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1. Geometric Deep Learning for Shape Correspondence in Mass Customization by Three-Dimensional Printing

   https://doi.org/doi.org/10.1115/1.4046746  

   Huang, Jida; Sun, Hongyue; Kwok, Tsz-Ho; Zhou, Chi; Xu, Wenyao (June 2020, Journal of manufacturing science and engineering)

   Many industries, such as human-centric product manufacturing, are calling for mass customization with personalized products. One key enabler of mass customization is 3D printing, which makes flexible design and manufacturing possible. However, the personalized designs bring challenges for the shape matching and analysis, owing to the high complexity and shape variations. Traditional shape matching methods are limited to spatial alignment and finding a transformation matrix for two shapes, which cannot determine a vertex-to-vertex or feature-to-feature correlation between the two shapes. Hence, such a method cannot measure the deformation of the shape and interested features directly. To measure the deformations widely seen in the mass customization paradigm and address the issues of alignment methods in shape matching, we identify the geometry matching of deformed shapes as a correspondence problem. The problem is challenging due to the huge solution space and nonlinear complexity, which is difficult for conventional optimization methods to solve. According to the observation that the well-established massive databases provide the correspondence results of the treated teeth models, a learning-based method is proposed for the shape correspondence problem. Specifically, a state-of-the-art geometric deep learning method is used to learn the correspondence of a set of collected deformed shapes. Through learning the deformations of the models, the underlying variations of the shapes are extracted and used for finding the vertex-to-vertex mapping among these shapes. We demonstrate the application of the proposed approach in the orthodontics industry, and the experimental results show that the proposed method can predict correspondence fast and accurate, also robust to extreme cases. Furthermore, the proposed method is favorably suitable for deformed shape analysis in mass customization enabled by 3D printing. 

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2. Radish: Radar Implicit Shapes Via Extreme-Wideband Sub-Terahertz Synthetic Aperture Radar

   https://doi.org/10.1109/CISA64343.2025.11091563  

   Farrell, Sean M; Li, Kris; Vargas, Edwin; Sabharwal, Ashutosh; Veeraraghavan, Ashok; Everitt, Henry O; Habshush, Ariel; Zhang, Li; Woods, Brian (June 2025, IEEE)

   We explore synthetic aperture radar (SAR) 3D imaging capabilities in the sub-THz band using a novel 110-260 GHz experimental testbed. We propose RADar Implicit SHapes (RADISH), a post-processing method that leverages the SAR’s millimeter-level imaging resolution to estimate an object’s 3D shape. RADISH first c onverts high-resolution SAR images to a detailed point cloud of a scanned object. The point cloud is then used to fit an implicit neural representation to the object’s surface by approximating the signed distance function of the scene. We experimentally validate RADISH’s ability to represent the salient geometric features of real-world 3D objects. 

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3. Directionally Convolutional Networks for 3D Shape Segmentation

   Xu, Haotian; Dong, Ming; Zhong, Zichun (January 2017, IEEE International Conference on Computer Vision (ICCV))

   Previous approaches on 3D shape segmentation mostly rely on heuristic processing and hand-tuned geometric descriptors. In this paper, we propose a novel 3D shape representation learning approach, Directionally Convolutional Network (DCN), to solve the shape segmentation problem. DCN extends convolution operations from images to the surface mesh of 3D shapes. With DCN, we learn effective shape representations from raw geometric features, i.e., face normals and distances, to achieve robust segmentation. More specifically, a two-stream segmentation framework is proposed: one stream is made up by the proposed DCN with the face normals as the input, and the other stream is implemented by a neural network with the face distance histogram as the input. The learned shape representations from the two streams are fused by an element-wise product. Finally, Conditional Random Field (CRF) is applied to optimize the segmentation. Through extensive experiments conducted on benchmark datasets, we demonstrate that our approach outperforms the current state-of-the-arts (both classic and deep learning-based) on a large variety of 3D shapes. 

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4. A Predictive and Generative Design Approach for Three-Dimensional Mesh Shapes Using Target-Embedding Variational Autoencoder

   https://doi.org/10.1115/1.4054906  

   Li, Xingang; Xie, Charles; Sha, Zhenghui (November 2022, Journal of Mechanical Design)

   Abstract In this paper, we present a predictive and generative design approach for supporting the conceptual design of product shapes in 3D meshes. We develop a target-embedding variational autoencoder (TEVAE) neural network architecture, which consists of two modules: (1) a training module with two encoders and one decoder (E2D network) and (2) an application module performing the generative design of new 3D shapes and the prediction of a 3D shape from its silhouette. We demonstrate the utility and effectiveness of the proposed approach in the design of 3D car body and mugs. The results show that our approach can generate a large number of novel 3D shapes and successfully predict a 3D shape based on a single silhouette sketch. The resulting 3D shapes are watertight polygon meshes with high-quality surface details, which have better visualization than voxels and point clouds, and are ready for downstream engineering evaluation (e.g., drag coefficient) and prototyping (e.g., 3D printing). 

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5. Deep learning-based surrogate model for three-dimensional patient-specific computational fluid dynamics

   https://doi.org/10.1063/5.0101128  

   Du, Pan; Zhu, Xiaozhi; Wang, Jian-Xun (August 2022, Physics of Fluids)

   Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant challenges, particularly when it comes to complex three-dimensional (3D) patient-specific shapes in the real world. First, it is notoriously challenging to parameterize the input space of arbitrary complex 3D geometries. Second, the process often involves massive forward simulations, which are extremely computationally demanding or even infeasible. We propose a novel deep learning surrogate modeling solution to address these challenges and enable rapid hemodynamic predictions. Specifically, a statistical generative model for 3D patient-specific shapes is developed based on a small set of baseline patient-specific geometries. An unsupervised shape correspondence solution is used to enable geometric morphing and scalable shape synthesis statistically. Moreover, a simulation routine is developed for automatic data generation by automatic meshing, boundary setting, simulation, and post-processing. An efficient supervised learning solution is proposed to map the geometric inputs to the hemodynamics predictions in latent spaces. Numerical studies on aortic flows are conducted to demonstrate the effectiveness and merit of the proposed techniques. 

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