Smaller core-sets for balls

In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J. Brauchart, P. Grabner, W. Kusner and J. Ziefle. It is shown that point sets which are hyperuniform for large balls, small balls, or balls of threshold order on the flat tori are uniformly distributed. Moreover, it is also shown that QMC-designs sequences for Sobolev classes, probabilistic point sets (obtained from jittered samplings), and some determinantal point process are hyperuniform.

Let P be a set of n points in ℝ^d in general position. A median hyperplane (roughly) splits the point set P in half. The yolk of P is the ball of smallest radius intersecting all median hyperplanes of P. The egg of P is the ball of smallest radius intersecting all hyperplanes which contain exactly d points of P. We present exact algorithms for computing the yolk and the egg of a point set, both running in expected time O(n^(d-1) log n). The running time of the new algorithm is a polynomial time improvement over existing algorithms. We also present algorithms for several related problems, such as computing the Tukey and center balls of a point set, among others.

Mold temperature control of a rubber injection-molding machine by TSK-type recurrent neural fuzzy network

We present a spectral analysis of a continuous scaling algorithm for matrix scaling and operator scaling. The main result is that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent algorithm also has linear convergence under the same assumption. The spectral gap condition for operator scaling is closely related to the notion of quantum expander studied in quantum information theory. The spectral analysis also provides bounds on some important quantities of the scaling problems, such as the condition number of the scaling solution and the capacity of the matrix and operator. These results can be used in various applications of scaling problems, including matrix scaling on expander graphs, permanent lower bounds on random matrices, the Paulsen problem on random frames, and Brascamp--Lieb constants on random operators. In some applications, the inputs of interest satisfy the spectral condition and we prove significantly stronger bounds than the worst case bounds.

Matching individuals within a group of spatially nonoverlapping surveillance cameras, also known as person reidentification, has recently attracted a lot of research interest. Current methods mainly focus on feature representation or distance measure, which directly compare person images captured by different cameras. However, it is still a problem because of various surveillance conditions; for example, view switching, lighting variations, and image scaling. Although the brightness transfer function was proposed to address the problem of illumination variation, it could not handle view and scale changes among various cameras. In this paper, we propose a new approach to compensate for the inconsistency of feature distributions of person images captured by different cameras. More precisely, a feature projection matrix (FPM) is learned to project image features of one camera to the feature space of another camera, from which the latent device difference can be effectively eliminated for the person reidentification task. In particular, we formulate the FPM learning as a smooth unconstrained convex optimization problem and use a simple gradient descent algorithm with stochastic samples to accelerate the solving process. Extensive comparative experiments conducted on three standard datasets have shown the promising prospect of the proposed method.

Microwave imaging technique allows obtaining images of hidden objects in structures and media using microwaves. This technique has various applications such as: nondestructive testing, medical imaging, concealed weapon detection, through-the-wall imaging, etc. Obtaining radar images in these applications is based on processing phase and amplitude of the reflected signal recorded over an aperture (a microwave hologram). Recently, systems began to appear in which the radar part is supplemented by an RGB-D sensor, which allows to obtain new capabilities. For example, there is the a microwave screening system architecture in which inverse synthetic aperture is formed by the natural motion of the subject in the vicinity of a stationary linear antenna array. The microwave system is complemented with an synchronous RGB-D video sensor which captures the trajectory of the moving subject in 3D and allows coherent processing of the radar signal. Another system detects objects buried under irregular surface and uses RGB-D sensor for capturing the surface relief for suppressing reflection of the sounding signal from the surface. Calibration between a radar and an RGB-D sensor is an essential process for microwave and optical data fusion. This article presents a novel approach for calibration, using a planar calibration target which is made of radiotransparent material (such a foam plastic sheet) with square marker and six small metal balls embedded in target surface and representing point objects. The proposed method exploits 3D-3D correspondences between coordinates of point objects in two coordinate systems associated to the sensor and to the radar. One points set is extracted from optical data, using marked corners of the target as a base points. Second points set is obtained from microwave data as local maxima of 3D volume of data reconstructed from one-frequency microwave hologram. Computer modeling were performed using Autodesk 3ds Max software by which models of all components of the system were built and the optical image from the sensor was modeled. Test experiments were carried out using a measurement system composed of the following components: a compact vector network analyzer (VNA), two mechanical scanners with stepper motors, one transmitting and one receiving horn antennas, mounted on the VNA, an RGB-D sensor, a microcontroller board, and a computer. The high accuracy of the method is confirmed both by computer modeling and physical experiment. The accuracy of determination of relative position between the radar and the sensor is about one fifth of the signal wavelength used.

