Shape-from-intrinsic operator

Shape-from-X is an important class of problems in the fields of geometry processing, computer graphics, and vision, attempting to recover the structure of a shape from some observations. In this paper, we formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic differential operators defined on the mesh. Particularly interesting instances of our SfO problem include synthesis of shape analogies, shape-from-Laplacian reconstruction, and shape exaggeration. Numerically, we approach the SfO problem by splitting it into two optimization sub-problems that are applied in an alternating scheme: metric-from-operator (reconstruction of the discrete metric from the intrinsic operator) and embedding-from-metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem)

OperatorNet: Recovering 3D Shapes From Difference Operators

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.Comment: Accepted to ICCV 201

Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

DeformSyncNet: Deformation Transfer via Synchronized Shape Deformation Spaces

Shape deformation is an important component in any geometry processing toolbox. The goal is to enable intuitive deformations of single or multiple shapes or to transfer example deformations to new shapes while preserving the plausibility of the deformed shape(s). Existing approaches assume access to point-level or part-level correspondence or establish them in a preprocessing phase, thus limiting the scope and generality of such approaches. We propose DeformSyncNet, a new approach that allows consistent and synchronized shape deformations without requiring explicit correspondence information. Technically, we achieve this by encoding deformations into a class-specific idealized latent space while decoding them into an individual, model-specific linear deformation action space, operating directly in 3D. The underlying encoding and decoding are performed by specialized (jointly trained) neural networks. By design, the inductive bias of our networks results in a deformation space with several desirable properties, such as path invariance across different deformation pathways, which are then also approximately preserved in real space. We qualitatively and quantitatively evaluate our framework against multiple alternative approaches and demonstrate improved performance

Deep Neural Networks for Visual Reasoning, Program Induction, and Text-to-Image Synthesis.

Deep neural networks excel at pattern recognition, especially in the setting of large scale supervised learning. A combination of better hardware, more data, and algorithmic improvements have yielded breakthroughs in image classification, speech recognition and other perception problems. The research frontier has shifted towards the weak side of neural networks: reasoning, planning, and (like all machine learning algorithms) creativity. How can we advance along this frontier using the same generic techniques so effective in pattern recognition; i.e. gradient descent with backpropagation? In this thesis I develop neural architectures with new capabilities in visual reasoning, program induction and text-to-image synthesis. I propose two models that disentangle the latent visual factors of variation that give rise to images, and enable analogical reasoning in the latent space. I show how to augment a recurrent network with a memory of programs that enables the learning of compositional structure for more data-efficient and generalizable program induction. Finally, I develop a generative neural network that translates descriptions of birds, flowers and other categories into compelling natural images.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135763/1/reedscot_1.pd

Societies against the Chief? Re-examining the value of ‘heterarchy’ as a concept for examining European Iron Age societies

Carole Crumley’s (1979; 1995a; 1995b; 2015) explorations on the applicability of heterarchy as a concept within archaeology have been highly influential in Anglo-American discourse on social organization. Despite largely emerging from Crumley’s work on Iron Age France (Crumley, 1979), however, the relevance of heterarchy as a concept for challenging hierarchical models of European Iron Age societies has largely been restricted to Britain (e.g. Moore, 2007a; Hill, 2011), where evidence for “elites” seems most obviously lacking. Northwestern Iberia has also been a locus for discussion of acephalous and nonhierarchical social forms (Fernández-Posse & Sánchez-Palencia, 1998; González-García et al., 2011; González-Ruibal, 2012; Sastre-Prats, 2011), but one where explicit discussions of heterarchy have rarely featured. More recently, it has been argued that almost all European Iron Age societies can be regarded as “broadly heterarchical” (e.g. Bradley et al., 2015: 260), although the wider implications of this have yet to be explored. What is the place, then, of heterarchy in Iron Age studies? Has it merely become a label for all nonhierarchical models (Fernández-Götz, 2014: 36), creating various Iron Age “societies against the state” (Clastres, 1977), or does it offer ways of exploring not just alternatives to hierarchies but thicker descriptions of how all Iron Age societies worked

Technical Challenges of Integrating the Space Shuttle

The Space Shuttle is a complex flight vehicle comprised of four major elements: orbiter, external tank, main engines, and solid rocket booster. Integrating the requirements, design, and verification requires resolution of challenging technical problems in flight performance, aerodynamics, aero thermodynamics, structural dynamics and loads, flight control, and propulsion. The departure from typical cylindrical booster and spacecraft launch configurations complicates analysis and design. Techniques being used to identify and resolve technical problems encountered in integrating the Space Shuttle are discussed