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Distribution-Sensitive Bounds on Relative Approximations of Geometric RangesMar 15 2019A family $\mathcal{R}$ of ranges and a set $X$ of points together define a range space $(X, \mathcal{R}|_X)$, where $\mathcal{R}|_X = \{X \cap h \mid h \in \mathcal{R}\}$. We want to find a structure to estimate the quantity $|X \cap h|/|X|$ for any range ... More
Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-AssemblyMar 14 2019Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must match and bind ... More
Bounded maximum degree conjecture holds precisely for $c$-crossing-critical graphs with $c \leq 12$Mar 13 2019We study $c$-crossing-critical graphs, which are the minimal graphs that require at least $c$ edge-crossings when drawn in the plane. For every fixed pair of integers with $c\ge 13$ and $d\ge 1$, we give first explicit constructions of $c$-crossing-critical ... More
Cubic Planar Graphs that cannot be Drawn on few LinesMar 12 2019For every integer $\ell$, we construct a cubic 3-vertex-connected planar bipartite graph $G$ with $O(\ell^3)$ vertices such that there is no planar straight-line drawing of $G$ whose vertices all lie on $\ell$ lines. This strengthens previous results ... More
Near-Optimal Algorithms for Shortest Paths in Weighted Unit-Disk GraphsMar 12 2019We revisit a classical graph-theoretic problem, the \textit{single-source shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in $O(n \log^2 n)$ time using linear ... More
Linear Encodings for Polytope Containment ProblemsMar 12 2019The polytope containment problem is deciding whether a polytope is a contained within another polytope. This problem is rooted in computational convexity, and arises in applications such as verification and control of dynamical systems. The complexity ... More
Efficient Algorithms for Ortho-Radial Graph DrawingMar 12 2019Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the existence of ... More
Counting Polygon Triangulations is HardMar 12 2019We prove that it is $\#\mathsf{P}$-complete to count the triangulations of a (non-simple) polygon.
Fitting Tractable Convex Sets to Support Function EvaluationsMar 11 2019The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the error over all ... More
NormalNet: Learning based Guided Normal Filtering for Mesh DenoisingMar 10 2019Mesh denoising is a critical technology in geometry processing, which aims to recover high-fidelity 3D mesh models of objects from noise-corrupted versions. In this work, we propose a deep learning based face normal filtering scheme for mesh denoising, ... More
Active Learning a Convex Body in Low DimensionsMar 08 2019Consider a set $P \subseteq \mathbb{R}^d$ of $n$ points, and a convex body $C$ provided via a separation oracle. The task at hand is to decide for each point of $P$ if it is in $C$. We show that one can solve this problem in two and three dimensions using ... More
The VC Dimension of Metric Balls under Fréchet and Hausdorff DistancesMar 07 2019The Vapnik-Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation ... More
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial LiftingMar 07 2019We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in $\mathbb{R}^3$. We show that this question, which is equivalent to deciding the emptiness of certain semi-algebraic ... More
Reparameterizing Distributions on Lie GroupsMar 07 2019Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due to the absence ... More
A face cover perspective to $\ell_1$ embeddings of planar graphsMar 07 2019It was conjectured by Gupta et. al. [Combinatorica04] that every planar graph can be embedded into $\ell_1$ with constant distortion. However, given an $n$-vertex weighted planar graph, the best upper bound is only $O(\sqrt{\log n})$ by Rao [SoCG99]. ... More
Encoding 3SUMMar 06 2019We consider the following problem: given three sets of real numbers, output a word-RAM data structure from which we can efficiently recover the sign of the sum of any triple of numbers, one in each set. This is similar to a previous work by some of the ... More
Controlling Meshes via Curvature: Spin Transformations for Pose-Invariant Shape ProcessingMar 06 2019We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion -- e.g., rebuilding ... More
The $k$-Fréchet distanceMar 06 2019We introduce a new distance measure for comparing polygonal chains: the $k$-Fr\'echet distance. As the name implies, it is closely related to the well-studied Fr\'echet distance but detects similarities between curves that resemble each other only piecewise. ... More
CPG graphs: Some structural and hardness resultsMar 05 2019In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in [11]. A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid in one-to-one correspondence ... More
Efficient representation and manipulation of quadratic surfaces using Geometric AlgebrasMar 05 2019Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these frameworks support ... More
Quantifying Gait Changes Using Microsoft Kinect and Sample EntropyMar 05 2019This study describes a method to quantify potential gait changes in human subjects. Microsoft Kinect devices were used to provide and track coordinates of fifteen different joints of a subject over time. Three male subjects walk a 10-foot path multiple ... More
