We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous elements in the medial axis representation to effectively shift the complexity away from the discrete elements. To that end, we introduce generalized enveloping primitives, an enhancement over the standard primitives in the medial axis, which ensure efficient coverage of intricate local features of the input shape and substantially reduce the number of discrete elements required. Moreover, we present a computational framework for constructing a medial skeletal diagram from an arbitrary closed manifold mesh. Our optimization pipeline ensures that the resulting medial skeletal diagram comprehensively covers the input shape with the fewest primitives. Additionally, each optimized primitive undergoes a post-refinement process to guarantee an accurate match with the source mesh in both geometry and tessellation. We validate our approach on a comprehensive benchmark of 100 shapes, demonstrating the sparsity of the discrete elements and superior reconstruction accuracy across a variety of cases. Finally, we exemplify the versatility of our representation in downstream applications such as shape generation, mesh decomposition, shape optimization, mesh alignment, mesh compression, and user-interactive design.
We introduce the Medial Skeletal Diagram - a representation with a sparse skeleton that generalizes the medial axis. Our representation reduces the number of discrete elementsrequired compared to both standard and simplified medial axes ((b) and (d)), using only 76 elements compared to their 40,808 and 690, respectively. This reduction is achieved while delivering the highest reconstruction accuracy (c). The sparsity of discrete elements and the completeness of our method facilitate a broad range of applications, such as shape generation, mesh decomposition, and shape optimization (e). In terms of continuous parameters, our method uses 117,082 scalars, whereas the medial axis and coverage axis use 56,960 and 1,016 scalars. Experimentally, even a 4.8x increase in the number of scalars for the medial axis (2.3x our method) - undesirably resulting in an approximate proportional increase in the number of discrete elements to 201,323 - still yields an average reconstruction error that is 9x higher than that of our method.
@article{guo2024medial,
title={Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape Representation},
author={Guo, Minghao and Wang, Bohan and Matusik, Wojciech},
journal={ACM Transactions on Graphics (TOG)},
volume={43},
number={6},
pages={1--23},
year={2024},
publisher={ACM New York, NY, USA}
}