Structural Analogy from a Single Image Pair

The task of unsupervised image‐to‐image translation has seen substantial advancements in recent years through the use of deep neural networks. Typically, the proposed solutions learn the characterizing distribution of two large, unpaired collections of images, and are able to alter the appearance of a given image, while keeping its geometry intact. In this paper, we explore the capabilities of neural networks to understand image structure given only a single pair of images, and . We seek to generate images that are structurally aligned: that is, to generate an image that keeps the appearance and style of , but has a structural arrangement that corresponds to . The key idea is to map between image patches at different scales. This enables controlling the granularity at which analogies are produced, which determines the conceptual distinction between style and content. In addition to structural alignment, our method can be used to generate high quality imagery in other conditional generation tasks utilizing images and only: guided image synthesis, style and texture transfer, text translation as well as video translation. Our code and additional results are available in https://github.com/rmokady/structural-analogy/     

Quantum Coin Method for Numerical Integration

Light transport simulation in rendering is formulated as a numerical integration problem in each pixel, which is commonly estimated by Monte Carlo integration. Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e. samples) of the function (integrand). For N queries of the integrand, Monte Carlo integration achieves the estimation error of . Recently, Johnston [Joh16] introduced quantum super-sampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the convergence rate of Monte Carlo integration and achieves the faster convergence rate of approximately which is the best possible bound of any quantum algorithms we know today [NW99]. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin) [AW99], and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS if we were to run light transport simulation in quantum computers in the future.     

Mixed coordination mechanisms for scheduling games on hierarchical machines

In this paper, we study scheduling games under mixed coordination mechanisms on hierarchical machines. The two scheduling policies involved are ‐ and ‐, where ‐ (resp., ‐) policy sequences jobs in nondecreasing order of their hierarchies, and jobs of the same hierarchy in nonincreasing (resp., nondecreasing) order of their processing times. We first show the existence of a Nash equilibrium. Then we present the price of anarchy and the price of stability for the games with social costs of minimizing the makespan and maximizing the minimum machine load. All the bounds given in this paper are tight.     

Optimizing LBVH‐Construction and Hierarchy‐Traversal to accelerate kNN Queries on Point Clouds using the GPU

Processing point clouds often requires information about the point neighbourhood in order to extract, calculate and determine characteristics. We continue the tradition of developing increasingly faster neighbourhood query algorithms and present a highly efficient algorithm for solving the exact neighbourhood problem in point clouds using the GPU. Both, the required data structures and the kNN query, are calculated entirely on the GPU. This enables real‐time performance for large queries in extremely large point clouds. Our experiments show a more than threefold acceleration, compared to state‐of‐the‐art GPU based methods including all memory transfers. In terms of pure query performance, we achieve over answered neighbourhood queries per millisecond for 16 nearest neighbours on common graphics hardware.     

Fast vision‐based autonomous detection of moving cooperative target for unmanned aerial vehicle landing

We propose a fast and effective method, fast target detection (FTD), to detect the moving cooperative target for the unmanned aerial vehicle landing, and the target is composed of double circles and a cross. The purpose of our strategy is to land on the target. The FTD method needs to detect the target at the high and low heights. At the high height, the target appears completely and stably in the camera field. The FTD method can detect the circle and cross to rapidly reach the target center, named cross and circle–FTD (). To detect the cross, we propose a slope distance equation to obtain the distance between two slopes. The proposed slopes cluster method, based on the distance equation and K‐means, is used to determine the cross center. At the low height, the target appears incompletely and unstably. Therefore, FTD methods detect only the cross, named cross–FTD (). We extract the cross features ( CFs) based on line segments. Then, four CFs are combined based on graph theory. Experiments on our four datasets show that FTD has rapid speed and good performance. (Our method is implemented in C++ and is available at https://github.com/Li-Zhaoxi/UAV-Vision-Servo .) On the Mohamed Bin Zayed International Robotics Challenge datasets made we constructed, detects the target from a image approximately per pipeline with F‐measure and tracks target approximately per pipeline with F‐measure. detects centers from a image at approximately per image with F‐measure.     

An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

We present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape is non‐intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex . and can be expressed similarly by parametrizing a topological constraint. A close approximation of , termed can be computed fast using a greedy algorithm. is then transformed into a closed interpolating boundary in two steps to satisfy ’s topological and minimization requirements. Computing exactly is an NP (Non‐Polynomial)‐hard problem, whereas is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.     