An Adaptive Grid Algorithm for Computing the Homology Group of Semialgebraic SetMar 04 2019Looking for an efficient algorithm for the computation of the homology groups of an algebraic set or even a semi-algebraic set is an important problem in the effective real algebraic geometry. Recently, Peter Burgisser, Felipe Cucker and Pierre Lairez ... More
A Divide-and-Conquer Algorithm for Two-Point $L_1$ Shortest Path Queries in Polygonal DomainsMar 04 2019Let $\mathcal{P}$ be a polygonal domain of $h$ holes and $n$ vertices. We study the problem of constructing a data structure that can compute a shortest path between $s$ and $t$ in $\mathcal{P}$ under the $L_1$ metric for any two query points $s$ and ... More
Decomposition of Map Graphs with ApplicationsMar 04 2019Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and Thomas that states ... More
Incremental Visual-Inertial 3D Mesh Generation with Structural RegularitiesMar 04 2019Visual-Inertial Odometry (VIO) algorithms typically rely on a point cloud representation of the scene that does not model the topology of the environment. A 3D mesh instead offers a richer, yet lightweight, model. Nevertheless, building a 3D mesh out ... More
Robust corner and tangent point detection for strokes with deep learning approachMar 03 2019A robust corner and tangent point detection (CTPD) tool is critical for sketch-based engineering modeling. This paper proposes a robust CTPD approach for hand-drawn strokes with deep learning approach. Its robustness for users, stroke shapes and biased ... More
DimDraw -- A novel tool for drawing concept latticesMar 02 2019Concept lattice drawings are an important tool to visualize complex relations in data in a simple manner to human readers. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although those methods are satisfying ... More
Fast Distance Fields for Fluid Dynamics Mesh Generation on Graphics HardwareMar 01 2019We present a CUDA accelerated implementation of the Characteristic/Scan Conversion algorithm to generate narrow band signed distance fields in logically Cartesian grids. We outline an approach of task and data management on GPUs based on an input of a ... More
A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network ModelsFeb 28 2019Antifragility is a property to not only resist stress and but also to benefit from it. Even though antifragile dynamics are found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively ... More
Dynamic Planar Convex HullFeb 28 2019In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points in amortized ... More
On the Area Requirements of Planar Straight-Line Orthogonal Drawings of Ternary TreesFeb 28 2019In this paper, we study the area requirements of planar straight-line orthogonal drawings of ternary trees. We prove that every ternary tree admits such a drawing in sub-quadratic area. Further, we present upper bounds, the outcomes of an experimental ... More
Probabilistic smallest enclosing ball in high dimensions via subgradient samplingFeb 28 2019We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is to improve the ... More
Private Center Points and Learning of HalfspacesFeb 27 2019We present a private learner for halfspaces over an arbitrary finite domain $X\subset \mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate ... More
Algorithm and Hardness results on Liar's Dominating Set and $k$-tuple Dominating SetFeb 27 2019Given a graph $G=(V,E)$, the dominating set problem asks for a minimum subset of vertices $D\subseteq V$ such that every vertex $u\in V\setminus D$ is adjacent to at least one vertex $v\in D$. That is, the set $D$ satisfies the condition that $|N[v]\cap ... More
Weighted Maximum Independent Set of Geometric Objects in Turnstile StreamsFeb 27 2019We study the Maximum Independent Set problem for geometric objects given in the data stream model. A set of geometric objects is said to be independent if the objects are pairwise disjoint. We consider geometric objects in one and two dimensions, i.e., ... More
Plane Hop Spanners for Unit Disk Graphs: Simpler and BetterFeb 26 2019The unit disk graph (UDG) is a widely employed model for the study of wireless networks. In this model, wireless nodes are represented by points in the plane and there is an edge between two points if and only if their Euclidean distance is at most one. ... More
A new lower bound on the maximum number of plane graphs using production matricesFeb 26 2019We use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\Omega(42.11^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\Omega(41.18^n)$ by Aichholzer et al. (2007). ... More
Towards Real-time 3D Reconstruction using Consumer UAVsFeb 26 2019We present a near real-time solution for 3D reconstruction from aerial images captured by consumer UAVs. Our core idea is to simplify the multi-view stereo problem into a series of two-view stereo matching problems. Our method applies to UAVs equipped ... More
Dynamic Maintenance of the Lower Envelope of Pseudo-LinesFeb 25 2019We present a fully dynamic data structure for the maintenance of lower envelopes of pseudo-lines. The structure has $O(\log^2 n)$ update time and $O(\log n)$ vertical ray shooting query time. To achieve this performance, we devise a new algorithm for ... More
