Shape Generation using Spatially Partitioned Point Clouds

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in reasonably good correspondences across all shapes. We then use PCA analysis to derive a linear shape basis across the spatially partitioned points, and optimize the point ordering by iteratively minimizing the PCA reconstruction error. Even with the spatial sorting, the point clouds are inherently noisy and the resulting distribution over the shape coefficients can be highly multi-modal. We propose to use the expressive power of neural networks to learn a distribution over the shape coefficients in a generative-adversarial framework. Compared to 3D shape generative models trained on voxel-representations, our point-based method is considerably more light-weight and scalable, with little loss of quality. It also outperforms simpler linear factor models such as Probabilistic PCA, both qualitatively and quantitatively, on a number of categories from the ShapeNet dataset. Furthermore, our method can easily incorporate other point attributes such as normal and color information, an additional advantage over voxel-based representations.Comment: To appear at BMVC 201

From euclidean field theory to quantum field theory

In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an appropriate set of euclidean n-point functions (Schwinger distributions), a Wightman theory can be reconstructed by an application of the famous Osterwalder-Schrader reconstruction theorem. This procedure (Wick rotation), which relates classical statistical mechanics and quantum field theory, is, however, somewhat subtle. It relies on the analytic properties of the euclidean n-point functions. We shall present here a C*-algebraic version of the Osterwalder-Scharader reconstruction theorem. We shall see that, via our reconstruction scheme, a Haag-Kastler net of bounded operators can directly be reconstructed. Our considerations also include objects, like Wilson loop variables, which are not point-like localized objects like distributions. This point of view may also be helpful for constructing gauge theories.Comment: 35 page

Distributed Storage Systems based on Equidistant Subspace Codes

Distributed storage systems based on equidistant constant dimension codes are presented. These equidistant codes are based on the Pl\"{u}cker embedding, which is essential in the repair and the reconstruction algorithms. These systems posses several useful properties such as high failure resilience, minimum bandwidth, low storage, simple algebraic repair and reconstruction algorithms, good locality, and compatibility with small fields

Single-Shot Clothing Category Recognition in Free-Configurations with Application to Autonomous Clothes Sorting

This paper proposes a single-shot approach for recognising clothing categories from 2.5D features. We propose two visual features, BSP (B-Spline Patch) and TSD (Topology Spatial Distances) for this task. The local BSP features are encoded by LLC (Locality-constrained Linear Coding) and fused with three different global features. Our visual feature is robust to deformable shapes and our approach is able to recognise the category of unknown clothing in unconstrained and random configurations. We integrated the category recognition pipeline with a stereo vision system, clothing instance detection, and dual-arm manipulators to achieve an autonomous sorting system. To verify the performance of our proposed method, we build a high-resolution RGBD clothing dataset of 50 clothing items of 5 categories sampled in random configurations (a total of 2,100 clothing samples). Experimental results show that our approach is able to reach 83.2\% accuracy while classifying clothing items which were previously unseen during training. This advances beyond the previous state-of-the-art by 36.2\%. Finally, we evaluate the proposed approach in an autonomous robot sorting system, in which the robot recognises a clothing item from an unconstrained pile, grasps it, and sorts it into a box according to its category. Our proposed sorting system achieves reasonable sorting success rates with single-shot perception.Comment: 9 pages, accepted by IROS201

Two Forms of Inconsistency in Quantum Foundations

Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger (2011) corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch Books can be interpreted normatively.Comment: 26 pages, 5 figure