The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art methods rely on patch-based or mapping-based techniques that introduce resampling operations in order to encode neighborhood information in a structured and regular manner. We investigate whether such resampling can be avoided, and propose a simple and direct encoding approach. It does not only increase processing efficiency due to its simplicity -its direct nature also avoids any loss in data fidelity. To evaluate the proposed method, we perform a number of experiments in the challenging domain of intrinsic, non-rigid shape correspondence estimation. In comparisons to current methods we observe that our approach is able to achieve highly competitive results.

We present a method that expands on previous work in learning human perceived style similarity across objects with different structures and functionalities. Unlike previous approaches that tackle this problem with the help of hand‐crafted geometric descriptors, we make use of recent advances in metric learning with neural networks (deep metric learning). This allows us to train the similarity metric on a shape collection directly, since any low‐ or high‐level features needed to discriminate between different styles are identified by the neural network automatically. Furthermore, we avoid the issue of finding and comparing sub‐elements of the shapes. We represent the shapes as rendered images and show how image tuples can be selected, generated and used efficiently for deep metric learning. We also tackle the problem of training our neural networks on relatively small datasets and show that we achieve style classification accuracy competitive with the state of the art. Finally, to reduce annotation effort we propose a method to incorporate heterogeneous data sources by adding annotated photos found online in order to expand or supplant parts of our training data.

Summary. A purely topological approach for the generation of hexahedral meshes from quadrilateral surface meshes of genus zero has been proposed by M. Müller-Hannemann: in a first stage, the input surface mesh is reduced to a single hexahedron by successively eliminating loops from the dual graph of the quad mesh; in the second stage, the hexahedral mesh is constructed by extruding a layer of hexahedra for each dual loop from the first stage in reverse elimination order. In this paper, we introduce several techniques to extend the scope of target shapes of the approach and significantly improve the quality of the generated hexahedral meshes. While the original method can only handle "almost convex" objects and requires mesh surgery and remeshing in case of concave geometry, we propose a method to overcome this issue by introducing the notion of concave dual loops. Furthermore, we analyze and improve the heuristic to determine the elimination order for the dual loops such that the inordinate introduction of interior singular edges, i.e. edges of degree other than four in the hexahedral mesh, can be avoided in many cases.

Automatic synthesis of high quality 3D shapes is an ongoing and challenging area of research. While several data‐driven methods have been proposed that make use of neural networks to generate 3D shapes, none of them reach the level of quality that deep learning synthesis approaches for images provide. In this work we present a method for a convolutional point cloud decoder/generator that makes use of recent advances in the domain of image synthesis. Namely, we use Adaptive Instance Normalization and offer an intuition on why it can improve training. Furthermore, we propose extensions to the minimization of the commonly used Chamfer distance for auto‐encoding point clouds. In addition, we show that careful sampling is important both for the input geometry and in our point cloud generation process to improve results. The results are evaluated in an auto‐encoding setup to offer both qualitative and quantitative analysis. The proposed decoder is validated by an extensive ablation study and is able to outperform current state of the art results in a number of experiments. We show the applicability of our method in the fields of point cloud upsampling, single view reconstruction, and shape synthesis.

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