Showing papers on "Point (geometry) published in 2013"

L1-medial skeleton of point cloud

Abstract: We introduce L1-medial skeleton as a curve skeleton representation for 3D point cloud data. The L1-median is well-known as a robust global center of an arbitrary set of points. We make the key observation that adapting L1-medians locally to a point set representing a 3D shape gives rise to a one-dimensional structure, which can be seen as a localized center of the shape. The primary advantage of our approach is that it does not place strong requirements on the quality of the input point cloud nor on the geometry or topology of the captured shape. We develop a L1-medial skeleton construction algorithm, which can be directly applied to an unoriented raw point scan with significant noise, outliers, and large areas of missing data. We demonstrate L1-medial skeletons extracted from raw scans of a variety of shapes, including those modeling high-genus 3D objects, plant-like structures, and curve networks.

Point-plane SLAM for hand-held 3D sensors

Abstract: We present a simultaneous localization and mapping (SLAM) algorithm for a hand-held 3D sensor that uses both points and planes as primitives. We show that it is possible to register 3D data in two different coordinate systems using any combination of three point/plane primitives (3 planes, 2 planes and 1 point, 1 plane and 2 points, and 3 points). Our algorithm uses the minimal set of primitives in a RANSAC framework to robustly compute correspondences and estimate the sensor pose. As the number of planes is significantly smaller than the number of points in typical 3D data, our RANSAC algorithm prefers primitive combinations involving more planes than points. In contrast to existing approaches that mainly use points for registration, our algorithm has the following advantages: (1) it enables faster correspondence search and registration due to the smaller number of plane primitives; (2) it produces plane-based 3D models that are more compact than point-based ones; and (3) being a global registration algorithm, our approach does not suffer from local minima or any initialization problems. Our experiments demonstrate real-time, interactive 3D reconstruction of indoor spaces using a hand-held Kinect sensor.

A shape-based segmentation method for mobile laser scanning point clouds

Abstract: Segmentation of mobile laser point clouds of urban scenes into objects is an important step for post-processing (e.g., interpretation) of point clouds. Point clouds of urban scenes contain numerous objects with significant size variability, complex and incomplete structures, and holes or variable point densities, raising great challenges for the segmentation of mobile laser point clouds. This paper addresses these challenges by proposing a shape-based segmentation method. The proposed method first calculates the optimal neighborhood size of each point to derive the geometric features associated with it, and then classifies the point clouds according to geometric features using support vector machines (SVMs). Second, a set of rules are defined to segment the classified point clouds, and a similarity criterion for segments is proposed to overcome over-segmentation. Finally, the segmentation output is merged based on topological connectivity into a meaningful geometrical abstraction. The proposed method has been tested on point clouds of two urban scenes obtained by different mobile laser scanners. The results show that the proposed method segments large-scale mobile laser point clouds with good accuracy and computationally effective time cost, and that it segments pole-like objects particularly well.

Towards 3D lidar point cloud registration improvement using optimal neighborhood knowledge

Abstract: Automatic 3D point cloud registration is a main issue in computer vision and remote sensing. One of the most commonly adopted solution is the well-known Iterative Closest Point (ICP) algorithm. This standard approach performs a fine registration of two overlapping point clouds by iteratively estimating the transformation parameters, assuming good a priori alignment is provided. A large body of literature has proposed many variations in order to improve each step of the process (namely selecting, matching, rejecting, weighting and minimizing). The aim of this paper is to demonstrate how the knowledge of the shape that best fits the local geometry of each 3D point neighborhood can improve the speed and the accuracy of each of these steps. First we present the geometrical features that form the basis of this work. These low-level attributes indeed describe the neighborhood shape around each 3D point. They allow to retrieve the optimal size to analyze the neighborhoods at various scales as well as the privileged local dimension (linear, planar, or volumetric). Several variations of each step of the ICP process are then proposed and analyzed by introducing these features. Such variants are compared on real datasets with the original algorithm in order to retrieve the most efficient algorithm for the whole process. Therefore, the method is successfully applied to various 3D lidar point clouds from airborne, terrestrial, and mobile mapping systems. Improvement for two ICP steps has been noted, and we conclude that our features may not be relevant for very dissimilar object samplings.

Robust Estimation of Nonrigid Transformation for Point Set Registration

Abstract: We present a new point matching algorithm for robust nonrigid registration. The method iteratively recovers the point correspondence and estimates the transformation between two point sets. In the first step of the iteration, feature descriptors such as shape context are used to establish rough correspondence. In the second step, we estimate the transformation using a robust estimator called L_2E. This is the main novelty of our approach and it enables us to deal with the noise and outliers which arise in the correspondence step. The transformation is specified in a functional space, more specifically a reproducing kernel Hilbert space. We apply our method to nonrigid sparse image feature correspondence on 2D images and 3D surfaces. Our results quantitatively show that our approach outperforms state-of-the-art methods, particularly when there are a large number of outliers. Moreover, our method of robustly estimating transformations from correspondences is general and has many other applications.