On One-Round Discrete Voronoi GamesFeb 25 2019Let $V$ be a multiset of $n$ points in $\mathbb{R}^d$, which we call voters, and let $k\geq 1$ and $\ell\geq 1$ be two given constants. We consider the following game, where two players $\mathcal{P}$ and $\mathcal{Q}$ compete over the voters in $V$: First, ... More
Near neighbor preserving dimension reduction for doubling subsets of $\ell_1$Feb 23 2019Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the Euclidean $(\ell_2)$ ... More
VoroCrust: Voronoi Meshing Without ClippingFeb 23 2019Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting ... More
Matching points with disks with a common intersectionFeb 22 2019We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p in R and q in B, we consider the disk through p and q with the smallest diameter. We prove that for any R and B such that ... More
Preconditioning for the Geometric Transportation ProblemFeb 22 2019In the geometric transportation problem, we are given a collection of points $P$ in $d$-dimensional Euclidean space, and each point is given a supply of $\mu(p)$ units of mass, where $\mu(p)$ could be a positive or a negative integer, and the total sum ... More
On the hardness of computing an average curveFeb 21 2019We study the complexity of clustering curves under $k$-median and $k$-center objectives in the metric space of the Fr\'echet distance and related distance measures. The $k$-center problem has recently been shown to be NP-hard, even in the case where $k=1$, ... More
Approximate Nearest Neighbor for Curves --- Simple, Efficient, and DeterministicFeb 20 2019In the $(1+\varepsilon,r)$-approximate-near-neighbor problem for curves (ANNC) under some distance measure $\delta$, the goal is to construct a data structure for a given set $\mathcal{C}$ of curves that supports approximate near-neighbor queries: Given ... More
Load-Balancing for Parallel Delaunay TriangulationsFeb 20 2019Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations ... More
Approximating Continuous Functions on Persistence Diagrams Using Template FunctionsFeb 19 2019The persistence diagram is an increasingly useful tool arising from the field of Topological Data Analysis. However, using these diagrams in conjunction with machine learning techniques requires some mathematical finesse. The most success to date has ... More
Shapes from Echoes: Uniqueness from Point-to-Plane Distance MatricesFeb 19 2019We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the notable "structure from sound" approach ... More
Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor ChainsFeb 19 2019We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for Euclidean TSP ... More
RACE: Sub-Linear Memory Sketches for Approximate Near-Neighbor Search on Streaming DataFeb 18 2019We demonstrate the first possibility of a sub-linear memory sketch for solving the approximate near-neighbor search problem. In particular, we develop an online sketching algorithm that can compress $N$ vectors into a tiny sketch consisting of small arrays ... More
Routing in HistogramsFeb 18 2019Let $P$ be an $x$-monotone orthogonal polygon with $n$ vertices. We call $P$ a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two points $p$ and ... More
Extending Upward Planar Graph DrawingsFeb 18 2019In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $\Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $\Gamma_H$ can be extended to an upward ... More
Geometric secluded paths and planar satisfiabilityFeb 18 2019We consider paths with low "exposure" to a polygonal domain, i.e., paths which are seen as little as possible; we differentiate between "integral" exposure (when we care for how long the path sees every point of the domain) and "0/1" exposure (just counting ... More
Using Persistent Homology to Quantify a Diurnal Cycle in Hurricane FelixFeb 17 2019The diurnal cycle of tropical cyclones (TCs) is a daily cycle in clouds that appears in satellite images and may have implications for TC structure and intensity. The diurnal pattern can be seen in infrared (IR) satellite imagery as cyclical pulses in ... More
Nearest neighbor decoding for Tardos fingerprinting codesFeb 17 2019Over the past decade, various improvements have been made to Tardos' collusion-resistant fingerprinting scheme [Tardos, STOC 2003], ultimately resulting in a good understanding of what is the minimum code length required to achieve collusion-resistance. ... More
Cellular morphogenesis of three-dimensional tensegrity structuresFeb 15 2019The topology and form finding of tensegrity structures have been studied extensively since the introduction of the tensegrity concept. However, most of these studies address topology and form separately, where the former represented a research focus of ... More
Proximity Queries for Absolutely Continuous Parametric CurvesFeb 13 2019In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex ... More
Task-based Augmented Contour Trees with Fibonacci HeapsFeb 13 2019This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of ... More
Computing the Yolk in Spatial Voting Games without Computing Median LinesFeb 13 2019The yolk is an important concept in spatial voting games as it generalises the equilibrium and provides bounds on the uncovered set. We present near-linear time algorithms for computing the yolk in the spatial voting model in the plane. To the best of ... More
