Pose Induction for Novel Object Categories

We address the task of predicting pose for objects of unannotated object categories from a small seed set of annotated object classes. We present a generalized classifier that can reliably induce pose given a single instance of a novel category. In case of availability of a large collection of novel instances, our approach then jointly reasons over all instances to improve the initial estimates. We empirically validate the various components of our algorithm and quantitatively show that our method produces reliable pose estimates. We also show qualitative results on a diverse set of classes and further demonstrate the applicability of our system for learning shape models of novel object classes

Dual description of the superconducting phase transition

The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It thereby breaks a {\it global} U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.Comment: Latex + Postscript file

Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity

In 2007, the first author gave an alternative proof of the refined alternating sign matrix theorem by introducing a linear equation system that determines the refined ASM numbers uniquely. Computer experiments suggest that the numbers appearing in a conjecture concerning the number of vertically symmetric alternating sign matrices with respect to the position of the first 1 in the second row of the matrix establish the solution of a linear equation system similar to the one for the ordinary refined ASM numbers. In this paper we show how our attempt to prove this fact naturally leads to a more general conjectural multivariate Laurent polynomial identity. Remarkably, in contrast to the ordinary refined ASM numbers, we need to extend the combinatorial interpretation of the numbers to parameters which are not contained in the combinatorial admissible domain. Some partial results towards proving the conjectured multivariate Laurent polynomial identity and additional motivation why to study it are presented as well

Hybrid Bayesian Eigenobjects: Combining Linear Subspace and Deep Network Methods for 3D Robot Vision

We introduce Hybrid Bayesian Eigenobjects (HBEOs), a novel representation for 3D objects designed to allow a robot to jointly estimate the pose, class, and full 3D geometry of a novel object observed from a single viewpoint in a single practical framework. By combining both linear subspace methods and deep convolutional prediction, HBEOs efficiently learn nonlinear object representations without directly regressing into high-dimensional space. HBEOs also remove the onerous and generally impractical necessity of input data voxelization prior to inference. We experimentally evaluate the suitability of HBEOs to the challenging task of joint pose, class, and shape inference on novel objects and show that, compared to preceding work, HBEOs offer dramatically improved performance in all three tasks along with several orders of magnitude faster runtime performance.Comment: To appear in the International Conference on Intelligent Robots (IROS) - Madrid, 201

CSGNet: Neural Shape Parser for Constructive Solid Geometry

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.Comment: Accepted at CVPR-201

Differential invariants of Einstein-Weyl structures in 3D

Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two Einstein-Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation $E/G$ whose solutions correspond to nonequivalent Einstein-Weyl structures. The approach uses symmetries of the Manakov-Santini integrable system and the action of the corresponding Lie pseudogroup

GRASS: Generative Recursive Autoencoders for Shape Structures

We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which reflects fundamental intra-shape relationships such as adjacency and symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a flat, unlabeled, arbitrary part layout to a compact code. The code effectively captures hierarchical structures of man-made 3D objects of varying structural complexities despite being fixed-dimensional: an associated decoder maps a code back to a full hierarchy. The learned bidirectional mapping is further tuned using an adversarial setup to yield a generative model of plausible structures, from which novel structures can be sampled. Finally, our structure synthesis framework is augmented by a second trained module that produces fine-grained part geometry, conditioned on global and local structural context, leading to a full generative pipeline for 3D shapes. We demonstrate that without supervision, our network learns meaningful structural hierarchies adhering to perceptual grouping principles, produces compact codes which enable applications such as shape classification and partial matching, and supports shape synthesis and interpolation with significant variations in topology and geometry.Comment: Corresponding author: Kai Xu ([email protected]

Shape matching and clustering in design

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored