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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. ALPACA: A fast and accurate computer vision approach for automated landmarking of three‐dimensional biological structures

   https://doi.org/10.1111/2041-210X.13689  

   Porto, Arthur; Rolfe, Sara; Maga, A_Murat (August 2021, Methods in Ecology and Evolution)

   Abstract Landmark‐based geometric morphometrics has emerged as an essential discipline for the quantitative analysis of size and shape in ecology and evolution. With the ever‐increasing density of digitized landmarks, the possible development of a fully automated method of landmark placement has attracted considerable attention. Despite the recent progress in image registration techniques, which could provide a pathway to automation, three‐dimensional (3D) morphometric data are still mainly gathered by trained experts. For the most part, the large infrastructure requirements necessary to perform image‐based registration, together with its system specificity and its overall speed, have prevented its wide dissemination.Here, we propose and implement a general and lightweight point cloud‐based approach to automatically collect high‐dimensional landmark data in 3D surfaces (Automated Landmarking through Point cloud Alignment and Correspondence Analysis). Our framework possesses several advantages compared with image‐based approaches. First, it presents comparable landmarking accuracy, despite relying on a single, random reference specimen and much sparser sampling of the structure's surface. Second, it can be efficiently run on consumer‐grade personal computers. Finally, it is general and can be applied at the intraspecific level to any biological structure of interest, regardless of whether anatomical atlases are available.Our validation procedures indicate that the method can recover intraspecific patterns of morphological variation that are largely comparable to those obtained by manual digitization, indicating that the use of an automated landmarking approach should not result in different conclusions regarding the nature of multivariate patterns of morphological variation.The proposed point cloud‐based approach has the potential to increase the scale and reproducibility of morphometrics research. To allow ALPACA to be used out‐of‐the‐box by users with no prior programming experience, we implemented it as a SlicerMorph module. SlicerMorph is an extension that enables geometric morphometrics data collection and 3D specimen analysis within the open‐source 3D Slicer biomedical visualization ecosystem. We expect that convenient access to this platform will make ALPACA broadly applicable within ecology and evolution. 

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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. 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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5. 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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