SkelBuilder: Computational Skeleton Frameworks

• SkelBuilder is a computational framework that constructs, extracts, and simulates skeletal representations using methods such as the Medial Axis Transform and graph separators.
• It spans various domains including interactive modeling, geological simulation, biomechanical analysis, and deep learning, with tailored domain-specific implementations.
• The framework integrates modular design, advanced preprocessing, and scalable algorithms to ensure real-time performance and high-fidelity skeleton extraction.

SkelBuilder is a term used in contemporary research to refer to a set of computational frameworks, algorithms, and software systems designed for constructing, extracting, or simulating skeletal representations in various domains. SkelBuilder enables the efficient encoding, manipulation, and analysis of shape and topology information via mixed, hierarchical, or parametric skeletons. These systems target applications in geometry processing, biomechanical modeling, shape analysis, simulation of geological features, human pose estimation, and interactive anatomical modeling.

1. Mathematical and Algorithmic Foundations

Skeletal representations generally encode the volume and topology of objects using lower-dimensional primitives. In $\mathbb{R}^2$, the Medial Axis Transform (MAT) reduces a solid object $O$ to a 1D set of curves, defined as the locus of centers of maximally inscribed disks: $$MA(O) = \{ x \in O : \exists p_1 \neq p_2 \in \partial O,\; \|x-p_1\| = \|x-p_2\| = f(x) \}$$ where $f(x)=\min_{p \in \partial O}\|x-p\|$ is the distance to the boundary. In $\mathbb{R}^3$, the MAT yields sheets; curve skeletons are one-dimensional graphs $G=(V,E)$ that approximate medial geometry while remaining homotopy-equivalent to the original solid. Curve skeleton extraction can be performed by contraction-based, thinning-based, or field-guided methods, with each method relying on mesh, graph, or volumetric data structures and leveraging algorithms such as mean-curvature flow, topological edge collapse, or scalar field tracing (Tagliasacchi, 2013).

SkelBuilder systems incorporate symmetry reduction, Voronoi-based medial axis extraction, dynamic pruning, and postprocessing. Algorithmic pipelines include mesh cleaning, normalization, skeleton extraction via module interfaces, topological and geometric corrections, and output formatting for integration with downstream analysis or animation frameworks (Tagliasacchi, 2013). Skeletonization quality is measured by topology preservation (Betti numbers), Hausdorff distance to true medial loci, centeredness, stability, and runtime performance.

2. Domain-Specific SkelBuilder Implementations

Across scientific domains, SkelBuilder denotes specific frameworks adapting general skeletonization principles:

• Interactive Sketch-based Modeling: SkelBuilder enables real-time straight skeleton extraction from user draw strokes, connection of local sub-skeletons through intersection analysis, and multi-level simplification via Douglas–Peucker algorithms constrained by generalized cylinder regions. Data structures include doubly-linked vertex lists, priority event queues, and graph representations of joints and bones. Interactive refinement is achieved through branch pruning, joint merging, edge collapsing, and threshold-based complexity control. Sub-skeleton placement employs geometric intersection and optimal attachment location selection (Ma et al., 2021).
• Geological Channel Simulation: The SKE-SIM SkelBuilder algorithm reduces binary training images to one-pixel skeletons, measures empirical length and bifurcation-angle distributions, and stochastically grows tree-like channel skeletons via multipoint geostatistics. Edge insertion employs collision detection; channel thickening to 3D is accomplished by extruding skeleton edges using elliptical cross-sections aligned to locally defined frames, with per-voxel marking of geological features. Validation includes connectivity metrics, variogram analysis, and bifurcation density statistics (Vargas et al., 2019).
• Programmatic Environment Synthesis for LLMs: In LLM agent training, SkelBuilder constructs diverse tool-interactive environment skeletons from existing multi-turn tasks via topic mining, logic modeling, and quality evaluation. This includes automated executable class generation (PyClass), interface schema extraction, and dual-agent QA loops using LLM test and checking agents. Deduplication, scenario generation, and scalability enable the synthesis of hundreds of validated environments for supervised and RL training (Song et al., 9 Jan 2026).