Surface Reconstruction through Point Set Structuring

Abstract: We present a method for reconstructing surfaces from point sets. The main novelty lies in a structure-preserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points. The final surface is obtained through solving a graph-cut problem formulated on the 3D Delaunay triangulation of the structured point set where the tetrahedra are labeled as inside or outside cells. Structuring facilitates the surface reconstruction as the point set is substantially reduced and the points are enriched with structural meaning related to adjacency between primitives. Our approach departs from the common dichotomy between smooth/piecewise-smooth and primitive-based representations by gracefully combining canonical parts from detected primitives and free-form parts of the inferred shape. Our experiments on a variety of inputs illustrate the potential of our approach in terms of robustness, flexibility and efficiency.

Support detection in super-resolution

Abstract: We study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as they are separated by 2/f and the noise level is small with respect to the amplitude of the signal.

Three-dimensional point processing and model generation

Abstract: A scene point cloud is processed and a solution to an inverse-function is determined to determine its source objects. A primitive extraction process and a part matching process are used to compute the inverse function solution. The extraction process estimates models and parameters based on evidence of cylinder and planar geometry in the scene. The matching process matches clusters of 3D points to models of parts from a library. A selected part and its associated polygon model is used to represent the point cluster. Iterations of the extraction and matching processes complete a 3D model for a complex scene made up of planes, cylinders, and complex parts from the parts library. Connecting regions between primitives and/or parts are processed to determine their existence and type. Constraints may be used to ensure a connected model and alignment of its components.

Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension

Abstract: We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up behavior first derived by Merle and Zaag. We also refine the geometry of the blow-up set near a charac- teristic point, and show that except may be for one exceptional situation, it is never symmetric with the respect to the characteristic point. Then, we show that all blow-up modalities predicted by those authors do occur. More precisely, given any integer k ≥ 2 and ζ0 ∈ , we construct a blow-up solution with a characteristic point a, such that the asymptotic behavior of the solution near (a,T(a)) shows a decoupled sum of k solitons with alternate signs, whose centers (in the hyperbolic geometry) have ζ0 as a center of mass, for all times.

stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns

Abstract: stpp is an R package for analyzing, simulating and displaying space-time point patterns. It covers many of the models encountered in applications of point process methods to the study of spatio-temporal phenomena. The package also includes estimators of the space-time inhomogeneous K-function and pair correlation function. stpp is the first dedicated unified computational environment in the area of spatio-temporal point processes. In this paper we describe space-time point processes and introduce the package stpp to new users.

Fully Automatic Registration of Image Sets on Approximate Geometry

Abstract: The photorealistic acquisition of 3D objects often requires color information from digital photography to be mapped on the acquired geometry, in order to obtain a textured 3D model. This paper presents a novel fully automatic 2D/3D global registration pipeline consisting of several stages that simultaneously register the input image set on the corresponding 3D object. The first stage exploits Structure From Motion (SFM) on the image set in order to generate a sparse point cloud. During the second stage, this point cloud is aligned to the 3D object using an extension of the 4 Point Congruent Set (4PCS) algorithm for the alignment of range maps. The extension accounts for models with different scales and unknown regions of overlap. In the last processing stage a global refinement algorithm based on mutual information optimizes the color projection of the aligned photos on the 3D object, in order to obtain high quality textures. The proposed registration pipeline is general, capable of dealing with small and big objects of any shape, and robust. We present results from six real cases, evaluating the quality of the final colors mapped onto the 3D object. A comparison with a ground truth dataset is also presented.

Best proximity points for α–ψ-proximal contractive type mappings and applications

Abstract: Let A and B be two nonempty subsets of a metric space (X,d). A best proximity point of a non-self-mapping T:A→B is a point x⁎∈A satisfying the equality d(x⁎,Tx⁎)=d(A,B), where d(A,B)=inf{d(a,b):a∈A,b∈B}. In this paper, we introduce a new concept of α–ψ-proximal contractive type mappings and establish best proximity point theorems for such mappings in complete metric spaces. Several applications and interesting consequences of our obtained results are presented.

