Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p -norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.
While we approach bone-like porous structures for their superior mechanical properties by using topology optimization, we note that other directions---considering different aspects of bone---exist for generating such structures. One such direction is material reconstruction. For instance, Liu and Shapiro @cite_23 proposed to reconstruct 3D micro-structures from 2D sample images using example-based texture synthesis @cite_39 , such that the synthesised structures preserve statistical features of the given sample.
@cite_23 @cite_39
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Abstract Computer models of random heterogeneous materials are becoming increasingly important in order to support the latest advances in material science, biomedical applications and manufacturing. Such models usually take the form of a microstructure whose geometry is reconstructed from a small material sample, an exemplar. A widely used traditional approach to material reconstruction relies on stochastic optimization to approximate the material descriptors of the exemplar, such as volume fraction and two-point correlation functions. This approach is computationally intensive and is limited to certain types of isotropic materials. We show that formulating material reconstruction as a Markov Random Field (MRF) texture synthesis leads to a number of advantages over the traditional optimization-based approaches. These include improved computational efficiency, preservation of many material descriptors, including correlation functions and Minkowski functionals, ability to reconstruct anisotropic materials, and direct use of the gray-scale material images and two-dimensional cross-sections. Quantifying the quality of reconstruction in terms of correlation functions as material descriptors suggests a systematic procedure for selecting a size of neighborhood, a key parameter in the texture synthesis procedure. We support our observations by experiments using implementation with Gaussian pyramid and periodic boundary conditions. Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view images is a fundamental yet active research area in computer vision. Despite the steady progress in multi-view stereo (MVS) reconstruction, many existing methods are still limited in recovering fine-scale details and sharp features while suppressing noises, and may fail in reconstructing regions with less textures. To address these limitations, this paper presents a detail-preserving and content-aware variational (DCV) MVS method, which reconstructs the 3D surface by alternating between reprojection error minimization and mesh denoising. In reprojection error minimization, we propose a novel inter-image similarity measure, which is effective to preserve fine-scale details of the reconstructed surface and builds a connection between guided image filtering and image registration. In mesh denoising, we propose a content-aware @math -minimization algorithm by adaptively estimating the @math value and regularization parameters. Compared with conventional isotropic mesh smoothing approaches, the proposed method is much more promising in suppressing noise while preserving sharp features. Experimental results on benchmark data sets demonstrate that our DCV method is capable of recovering more surface details, and obtains cleaner and more accurate reconstructions than the state-of-the-art methods. In particular, our method achieves the best results among all published methods on the Middlebury dino ring and dino sparse data sets in terms of both completeness and accuracy. In this paper, we present a learning based approach to depth fusion, i.e., dense 3D reconstruction from multiple depth images. The most common approach to depth fusion is based on averaging truncated signed distance functions, which was originally proposed by Curless and Levoy in 1996. While this method is simple and provides great results, it is not able to reconstruct (partially) occluded surfaces and requires a large number frames to filter out sensor noise and outliers. Motivated by the availability of large 3D model repositories and recent advances in deep learning, we present a novel 3D CNN architecture that learns to predict an implicit surface representation from the input depth maps. Our learning based method significantly outperforms the traditional volumetric fusion approach in terms of noise reduction and outlier suppression. By learning the structure of real world 3D objects and scenes, our approach is further able to reconstruct occluded regions and to fill in gaps in the reconstruction. We demonstrate that our learning based approach outperforms both vanilla TSDF fusion as well as TV-L1 fusion on the task of volumetric fusion. Further, we demonstrate state-of-the-art 3D shape completion results. In this paper, we present a learning based approach to depth fusion, i.e., dense 3D reconstruction from multiple depth images. The most common approach to depth fusion is based on averaging truncated signed distance functions, which was originally proposed by Curless and Levoy in 1996. While this method is simple and provides great results, it is not able to reconstruct (partially) occluded surfaces and requires a large number frames to filter out sensor noise and outliers. Motivated by the availability of large 3D model repositories and recent advances in deep learning, we present a novel 3D CNN architecture that learns to predict an implicit surface representation from the input depth maps. Our learning based method significantly outperforms the traditional volumetric fusion approach in terms of noise reduction and outlier suppression. By learning the structure of real world 3D objects and scenes, our approach is further able to reconstruct occluded regions and to fill in gaps in the reconstruction. We demonstrate that our learning based approach outperforms both vanilla TSDF fusion as well as TV-L1 fusion on the task of volumetric fusion. Further, we demonstrate state-of-the-art 3D shape completion results.