In the paper, we present and prove Castle Theorem of Convex Hull, design and realize the Fast Rampart Searching Algorithm. The algorithm can be treated as the preprocess of Convex Hull calculation of very large planar point set. When calculating the Convex Hull of a very large planar point set, we can use the Fast Rampart Searching Algorithm to get a very small part points as candidate point set, and then we can get the Convex Hull of the whole planar point set from the candidate point set through other algorithms. Keywords-fast rampart searching algorithm; castle theorem; convex hull; computational geometry

Fast algorithms for least-squares-based minimum variance spectral estimation

Probabilities of hitting a convex hull

Our goal is the registration of multiple 3D point clouds obtained from LIDAR scans of underground mines. Such a capability is crucial to the surveying and planning operations in mining. Often, the point clouds only partially overlap and initial alignment is unavailable. Here, we propose an interactive user-assisted point cloud registration system. Guided by the system, the user's role is simply to identify and search for overlapping regions across the point clouds. Specifically, given two point sets, the user clicks on a point in one set, then simply hovers the mouse on the other set to find a matching point. Each mouse position gives rise to a translation, and our system instantly optimises the rotation that aligns the point clouds. Assuming that each individual point set is horizontally levelled with the ground by the level compensator on the LIDAR device, given a candidate 3D translation only one angular parameter needs to be estimated to rotationally align two 3D point sets. We propose a fast rotation search algorithm that delivers globally optimal results in real time. Our method conducts branch-and-bound optimisation with a novel bounding function whose evaluation amounts to simple sorted array operations. This provides smooth and accurate feedback to the user's search for overlapping regions. Our system is intuitive and helps to accelerate the registration of multiple scans.

Higher order digital nets are special classes of point sets for quasi-Monte Carlo rules which achieve the optimal convergence rate for numerical integration of smooth functions. An explicit construction of higher order digital nets was proposed by Dick, which is based on digitally interlacing in a certain way the components of classical digital nets whose number of components is a multiple ds of the dimension s. In this paper we give a fast computer search algorithm to find good classical digital nets suitable for interlaced components by using polynomial lattice point sets. We consider certain weighted Sobolev spaces of smoothness of arbitrarily high order, and derive an upper bound on the mean square worst-case error for digitally shifted higher order digital nets. Employing this upper bound as a quality criterion, we prove that the component-by-component construction can be used efficiently to find good polynomial lattice point sets suitable for interlaced components. Through this approach we are able to get some tractability results under certain conditions on the weights. Fast construction using the fast Fourier transform requires the construction cost of \(O(dsN \log N)\) operations using O(N) memory, where N is the number of points and s is the dimension. This implies a significant reduction in the construction cost as compared to higher order polynomial lattice point sets. Numerical experiments confirm that the performance of our constructed point sets often outperforms those of higher order digital nets with Sobol’ sequences and Niederreiter-Xing sequences used for interlaced components, indicating the usefulness of our algorithm.

In TSP with neighborhoods (TSPN) we are given a collection X of k polygonal regions, called neighborhoods, with totally n vertices, and we seek the shortest tour that visits each neighborhood. The Euclidean TSP is a special case of the TSPN problem, so TSPN is also NP-hard. In this paper we present a simple and fast algorithm that, given a start point, computes a TSPN tour of length O(log k) times the optimum in time O(n + k log k). When no start point is given we show how to compute a “good” start point in time O(n 2 log n), hence we obtain a logarithmic approximation algorithm that runs in time O(n 2 log n). We also present an algorithm which performs at least one of the following two tasks (which of these tasks is performed depends on the given input): (1) It outputs in time O(n log n) a TSPN tour of length O(log k) times the optimum. (2) It outputs a TSPN tour of length less than (1+∈) times the optimum in cubic time, where ∈ is an arbitrary real constant given as an optional parameter.The results above are significant improvements, since the best previously known logarithmic approximation algorithm runs in Ω(n 5) time in the worst case.KeywordsApproximation AlgorithmLength FunctionSimple PolygonBlue PointLower EnvelopeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A collaborative light control system considering uniformity and illuminance in WSAN

Optimal projections onto grids and finite resolution images

This paper presents a theoretically simple, yet efficient approach for the problem of matching the 2-D point sets under rigid motion, where jitter is allowed. It is a fundamental problem in pattern recognition, having applications ranging from robotics to astronautics. Commonly, the previous methods tend to use symbolic arithmetic to solve this problem. However, they are always complex and limited by computational cost. In this paper, we present a visual analysis for the point set matching problem and develop a geometrical arithmetic which is proven to yield equivalent results to the symbolic arithmetic. This allows us to view the problem as one of shape matching and obtain an algorithm that firstly generates a probabilistic shape descriptor (PSD) to describe the local geometric property of each point in the point sets, then acquires the local correspondence from the Euclidean distance matrix of the descriptors, and validates the global transformation finally. Experimental results demonstrate that our simple algorithm with a lower computation complexity effectively improves accuracy over current method, particularly when matching equal-size patterns under varying jitter.