3,453 research outputs found
Causal categories: relativistically interacting processes
A symmetric monoidal category naturally arises as the mathematical structure
that organizes physical systems, processes, and composition thereof, both
sequentially and in parallel. This structure admits a purely graphical
calculus. This paper is concerned with the encoding of a fixed causal structure
within a symmetric monoidal category: causal dependencies will correspond to
topological connectedness in the graphical language. We show that correlations,
either classical or quantum, force terminality of the tensor unit. We also show
that well-definedness of the concept of a global state forces the monoidal
product to be only partially defined, which in turn results in a relativistic
covariance theorem. Except for these assumptions, at no stage do we assume
anything more than purely compositional symmetric-monoidal categorical
structure. We cast these two structural results in terms of a mathematical
entity, which we call a `causal category'. We provide methods of constructing
causal categories, and we study the consequences of these methods for the
general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure
Persistent homology for 3D reconstruction evaluation
Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the subject. In [1], the authors present a technique to quantitatively evaluate spatially carved volumetric representations of humans using a synthetic dataset of typical sports motion in a tennis court scenario, with regard to the number of cameras used. In this paper, we compute persistent homology over the sequence of chain complexes obtained from the 3D outcomes with increasing number of cameras. This allows us to analyze the topological evolution of the reconstruction process, something which as far as we are aware has not been investigated to date
Building Proteins in a Day: Efficient 3D Molecular Reconstruction
Discovering the 3D atomic structure of molecules such as proteins and viruses
is a fundamental research problem in biology and medicine. Electron
Cryomicroscopy (Cryo-EM) is a promising vision-based technique for structure
estimation which attempts to reconstruct 3D structures from 2D images. This
paper addresses the challenging problem of 3D reconstruction from 2D Cryo-EM
images. A new framework for estimation is introduced which relies on modern
stochastic optimization techniques to scale to large datasets. We also
introduce a novel technique which reduces the cost of evaluating the objective
function during optimization by over five orders or magnitude. The net result
is an approach capable of estimating 3D molecular structure from large scale
datasets in about a day on a single workstation.Comment: To be presented at IEEE Conference on Computer Vision and Pattern
Recognition (CVPR) 201
Weakly supervised 3D Reconstruction with Adversarial Constraint
Supervised 3D reconstruction has witnessed a significant progress through the
use of deep neural networks. However, this increase in performance requires
large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D
supervision as an alternative for expensive 3D CAD annotation. Specifically, we
use foreground masks as weak supervision through a raytrace pooling layer that
enables perspective projection and backpropagation. Additionally, since the 3D
reconstruction from masks is an ill posed problem, we propose to constrain the
3D reconstruction to the manifold of unlabeled realistic 3D shapes that match
mask observations. We demonstrate that learning a log-barrier solution to this
constrained optimization problem resembles the GAN objective, enabling the use
of existing tools for training GANs. We evaluate and analyze the manifold
constrained reconstruction on various datasets for single and multi-view
reconstruction of both synthetic and real images
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