Privacy-preserving nearest neighbor methods: comparing signals without revealing them

Abstract: Comparing two signals is one of the most essential and prevalent tasks in signal processing. A large number of applications fundamentally rely on determining the answers to the following two questions: 1) How should two signals be compared? 2) Given a set of signals and a query signal, which signals are the nearest neighbors (NNs) of the query signal, i.e., which signals in the database are most similar to the query signal? The NN search problem is defined as follows: Given a set S containing points in a metric space M, and a query point x !M, find the point in S that is closest to x. The problem can be extended to K-NN, i.e., determining the K signals nearest to x. In this context, the points in question are signals, such as images, videos, or other waveforms. The qualifier closest refers to a distance metric, such as the Euclidean distance or Manhattan distance between pairs of points in S. Finding the NN of the query point should be at most linear in the database size and is a well-studied problem in conventional NN settings.

Weighted averages on surfaces

Abstract: We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem, namely computing an average of given anchor points on the mesh with given weights, and the inverse problem, which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.

Improving Point Selection in Cubature by a New Discrepancy

Abstract: Reasonable point set selection is of paramount importance to the accuracy of high-dimensional integrals that will be encountered in various disciplines. In the present paper, to improve the point selection and to overcome the computational complexity of evaluating classical discrepancies, the concept of extended F-discrepancy (EF-discrepancy) and generalized F-discrepancy (GF-discrepancy) of a point set is introduced and justified by comparative studies with other existing discrepancies. Meanwhile, the extensions of the Koksma--Hlawka inequality for EF-discrepancy are proved and a conjecture for GF-discrepancy is put forward and discussed. This GF-discrepancy is then employed as the objective function when selecting the optimal rotation angles in the rotation transform of the quasi-symmetric point method (Q-SPM). Meanwhile, it is also proved that the rotation transform will keep the degree of algebraic accuracy. A genetic algorithm is adopted to solve the optimization problem. Several numerical examples a...

Best proximity points for Geraghty’s proximal contraction mappings

Abstract: In this paper, we generalized the notion of proximal contractions of the first and second kinds by using Geraghty’s theorem and establish best proximity point theorems for proximal contractions. Our results improve and extend the recent results of Sadiq Basha and some others.

Method for processing space hand signal gesture command based on depth camera

Abstract: The invention discloses a method for processing a space hand signal gesture command based on a depth camera and relates to the method for processing the space hand signal gesture command based the depth camera. The method for processing the space hand signal gesture command based the depth camera is capable of recognizing space hand signal gesture command information fast and accurately, improving working efficiency and precision greatly and being high in robustness, strong in practical applicability and good in anti-jamming capability when applied to a complex and changeable environment. The method comprises the steps of acquiring a real-time image by the depth camera, obtaining hand signal point cloud data by using three-dimensional point cloud computation and obtaining hand signal point cloud information, achieving a plane registering of the hand signal point cloud information and extracting contour feature point information, resuming a hand signal gesture, recognizing the hand signal gesture, recognizing a corresponding movement track and defining operation content of the movement track and finally achieving data smoothing of a dynamic hand signal gesture mouse output point according to a protocol for table-top tangible user interfaces (TUIO). The method for processing the space hand signal gesture command based the depth camera has the advantages of being fast , comprehensive and accurate in acquiring target information, establishing a space motion detecting area, extracting information with different depth, achieving multi-touch and improving integral operating performance.

Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates

Abstract: We first introduce a surface normal estimation procedure for point clouds capable of handling geometric singularities in the data, such as edges and corners. Our formulation is based on recasting the popular Principal Component Analysis (PCA) method as a constrained nonlinear least squares (NLSQ) problem. In contrast to traditional PCA, the new formulation assigns appropriate weights to neighboring points automatically during the optimization process in order to minimize the contributions of points located across singularities. We extend this strategy to point cloud denoising by combining normal estimation, point projection, and declustering into one NLSQ formulation. Finally, we propose a point cloud segmentation technique based on surface normal estimates and local point connectivity. In addition to producing consistently oriented surface normals, the process segments the point cloud into disconnected components that can each be segmented further into piecewise smooth components as needed.

Multipoint potential field method for path planning of autonomous underwater vehicles in 3D space

Abstract: A multipoint potential field method (MPPF) for path planning of autonomous underwater vehicles (AUV) in 3D space is presented in this paper. The algorithm is developed based on potential field method by incorporating a directed search method for sampling the potential field. In this approach, the analytical gradient of the total potential function is not computed, as it is not essentially required for moving the vehicle to the next position. Rather, a hemispherical region in the direction of motion around the AUV's bow is discretized into equiangular points with center as the current position. By determining the point at which the minimum potential exists, the vehicle can be moved towards that point in 3D space. This method is very simple and applicable for real-time implementation. The problem of local minima is also analyzed and found that the local minima in 2D space can be easily overcome with the MPPF. A simple strategy to avoid the local minima in 3D space is also proposed. The proposed method reduces the burden of fine-tuning the positive scaling factors of potential functions to avoid local minimum. The algorithm development and the simulation results are presented.