3. Parametric and Biomechanical SkelBuilder Pipelines

In digital human modeling and biomechanics, SkelBuilder is synonymous with pipelines that rigorously fit anatomical skeletons to surface meshes or image data:

• Parametric Human Models (SKEL/SMPL/BSM): SKELBuilder techniques re-rig SMPL meshes using anatomical joint hierarchies (46 DOF, ball-and-hinge joints) and learn a regression matrix $R$ from mesh vertices to joint positions. Optimization objectives employ marker-to-model, joint location, bone length, and mesh containment losses. Pose extraction reduces parameter space compared to SMPL, enforcing biomechanically accurate constraints. Quantitative results demonstrate doubled joint location accuracy and sub-centimeter skin-surface fidelity (Keller et al., 8 Sep 2025). Extensions such as SKEL-CF introduce transformer encoder–decoder architectures, hierarchical coarse-to-fine parameter estimation, camera modeling, mesh-to-mesh alignment, and loss terms tailored to anatomical realism (Li et al., 25 Nov 2025).
• Musculoskeletal Anatomy Modeling: SkelBuilder authoring tools support part-based skeleton construction within skin meshes using libraries of cylinder, curve, and shape-based bones. Interactive placement leverages ray casting, rigid/nonrigid ICP, and cage-based regularization. Post-placement processing produces combined skeleton meshes, with downstream volumetric segmentation for muscle and fat via anisotropic Poisson-driven PDEs (Abdrashitov et al., 2021).

4. Skeletal Deep Learning and Statistical Shape Representation

SkelBuilder also encompasses frameworks for learning skeletal representations from data via geometric deep networks:

• Geometric Deep Skeletonization: SkelBuilder networks use PointNet++ encoders, shared MLP weight predictors, and structured loss functions including Chamfer, spread regularization, and medial enforcement to optimize skeletal point sets $(s_j, r_j, u_j)$ from boundary clouds. Weak supervision via optimized s-reps ensures structural fidelity, with ablation studies confirming the contribution of each geometric term to skeleton and surface reconstruction accuracy (Khargonkar et al., 2023).
• Discrete Swept Skeletal Fitting: SkelBuilder systems for slabular objects model skeletons as locally parameterized central spines with attached spokes, employing boundary division by spectral partitioning, medial sheet extraction via Voronoi, surface and spine fitting with polynomial regression and flattening, vein construction via cross-sectional intersection, and evaluation by volume-boundary consistency, symmetry, and tidiness metrics. These enable improved accuracy in disease shape analysis and statistical shape modeling (Taheri et al., 2024).

5. Multilevel Skeletonization via Graph Separators

Advanced SkelBuilder algorithms employ graph-theoretic approaches for skeleton extraction from spatially embedded graphs:

• Local Separator Algorithm: The multilevel SkelBuilder approach constructs curve skeletons by iteratively contracting light-edge matchings to produce detail hierarchies, performing restricted separator searches up to a threshold $\alpha$, projecting and refining separators, packing minimal non-overlapping sets based on vertex capacity, and extracting central curve skeletons by centroid computation and adjacency analysis. Efficiency and quality metrics (directed Hausdorff, genus, branch counts) confirm fast convergence to skeletons with high locality and global structure preservation (Bærentzen et al., 2023).

6. Skeleton Ground Truth Extraction and Annotation

For supervised learning and benchmarking, SkelBuilder encompasses tools and methodologies for high-fidelity skeleton ground truth (GT) generation:

• Annotation Pipeline: Methodologies integrate automatic dense skeleton extraction, interactive pruning guided by reconstruction error and simplicity metrics, and consistency validation via human-in-the-loop annotation with context-dependent diagnosticity analysis. Standardized formats, GUI (SkeView), and evaluation scripts (AEP, F₁, Bulls-Eye Score) are provided across shape and image datasets to facilitate fair benchmarking, annotation consistency, and integration into algorithmic research (Yang et al., 2023).

7. Integration, Optimization, and Practical Considerations

SkelBuilder implementations feature modular design (separation of algorithmic core, GUI, disk I/O), lazy evaluation (distance fields/computation-on-demand), multithreading, memory-streaming for large inputs, and level-of-detail control. API interfaces support skeleton extraction, refinement, and export in interoperable formats (JSON/XML), enabling flexible adaptation to application-specific requirements in shape editing, rigging, simulation, and segmentation (Tagliasacchi, 2013, Ma et al., 2021). Performance benchmarks demonstrate real-time operation (under 20 ms per interactive action), scalability to large-scale datasets, and robustness across data modalities and input noise.

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SkelBuilder thus represents a unified paradigm for computational skeletonization, supporting diverse mathematical frameworks, pipeline architectures, domain-specific adaptations, and performance-optimized toolkits for rigorous shape and topology analysis across scientific and engineering disciplines.