Constrained shortest path tour problem: models,valid inequalities,and Lagrangian heuristics

The constrained shortest path tour problem (CSPTP) is an NP‐hard combinatorial optimization problem defined on a connected directed graph , where V is the set of nodes and A is the set of nonnegative weighted arcs. Given two distinct nodes , an integer value , and node disjoint subsets , , the CSPTP aims at finding the shortest trail from s to t while visiting at least one node in every subset , in this order. In this paper, we perform a comparative analysis between two integer programming (IP) models for the problem. We also propose valid inequalities and a Lagrangian‐based heuristic framework. Branch‐and‐bound algorithms from the literature, as well as a metaheuristic approach, are used for comparison. Extensive computational experiments carried out on benchmark data sets show the effective use of valid inequalities and the quality of bounds obtained by the Lagrangian framework. Because benchmark instances do not require a great computational effort of IP models in the sense that their optimality is reached at the root node of the CPLEX branch‐and‐cut search tree, we introduce new challenging CSPTP instances for which our solution approaches outperform existing ones for the problem.     

Laplace–Beltrami Operator on Point Clouds Based on Anisotropic Voronoi Diagram

The symmetrizable and converged Laplace–Beltrami operator () is an indispensable tool for spectral geometrical analysis of point clouds. The , introduced by Liu et al. [LPG12] is guaranteed to be symmetrizable, but its convergence degrades when it is applied to models with sharp features. In this paper, we propose a novel , which is not only symmetrizable but also can handle the point‐sampled surface containing significant sharp features. By constructing the anisotropic Voronoi diagram in the local tangential space, the can be well constructed for any given point. To compute the area of anisotropic Voronoi cell, we introduce an efficient approximation by projecting the cell to the local tangent plane and have proved its convergence. We present numerical experiments that clearly demonstrate the robustness and efficiency of the proposed for point clouds that may contain noise, outliers, and non‐uniformities in thickness and spacing. Moreover, we can show that its spectrum is more accurate than the ones from existing for scan points or surfaces with sharp features.     

Greedy Geometric Algorithms for Collection of Balls,with Applications to Geometric Approximation and Molecular Coarse‐Graining

Choosing balls that best approximate a 3D object is a non‐trivial problem. To answer it, we first address the inner approximation problem, which consists of approximating an object defined by a union of n balls with balls defining a region . This solution is further used to construct an outer approximation enclosing the initial shape, and an interpolated approximation sandwiched between the inner and outer approximations. The inner approximation problem is reduced to a geometric generalization of weighted max k‐cover, solved with the greedy strategy which achieves the classical lower bound. The outer approximation is reduced to exploiting the partition of the boundary of by the Apollonius Voronoi diagram of the balls defining the inner approximation. Implementation‐wise, we present robust software incorporating the calculation of the exact Delaunay triangulation of points with degree two algebraic coordinates, of the exact medial axis of a union of balls, and of a certified estimate of the volume of a union of balls. Application‐wise, we exhibit accurate coarse‐grain molecular models using a number of balls 20 times smaller than the number of atoms, a key requirement to simulate crowded cellular environments.     

Turning a Digital Camera into an Absolute 2D Tele‐Colorimeter

We present a simple and effective technique for absolute colorimetric camera characterization, invariant to changes in exposure/aperture and scene irradiance, suitable in a wide range of applications including image‐based reflectance measurements, spectral pre‐filtering and spectral upsampling for rendering, to improve colour accuracy in high dynamic range imaging. Our method requires a limited number of acquisitions, an off‐the‐shelf target and a commonly available projector, used as a controllable light source, other than the reflected radiance to be known. The characterized camera can be effectively used as a 2D tele‐colorimeter, providing the user with an accurate estimate of the distribution of luminance and chromaticity in a scene, without requiring explicit knowledge of the incident lighting power spectra. We validate the approach by comparing our estimated absolute tristimulus values (XYZ data in ) with the measurements of a professional 2D tele‐colorimeter, for a set of scenes with complex geometry, spatially varying reflectance and light sources with very different spectral power distribution.     

