38-Issue 5

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https://diglib.eg.org/handle/10.2312/2632795

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A Convolutional Decoder for Point Clouds using Adaptive Instance Normalization
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Lim, Isaak; Ibing, Moritz; Kobbelt, Leif; Bommes, David and Huang, Hui
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 autoencoding 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.
Limit Shapes - A Tool for Understanding Shape Differences and Variability in 3D Model Collections
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Huang, Ruqi; Achlioptas, Panos; Guibas, Leonidas; Ovsjanikov, Maks; Bommes, David and Huang, Hui
We propose a novel construction for extracting a central or limit shape in a shape collection, connected via a functional map network. Our approach is based on enriching the latent space induced by a functional map network with an additional natural metric structure. We call this shape-like dual object the limit shape and show that its construction avoids many of the biases introduced by selecting a fixed base shape or template. We also show that shape differences between real shapes and the limit shape can be computed and characterize the unique properties of each shape in a collection - leading to a compact and rich shape representation. We demonstrate the utility of this representation in a range of shape analysis tasks, including improving functional maps in difficult situations through the mediation of limit shapes, understanding and visualizing the variability within and across different shape classes, and several others. In this way, our analysis sheds light on the missing geometric structure in previously used latent functional spaces, demonstrates how these can be addressed and finally enables a compact and meaningful shape representation useful in a variety of practical applications.
On Evaluating Consensus in RANSAC Surface Registration
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Hruda, Lukáš; Dvořák, Jan; Vasa, Libor; Bommes, David and Huang, Hui
Random Sample Consensus is a powerful paradigm that was successfully applied in various contexts, including Location Determination Problem, fundamental matrix estimation and global 3D surface registration, where many previously proposed algorithms can be interpreted as a particular implementation of this concept. In general, a set of candidate transformations is generated by some simple procedure, and an aligning transformation is chosen within this set, such that it aligns the largest portion of the input data. We observe that choosing the aligning transformation may also be interpreted as finding consensus among the candidates, which in turn involves measuring similarity of candidate rigid transformations. While it is not difficult to construct a metric that provides reasonable results, most approaches come with certain limitations and drawbacks. In this paper, we investigate possible means of measuring distances in SE(3) and compare their properties both theoretically and experimentally in a model RANSAC registration algorithm. We also propose modifications to existing measures and propose a novel method of locating the consensus transformation based on Vantage Point Tree data structure.
Parallel Globally Consistent Normal Orientation of Raw Unorganized Point Clouds
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jakob, Johannes; Buchenau, Christoph; Guthe, Michael; Bommes, David and Huang, Hui
A mandatory component for many point set algorithms is the availability of consistently oriented vertex-normals (e.g. for surface reconstruction, feature detection, visualization). Previous orientation methods on meshes or raw point clouds do not consider a global context, are often based on unrealistic assumptions, or have extremely long computation times, making them unusable on real-world data. We present a novel massively parallelized method to compute globally consistent oriented point normals for raw and unsorted point clouds. Built on the idea of graph-based energy optimization, we create a complete kNN-graph over the entire point cloud. A new weighted similarity criterion encodes the graph-energy. To orient normals in a globally consistent way we perform a highly parallel greedy edge collapse, which merges similar parts of the graph and orients them consistently. We compare our method to current state-of-the-art approaches and achieve speedups of up to two orders of magnitude. The achieved quality of normal orientation is on par or better than existing solutions, especially for real-world noisy 3D scanned data.
Structural Design Using Laplacian Shells
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ulu, Erva; McCann, Jim; Kara, Levent Burak; Bommes, David and Huang, Hui
We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self-intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection-free shell boundaries. Combined with our gradient-free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.
Structured Regularization of Functional Map Computations
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ren, Jing; Panine, Mikhail; Wonka, Peter; Ovsjanikov, Maks; Bommes, David and Huang, Hui
We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.

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Browsing 38-Issue 5 by Subject "Shape analysis"

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