Constructing a proposal as a thought: a way to manage problems in the initiation of joint decision-making in finnish workplace interaction

Abstract: Drawing on fifteen video-recorded planning meetings as data, and on conversation analysis as a method, I examine the interactional import of the common Finnish practice of constructing a proposal as a thought. As a point of departure, I consider two different types of conditional utterances in which a speaker presents a plan: (1) ‘asking conditionals’ (jos ‘what if’ prefaced declarative conditionals and interrogative conditionals) and (2) ‘stating conditionals’ (declarative conditionals). While asking conditionals mark the plan as contingent on the recipient’s approval and involve a straightforward request for the recipient to engage in joint decision-making about the proposed plan, stating conditionals are regularly treated as informings about plans in which the recipients have actually no word to say. However, when asking and stating conditionals are prefaced with references to the speakers’ thoughts (ma aattelin et ‘I was thinking that’), the projected responses and sequential trajectories are more open-ended: The participants have the opportunity to share the responsibility, not only for what is to be decided with respect to the proposed plan, but also for what is to be jointly decided upon in the first place. Constructing a proposal as a thought seems thus to be a practice with which participants may enable the symmetrical distribution of deontic rights at the very beginning of joint decision-making sequences.

Adaptivity to Local Smoothness and Dimension in Kernel Regression

Abstract: We present the first result for kernel regression where the procedure adapts locally at a point x to both the unknown local dimension of the metric space X and the unknown Holder-continuity of the regression function at x. The result holds with high probability simultaneously at all points x in a general metric space X of unknown structure.

An automatic registration algorithm for the scattered point clouds based on the curvature feature

Abstract: Object modeling by the registration of multiple range images has important applications in reverse engineering and computer vision. In order to register multi-view scattered point clouds, a novel curvature-based automatic registration algorithm is proposed in this paper, which can solve the registration problem with partial overlapping point clouds. For two sets of scattered point clouds, the curvature of each point is estimated by using the quadratic surface fitting method. The feature points that have the maximum local curvature variations are then extracted. The initial matching points are acquired by computing the Hausdorff distance of curvature, and then the circumference shape feature of the local surface is used to obtain the accurate matching points from the initial matching points. Finally, the rotation and translation matrix are estimated by the quaternion, and an iterative algorithm is used to improve the registration accuracy. Experimental results show that the algorithm is effective.

Remote sensing image registration method of multi-source sensor

Abstract: The invention provides a remote sensing image registration method of a multi-source sensor, relating to an image processing technology. The remote sensing image registration method comprises the following steps of: respectively carrying out scale-invariant feature transform (SIFT) on a reference image and a registration image, extracting feature points, calculating the nearest Euclidean distances and the nearer Euclidean distances of the feature points in the image to be registered and the reference image, and screening an optimal matching point pair according to a ratio; rejecting error registration points through a random consistency sampling algorithm, and screening an original registration point pair; calculating distribution quality parameters of feature point pairs and selecting effective control point parts with uniform distribution according to a feature point weight coefficient; searching an optimal registration point in control points of the image to be registered according to a mutual information assimilation judging criteria, thus obtaining an optimal registration point pair of the control points; and acquiring a geometric deformation parameter of the image to be registered by polynomial parameter transformation, thus realizing the accurate registration of the image to be registered and the reference image. The remote sensing image registration method provided by the invention has the advantages of high calculation speed and high registration precision, and can meet the registration requirements of a multi-sensor, multi-temporal and multi-view remote sensing image.

Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below

Abstract: We show that in any infinitesimally Hilbertian $CD^*(K,N)$-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian $CD^*(0,N)$-spaces.

A simple projection method for solving the multiple-sets split feasibility problem

Abstract: In this article, we first introduce a simple but practical projection method for solving the multiple-sets split feasibility problem, which is to find a point in the intersection of a family of closed convex sets in one space, such that its image under a linear transformation is in the intersection of another family of closed convex sets in the image space. In each iteration of this method, the step-size is directly computed, and is shown to be the best for the current direction. Then we consider the corresponding relaxed projection scheme for the proposed method. The theoretical convergence results are established. Preliminary numerical experiments show that this simple method and its relaxed scheme are easy to implement and practical.

Best Proximity Point Results for Modified --Proximal Rational Contractions

Abstract: We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.