Crowdfunding mechanism comparison when product quality is uncertain

Many entrepreneurs have recently employed crowdfunding to raise money. Although there are several crowdfunding mechanisms, there is no clear dominant strategy for the type of mechanisms that should be adopted by the entrepreneur. This paper compares two commonly used mechanisms of crowdfunding by building a two‐person and two‐period model where the entrepreneur first makes the decision then two consumers follow. The all‐or‐nothing () mechanism allows entrepreneurs to set a funding target and keep nothing unless the goal is achieved. In contrast, entrepreneurs under the keep‐it‐all () mechanism must also set a target and keep any funds regardless of whether the goal has been achieved. To compare these two mechanisms, we assume that customers are not sure about the quality of the product, which is very common in reward‐based crowdfunding. Using a unified model, our results show that large or poorly scalable projects are more likely to choose the mechanism.     

Revectorization-Based Soft Shadow Mapping

In this paper, we present revectorization-based soft shadow mapping, an algorithm that enables the rendering of visually plausible anti-aliased soft shadows in real time. In revectorization-based shadow mapping, shadow silhouettes are anti-aliased and filtered on the basis of a discontinuity space. By replacing the filtering step of the theoretical framework of the percentage-closer soft shadow algorithm by a revectorization-based filtering algorithm, we are able to provide anti-aliasing mainly for near contact shadows or small penumbra sizes generated from low-resolution shadow maps. Moreover, we present a screen-space variant of our technique that generates visually plausible soft shadows with an overhead of only in processing time, when compared to the fastest soft shadow algorithms proposed in the literature, but that introduces shadow overestimation artefacts in the final rendering.     

Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis

In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.     

Approximate Controllabilty of Semilinear Dynamic Equations on Time Scale

In this paper we study the approximate controllability of semilinear systems on time scale. In order to do so, we first give a complete characterization for the controllability of linear systems on time scale in terms of surjective linear operators in Hilbert spaces. Then we will prove that, under certain conditions on the nonlinear term, if the corresponding linear system is exactly controllable on , for any , then semilinear system on time scale is approximately controllable on .     

TDBF: Two-dimensional belief function

How to efficiently handle uncertain information is still an open issue. In this paper, a new method to deal with uncertain information, named as two-dimensional belief function (TDBF), is presented. A TDBF has two components, T = (), both and are classical belief functions, while is a measure of reliable of . The definition of TDBF and the discounting algorithm are proposed. Compared with the classical discounting model, the proposed TDBF is more flexible and reasonable. Numerical examples are used to show the efficiency and application of the proposed method.     

Enhancing Bayesian Estimators for Removing Camera Shake

The aim of removing camera shake is to estimate a sharp version x from a shaken image y when the blur kernel k is unknown. Recent research on this topic evolved through two paradigms called and . only solves for k by marginalizing the image prior, while recovers both x and k by selecting the mode of the posterior distribution. This paper first systematically analyses the latent limitations of these two estimators through Bayesian analysis. We explain the reason why it is so difficult for image statistics to solve the previously reported failure. Then we show that the leading methods, which depend on efficient prediction of large step edges, are not robust to natural images due to the diversity of edges. , although much more robust to diverse edges, is constrained by two factors: the prior variation over different images, and the ratio between image size and kernel size. To overcome these limitations, we introduce an inter‐scale prior prediction scheme and a principled mechanism for integrating the sharpening filter into . Both qualitative results and extensive quantitative comparisons demonstrate that our algorithm outperforms state‐of‐the‐art methods.     

Direct synthesis of reduced order H controllers for a class of multivariable plants

Given an nth order, -control input, p-measured output generalized plant, this article proposes a simple, direct approach to design an output feedback H controller with order satisfying for , or for . For this purpose, the output feedback H control problem is transformed into an H state feedback problem for an augmented generalized system. A class of plants for which this transformation always exists and the ensuing controller has order as above, is identified. As a result, for such plants, the reduced order H controller gains are found just by solving a simple linear matrix inequality problem used in state feedback based H control. The efficacy of the proposed approach is studied on some benchmark examples.     

Correlation and correlation coefficient of generalized orthopair fuzzy sets

Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two -rung orthopair fuzzy sets, whose range is the unit interval . First, the correlation and correlation coefficient of -rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to -rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real-world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of -rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments.     

Set stabilization of boolean networks via sampled‐data control

The paper investigates the sampled‐data state feedback control (SDSFC) for set stabilization of Boolean control networks (BCNs). Set stabilization means that a system converges to a subset of the state space under certain controllers. Assume that the given subset is , where and sampling period is τ. We consider two conditions q ≤ τ;q > τ and for any given subset , calculate the corresponding largest control invariant subset (LCIS). Moreover, a design procedure to calculate all possible SDSFCs for set stabilization of BCNs is obtained. Ultimately, we provide an example to demonstrate the efficiency of the results.