Generalized intrinsic symmetry detection

In this paper, we address the problem of detecting partial symmetries in 3D objects. In contrast to previous work, our algorithm is able to match deformed symmetric parts: We first develop an algorithm for the case of approximately isometric deformations, based on matching graphs of surface feature lines that are annotated with intrinsic geometric properties. The sensitivity to non-isometry is controlled by tolerance parameters for each such annotation. Using large tolerance values for some of these annotations and a robust matching of the graph topology yields a more general symmetry detection algorithm that can detect similarities in structures that have undergone strong deformations. This approach for the first time allows for detecting partial intrinsic as well as more general, non-isometric symmetries. We evaluate the recognition performance of our technique for a number synthetic and real-world scanner data sets

Quantum Field Theory: Where We Are

We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.Comment: To appear in: An Assessment of Current Paradigms in the Physics of Fundamental Phenomena, to be published by Springer Verlag (2006

Learning to Reconstruct Shapes from Unseen Classes

From a single image, humans are able to perceive the full 3D shape of an object by exploiting learned shape priors from everyday life. Contemporary single-image 3D reconstruction algorithms aim to solve this task in a similar fashion, but often end up with priors that are highly biased by training classes. Here we present an algorithm, Generalizable Reconstruction (GenRe), designed to capture more generic, class-agnostic shape priors. We achieve this with an inference network and training procedure that combine 2.5D representations of visible surfaces (depth and silhouette), spherical shape representations of both visible and non-visible surfaces, and 3D voxel-based representations, in a principled manner that exploits the causal structure of how 3D shapes give rise to 2D images. Experiments demonstrate that GenRe performs well on single-view shape reconstruction, and generalizes to diverse novel objects from categories not seen during training.Comment: NeurIPS 2018 (Oral). The first two authors contributed equally to this paper. Project page: http://genre.csail.mit.edu

PRS-Net: planar reflective symmetry detection net for 3D models

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces