Complex Kerr Geometry, Twistors and the Dirac Electron

The Kerr-Newman spinning particle displays some remarkable relations to the Dirac electron and has a reach spinor structure which is based on a twistorial description of the Kerr congruence determined by the Kerr theorem. We consider the relation between this spinor-twistorial structure and spinors of the Dirac equation, and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the twistorial structure of Kerr geometry. As a result, the Dirac electron acquires an extended space-time structure having clear coordinate description with natural incorporation of a gravitational field. The relation between the Dirac wave function and Kerr geometry is realized via a chain of links: {\it Dirac wave function $\Rightarrow$ Complex Kerr-Newman Source $\Rightarrow$ Kerr Theorem $\Rightarrow$ Real Kerr geometry.} As a result, the wave function acquires the role of an ``order parameter'' which controls spin, dynamics, and twistorial polarization of Kerr-Newman space-time.Comment: 12 pages, 3 figs. Talk at the conference QFEXT'0

Learning to Synthesize a 4D RGBD Light Field from a Single Image

We present a machine learning algorithm that takes as input a 2D RGB image and synthesizes a 4D RGBD light field (color and depth of the scene in each ray direction). For training, we introduce the largest public light field dataset, consisting of over 3300 plenoptic camera light fields of scenes containing flowers and plants. Our synthesis pipeline consists of a convolutional neural network (CNN) that estimates scene geometry, a stage that renders a Lambertian light field using that geometry, and a second CNN that predicts occluded rays and non-Lambertian effects. Our algorithm builds on recent view synthesis methods, but is unique in predicting RGBD for each light field ray and improving unsupervised single image depth estimation by enforcing consistency of ray depths that should intersect the same scene point. Please see our supplementary video at https://youtu.be/yLCvWoQLnmsComment: International Conference on Computer Vision (ICCV) 201

GAGAN: Geometry-Aware Generative Adversarial Networks

Deep generative models learned through adversarial training have become increasingly popular for their ability to generate naturalistic image textures. However, aside from their texture, the visual appearance of objects is significantly influenced by their shape geometry; information which is not taken into account by existing generative models. This paper introduces the Geometry-Aware Generative Adversarial Networks (GAGAN) for incorporating geometric information into the image generation process. Specifically, in GAGAN the generator samples latent variables from the probability space of a statistical shape model. By mapping the output of the generator to a canonical coordinate frame through a differentiable geometric transformation, we enforce the geometry of the objects and add an implicit connection from the prior to the generated object. Experimental results on face generation indicate that the GAGAN can generate realistic images of faces with arbitrary facial attributes such as facial expression, pose, and morphology, that are of better quality than current GAN-based methods. Our method can be used to augment any existing GAN architecture and improve the quality of the images generated

Neural View-Interpolation for Sparse Light Field Video

We suggest representing light field (LF) videos as "one-off" neural networks (NN), i.e., a learned mapping from view-plus-time coordinates to high-resolution color values, trained on sparse views. Initially, this sounds like a bad idea for three main reasons: First, a NN LF will likely have less quality than a same-sized pixel basis representation. Second, only few training data, e.g., 9 exemplars per frame are available for sparse LF videos. Third, there is no generalization across LFs, but across view and time instead. Consequently, a network needs to be trained for each LF video. Surprisingly, these problems can turn into substantial advantages: Other than the linear pixel basis, a NN has to come up with a compact, non-linear i.e., more intelligent, explanation of color, conditioned on the sparse view and time coordinates. As observed for many NN however, this representation now is interpolatable: if the image output for sparse view coordinates is plausible, it is for all intermediate, continuous coordinates as well. Our specific network architecture involves a differentiable occlusion-aware warping step, which leads to a compact set of trainable parameters and consequently fast learning and fast execution