Geometric MulticutFeb 11 2019We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" $F$, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated ... More
Fixed-Parameter Tractable Algorithms for Corridor Guarding ProblemsFeb 11 2019Given an orthogonal connected arrangement of line-segments, Minimum Corridor Guarding(MCG) problem asks for an optimal tree/closed walk such that, if a guard moves through the tree/closed walk, all the line-segments are visited by the guard. This problem ... More
Metric Curvatures and their Applications 2: Metric Ricci Curvature and FlowFeb 09 2019In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies ... More
Diffeomorphic Medial ModelingFeb 06 2019Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological structures, such ... More
Diffeomorphic Medial ModelingFeb 06 2019Feb 28 2019Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological structures, such ... More
A Composable Coreset for k-Center in Doubling MetricsFeb 05 2019A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as \textit{centers} among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized. Doubling ... More
A non-iterative method for robustly computing the intersections between a line and a curve or surfaceFeb 05 2019The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a non-iterative method ... More
Classifying Convex Bodies by their Contact and Intersection GraphsFeb 05 2019Suppose that $A$ is a convex body in the plane and that $A_1,\dots,A_n$ are translates of $A$. Such translates give rise to an intersection graph of $A$, $G=(V,E)$, with vertices $V=\{1,\dots,n\}$ and edges $E=\{uv\mid A_u\cap A_v\neq \emptyset\}$. The ... More
External Labeling Techniques: A Taxonomy and SurveyFeb 04 2019External labeling is frequently used for annotating features in graphical displays and visualizations, such as technical illustrations, anatomical drawings, or maps, with textual information. Such a labeling connects features within an illustration by ... More
Parametric FEM for Shape Optimization applied to Golgi StackFeb 02 2019The thesis is about an application of the shape optimization to the morphological evolution of Golgi stack. Golgi stack consists of multiple layers of cisternae. It is an organelle in the biological cells. Inspired by the Helfrich Model \cite{Helfrich}, ... More
A note on self-improving sorting with hidden partitionsFeb 01 2019We study self-improving sorting with hidden partitions. Our result is an optimal algorithm which runs in expected time O(H(\pi(I)) + n), where I is the given input which contains n elements to be sorted, \pi(I) is the output which are the ranks of all ... More
Advances in the Treatment of Trimmed CAD Models due to Isogeometric AnalysisJan 31 2019Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models and highlights ... More
DDSL: Deep Differentiable Simplex Layer for Learning Geometric SignalsJan 30 2019We present a Deep Differentiable Simplex Layer (DDSL) for neural networks for geometric deep learning. The DDSL is a differentiable layer compatible with deep neural networks for bridging simplex mesh-based geometry representations (point clouds, line ... More
Manifold-based B-splines on unstructured meshesJan 30 2019We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent computer-aided ... More
Persistent Homology of Geospatial Data: A Case Study with VotingJan 29 2019A crucial step in the analysis of persistent homology is transformation of data into a simplicial complex. Modern packages for persistent homology often construct Vietoris--Rips or other distance-based simplicial complexes on point clouds because they ... More
Plantinga-Vegter algorithm takes average polynomial timeJan 26 2019We exhibit a condition-based analysis of the adaptive subdivision algorithm due to Plantinga and Vegter. The first complexity analysis of the PV Algorithm is due to Burr, Gao and Tsigaridas who proved a $O\big(2^{\tau d^{4}\log d}\big)$ worst-case cost ... More
Metric Spaces with Expensive DistancesJan 25 2019In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We introduce a different ... More
Deterministic 2-Dimensional Temperature-1 Tile Assembly Systems Cannot ComputeJan 24 2019We consider non cooperative binding in so called `temperature 1', in deterministic (here called {\it confluent}) tile self-assembly systems (1-TAS) and prove the standing conjecture that such systems do not have universal computational power. We call ... More
Infinite All-Layers Simple FoldabilityJan 24 2019We study the problem of deciding whether a crease pattern can be folded by simple folds (folding along one line at a time) under the infinite all-layers model introduced by [Akitaya et al., 2017], in which each simple fold is defined by an infinite line ... More
Learning Sublinear-Time Indexing for Nearest Neighbor SearchJan 24 2019Most of the efficient sublinear-time indexing algorithms for the high-dimensional nearest neighbor search problem (NNS) are based on space partitions of the ambient space $\mathbb{R}^d$. Inspired by recent theoretical work on NNS for general metric spaces ... More
