Polygonal Building Segmentation by Frame Field Learning

While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons. To help bridge the gap between deep network output and the format used in downstream tasks, we add a frame field output to a deep segmentation model for extracting buildings from remote sensing images. We train a deep neural network that aligns a predicted frame field to ground truth contours. This additional objective improves segmentation quality by leveraging multi-task learning and provides structural information that later facilitates polygonization; we also introduce a polygonization algorithm that utilizes the frame field along with the raster segmentation. Our code is available at https://github.com/Lydorn/Polygonization-by-Frame-Field-Learning.Comment: CVPR 2021 - IEEE Conference on Computer Vision and Pattern Recognition, Jun 2021, Pittsburg / Virtual, United State

Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic.

Techniques based on interval and previous termaffine arithmetic next term and their modifications are shown to provide previous term reliable next term function range evaluation for the purposes of previous termsurface interrogation.next term In this paper we present a technique for the previous termreliable interrogation of implicit surfacesnext term using a modification of previous termaffine arithmeticnext term called previous term revised affine arithmetic.next term We extend the range of functions presented in previous termrevised affine arithmeticnext term by introducing previous termaffinenext term operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained previous termaffinenext term forms of arbitrary functions provide previous termfasternext term and tighter function range evaluation. Several case studies for operations using previous termaffinenext term forms are presented. The proposed techniques for previous termsurface interrogationnext term are tested using ray-previous termsurfacenext term intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide previous termfast and reliablenext term rendering of a wide range of arbitrary previous termprocedurally defined implicit surfacesnext term (including polynomial previous termsurfaces,next term constructive solids, pseudo-random objects, previous termprocedurally definednext term microstructures, and others). We compare the function range evaluation technique based on previous termextended revised affine arithmeticnext term with other previous termreliablenext term techniques based on interval and previous termaffine arithmeticnext term to show that our technique provides the previous termfastestnext term and tightest function range evaluation for previous termfast and reliable interrogation of procedurally defined implicit surfaces.next term Research Highlights The main contributions of this paper are as follows. ► The widening of the scope of previous termreliablenext term ray-tracing and spatial enumeration algorithms for previous termsurfacesnext term ranging from algebraic previous termsurfaces (definednext term by polynomials) to general previous termimplicit surfaces (definednext term by function evaluation procedures involving both previous termaffinenext term and non-previous termaffinenext term operations based on previous termrevised affine arithmetic)next term. ► The introduction of a technique for representing procedural models using special previous termaffinenext term forms (illustrated by case studies of previous termaffinenext term forms for set-theoretic operations in the form of R-functions, blending operations and conditional operations). ► The detailed derivation of special previous termaffinenext term forms for arbitrary operators

Handling Handles: Nonplanar Integrability in N=4\mathcal{N}=4 Supersymmetric Yang-Mills Theory

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.Comment: 6 pages, 4 figures; v2: updated references, typos, minor improvements (published version

On kk-Gons and kk-Holes in Point Sets

We consider a variation of the classical Erd\H{o}s-Szekeres problems on the existence and number of convex $k$-gons and $k$-holes (empty $k$-gons) in a set of $n$ points in the plane. Allowing the $k$-gons to be non-convex, we show bounds and structural results on maximizing and minimizing their numbers. Most noteworthy, for any $k$ and sufficiently large $n$, we give a quadratic lower bound for the number of $k$-holes, and show that this number is maximized by sets in convex position

Linking climate history and ice crystalline fabric evolution in polar ice sheets

Thesis (Ph.D.) University of Alaska Fairbanks, 2015An ice sheet consists of an unfathomable number of ice crystallites (grains) that typically have a preferred orientation of the crystalline lattices, termed fabric. At the surface of ice sheets, the microstructural processes that control the grain structure and fabric evolution are influenced by climate variables. Layers of firn, in different climate regimes, may have an observable variation in fabric which can persist deep into the ice sheet; fabric may have 'memory' of these past climate regimes. To model the evolution of a subtle variation in fabric below the firn-ice transition, we have developed and released an open-source Fabric Evolution with Recrystallization (FEvoR) model. FEvoR is an anisotropic stress model that distributes stresses through explicit nearest-neighbor interaction. The model includes parameterizations of grain growth, rotation recrystallization and migration recrystallization which account for the major recrystallization processes that affect the macroscopic grain structure and fabric evolution. Using this model, we explore the evolution of a subtle variation in near-surface fabric using both constant applied stress and a stress-temperature history based on data from Taylor Dome, East Antarctica. Our results show that a subtle fabric variation will be preserved for ~200ka in compressive stress regimes with temperatures typical of polar ice-sheets. The addition of shear to compressive stress regimes preserves fabric variations longer than in compression-only regimes because shear drives a positive feedback between crystal rotation and deformation. We find that temperature affects how long the fabric variation is preserved, but does not affect the strain-integrated fabric evolution profile except when crossing the thermal-activation-energy threshold (~-10°C). Even at high temperatures, migration recrystallization does not rid the fabric of its memory under most conditions. High levels of nearest-neighbor interactions between grains will rid the fabric of its memory more quickly than low levels of nearest-neighbor interactions. Because FEvoR does not compute flow, an integrated fabric-flow model is needed to investigate the flow-fabric feedbacks that arise in ice sheets. Using the open-source Parallel Ice Sheet Model (PISM) and FEvoR, we develop a combined flow-fabric model (PISM-FEvoR). We provide the first integrated flow-fabric model that explicitly computes the fabric evolution and includes all three major recrystallization processes. We show that PISM-FEvoR is able to capture the flow enhancement due to fabric by modeling a slab-on-slope glacier, initialized with a variety of fabric profiles. We also show that the entire integrated fabric-flow history affects the final simulated flow. This provides a further, independent validation of using an integrated fabric-flow model over a constant enhancement factor in ice-sheet models