11463}
}
Metadata:arXiv

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