Vector models and generalized SYK models

We consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. A chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.Comment: 36 pages, 12 figure

Adaptive View Planning for Aerial 3D Reconstruction

With the proliferation of small aerial vehicles, acquiring close up aerial imagery for high quality reconstruction of complex scenes is gaining importance. We present an adaptive view planning method to collect such images in an automated fashion. We start by sampling a small set of views to build a coarse proxy to the scene. We then present (i)~a method that builds a view manifold for view selection, and (ii) an algorithm to select a sparse set of views. The vehicle then visits these viewpoints to cover the scene, and the procedure is repeated until reconstruction quality converges or a desired level of quality is achieved. The view manifold provides an effective efficiency/quality compromise between using the entire 6 degree of freedom pose space and using a single view hemisphere to select the views. Our results show that, in contrast to existing "explore and exploit" methods which collect only two sets of views, reconstruction quality can be drastically improved by adding a third set. They also indicate that three rounds of data collection is sufficient even for very complex scenes. We compare our algorithm to existing methods in three challenging scenes. We require each algorithm to select the same number of views. Our algorithm generates views which produce the least reconstruction error

View Selection with Geometric Uncertainty Modeling

Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is a dominant ground plane $\mathcal{G}$ viewed from a parallel viewing plane $\mathcal{S}$ above it. Such instances commonly arise, for example, in aerial photography. Consider a world point $g \in \mathcal{G}$ and its worst case reconstruction uncertainty $\varepsilon(g,\mathcal{S})$ obtained by merging \emph{all} possible views of $g$ chosen from $\mathcal{S}$. We first show that one can pick two views $s_p$ and $s_q$ such that the uncertainty $\varepsilon(g,\{s_p,s_q\})$ obtained using only these two views is almost as good as (i.e. within a small constant factor of) $\varepsilon(g,\mathcal{S})$. Next, we extend the result to the entire ground plane $\mathcal{G}$ and show that one can pick a small subset of $\mathcal{S'} \subseteq \mathcal{S}$ (which grows only linearly with the area of $\mathcal{G}$) and still obtain a constant factor approximation, for every point $g \in \mathcal{G}$, to the minimum worst case estimate obtained by merging all views in $\mathcal{S}$. Finally, we present a multi-resolution view selection method which extends our techniques to non-planar scenes. We show that the method can produce rich and accurate dense reconstructions with a small number of views. Our results provide a view selection mechanism with provable performance guarantees which can drastically increase the speed of scene reconstruction algorithms. In addition to theoretical results, we demonstrate their effectiveness in an application where aerial imagery is used for monitoring farms and orchards