Greedy Strategy Works for Clustering with Outliers and Coresets ConstructionJan 24 2019We study the problems of clustering with outliers in high dimension. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithms with low complexities for the problems. Our ... More
Spherical sampling methods for the calculation of metamer mismatch volumesJan 23 2019In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both methods utilize ... More
B-spline-like bases for $C^2$ cubics on the Powell-Sabin 12-splitJan 21 2019For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell-Sabin 12-split of a triangle, the so-called S-bases were recently introduced. These are simplex spline bases with B-spline-like properties on the 12-split of a single ... More
A common lines approach for ab-initio modeling of cyclically-symmetric moleculesJan 20 2019One of the challenges in single particle reconstruction in cryo-electron microscopy is to find a three-dimensional model of a molecule using its two-dimensional noisy projection-images. In this paper, we propose a robust "angular reconstitution" algorithm ... More
Efficient Algorithms to Test Digital ConvexityJan 15 2019A set $S \subset \mathbb{Z}^d$ is digital convex if $conv(S) \cap \mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points is digital ... More
An Elastic Energy Minimization Framework for Mean Contour CalculationJan 09 2019In this paper we propose a contour mean calculation and interpolation method designed for averaging manual delineations of objects performed by experts and interpolate 3D layer stack images. The proposed method retains all visible information of the input ... More
An Application of Manifold Learning in Global Shape DescriptorsJan 08 2019With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) ... More
Convolutional Neural Networks on non-uniform geometrical signals using Euclidean spectral transformationJan 07 2019Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a ... More
A semi-structured approach to curvilinear mesh generation around streamlined bodiesJan 07 2019We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-sructured approach which combines the high quality of structured meshes in the near-field with the flexibility of unstructured ... More
Approximate Discontinuous Trajectory HotspotsJan 07 2019A hotspot is an axis-aligned square of fixed side length $s$, the duration of the presence of an entity moving in the plane in which is maximised. An exact hotspot of a polygonal trajectory with $n$ edges can be found in $O(n^2)$. Defining a $c$-approximate ... More
Tooth morphometry using quasi-conformal theoryJan 07 2019Shape analysis is important in anthropology, bioarchaeology and forensic science for interpreting useful information from human remains. In particular, teeth are morphologically stable and hence well-suited for shape analysis. In this work, we propose ... More
Search Space Reduction of Asynchrony Immune Cellular Automata by Center PermutivityJan 06 2019We continue the study of asynchrony immunity in cellular automata (CA), which can be considered as a weaker version of correlation immunity in the context of vectorial Boolean functions. The property could have applications as a countermeasure for side-channel ... More
Maximum Matchings and Minimum Blocking Sets in $Θ_6$-GraphsJan 06 2019$\Theta_6$-Graphs are important geometric graphs that have many applications especially in wireless sensor networks. They are equivalent to Delaunay graphs where empty equilateral triangles take the place of empty circles. We investigate lower bounds ... More
Maximum Matchings and Minimum Blocking Sets in $Θ_6$-GraphsJan 06 2019Mar 11 2019$\Theta_6$-Graphs graphs are important geometric graphs that have many applications especially in wireless sensor networks. They are equivalent to Delaunay graphs where empty equilateral triangles take the place of empty circles. We investigate lower ... More
Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric FitsJan 04 2019We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of our environments ... More
High-order curvilinear hybrid mesh generation for CFD simulationsJan 04 2019We describe a semi-structured method for the generation of high-order hybrid meshes suited for the simulation of high Reynolds number flows. This is achieved through the use of highly stretched elements in the viscous boundary layers near the wall surfaces. ... More
A variational approach to high-order r-adaptationJan 04 2019A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the initial mesh are ... More
Singularity Structure Simplification of Hexahedral Mesh via Weighted RankingJan 02 2019Jan 03 2019In this paper, we propose an improved singularity structure simplification method for hexahedral (hex) meshes using a weighted ranking approach. In previous work, the selection of to-be-collapsed base complex sheets/chords is only based on their thickness, ... More
Spacetime Symmetries, Invariant Sets, and Additive Subdynamics of Cellular AutomataDec 30 2018Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured, complex behaviors. ... More
Convex Polygons in Cartesian ProductsDec 29 2018We study several problems concerning convex polygons whose vertices lie in a Cartesian product (for short, grid) of two sets of n real numbers. First, we prove that every such grid contains a convex polygon with $\Omega$(log n) vertices and that this ... More