Showing papers on "Point (geometry) published in 2009"

Möbius voting for surface correspondence

Abstract: The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric.Our approach is based on three observations. First, isometries are a subset of the Mobius group, which has low-dimensionality -- six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Mobius transformation that interpolates any three points can be computed in closed-form after a mid-edge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportation-type distance between corresponding points in that plane.Motivated by these observations, we have developed a Mobius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Mobius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces "votes" for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values.The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.

Curve skeleton extraction from incomplete point cloud

Abstract: We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of oriented points, we introduce a variational definition for an oriented point that is most rotationally symmetric with respect to S. Our formulation effectively utilizes normal information to compensate for the missing data and leads to robust curve skeleton computation over regions of a shape that are generally cylindrical. We present an iterative algorithm via planar cuts to compute the ROSA of a point cloud. This is complemented by special handling of non-cylindrical joint regions to obtain a centered, topologically clean, and complete 1D skeleton. We demonstrate that quality curve skeletons can be extracted from a variety of shapes captured by incomplete point clouds. Finally, we show how our algorithm assists in shape completion under these challenges by developing a skeleton-driven point cloud completion scheme.

Capacity-constrained point distributions: a variant of Lloyd's method

Abstract: We present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

Real-time object classification in 3D point clouds using point feature histograms

Abstract: This paper describes a LIDAR-based perception system for ground robot mobility, consisting of 3D object detection, classification and tracking. The presented system was demonstrated on-board our autonomous ground vehicle MuCAR-3, enabling it to safely navigate in urban traffic-like scenarios as well as in off-road convoy scenarios. The efficiency of our approach stems from the unique combination of 2D and 3D data processing techniques. Whereas fast segmentation of point clouds into objects is done in a 2 D occupancy grid, classifying the objects is done on raw 3D point clouds. For fast object feature extraction, we advocate the use of statistics of local point cloud properties, captured by histograms over point features. In contrast to most existing work on 3D point cloud classification, where real-time operation is often impossible, this combination allows our system to perform in real-time at 0.1s frame-rate.

Control system for navigating a principal dimension of a data space

Abstract: Systems and methods are described for navigating through a data space. The navigating comprises detecting a gesture of a body from gesture data received via a detector. The gesture data is absolute three-space location data of an instantaneous state of the body at a point in time and physical space. The detecting comprises identifying the gesture using the gesture data. The navigating comprises translating the gesture to a gesture signal, and navigating through the data space in response to the gesture signal. The data space is a data-representational space comprising a dataset represented in the physical space.

A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method

Abstract: This paper presents a normed G1 space and a weakened weak (W2) formulation of a cell-based smoothed point interpolation method (CS-PIM) for 2D solid mechanics problems using three-node triangular cells. Displacement fields in the CS-PIM are constructed using the point interpolation method (polynomial PIM or radial PIM) and hence the shape functions possess the Kronecker delta property facilitating the easy enforcement of Dirichlet boundary conditions. The edge-based T-schemes are introduced for selecting supporting nodes for creating the PIM shape functions and an adaptive coordinate transformation (CT) technique is proposed to solve the singularity problem for the moment matrix. Smoothed strains are obtained by performing the generalized smoothing operation over each triangular background cell. Because the nodal PIM shape functions can be discontinuous, a W2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is then used to create the discretized system equations. Numerical examples including static, free and forced vibration problems have been studied to examine the present method in terms of accuracy, convergence, efficiency and temporal stability.

Pure Point Dynamical and Diffraction Spectra

Abstract: We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.

Detecting and segmenting objects for mobile manipulation

Abstract: This paper proposes a novel 3D scene interpretation approach for robots in mobile manipulation scenarios using a set of 3D point features (Fast Point Feature Histograms) and probabilistic graphical methods (Conditional Random Fields). Our system uses real time stereo with textured light to obtain dense depth maps in the robot's manipulators working space. For the purposes of manipulation, we want to interpret the planar supporting surfaces of the scene, recognize and segment the object classes into their primitive parts in 6 degrees of freedom (6DOF) so that the robot knows what it is attempting to use and where it may be handled. The scene interpretation algorithm uses a two-layer classification scheme: i) we estimate Fast Point Feature Histograms (FPFH) as local 3D point features to segment the objects of interest into geometric primitives; and ii) we learn and categorize object classes using a novel Global Fast Point Feature Histogram (GFPFH) scheme which uses the previously estimated primitives at each point. To show the validity of our approach, we analyze the proposed system for the problem of recognizing the object class of 20 objects in 500 table settings scenarios. Our algorithm identifies the planar surfaces, decomposes the scene and objects into geometric primitives with 98.27% accuracy and uses the geometric primitives to identify the object's class with an accuracy of 96.69%.

New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces

Abstract: A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension. This work is settled in the framework of cubical complexes, which provides a sound topological basis for image analysis, and allows to retrieve the main notions and results of digital topology, in particular the notion of simple point.

Fast geometric point labeling using conditional random fields

Abstract: In this paper we present a new approach for labeling 3D points with different geometric surface primitives using a novel feature descriptor - the Fast Point Feature Histograms, and discriminative graphical models. To build informative and robust 3D feature point representations, our descriptors encode the underlying surface geometry around a point p using multi-value histograms. This highly dimensional feature space copes well with noisy sensor data and is not dependent on pose or sampling density. By defining classes of 3D geometric surfaces and making use of contextual information using Conditional Random Fields (CRFs), our system is able to successfully segment and label 3D point clouds, based on the type of surfaces the points are lying on. We validate and demonstrate the method's efficiency by comparing it against similar initiatives as well as present results for table setting datasets acquired in indoor environments.

High-Resolution Three-Dimensional Imaging of Spinning Space Debris

Abstract: Since space debris could post a significant threat to orbiting objects around the Earth, their reorganization, measurement, and catalogue are of great importance. This paper establishes a 3-D inverse synthetic aperture radar (ISAR) imaging geometry and signal model for space debris. Then, a 3-D imaging algorithm is proposed to realize coherent imaging in the range-slow-time domain. This algorithm is based on the complex-valued back-projection transform according to the spinning nature of space debris. The simulation results for both point scattering and continuous targets have proved the validity of the proposed algorithm.

A progressive point cloud simplification algorithm with preserved sharp edge data

Abstract: Due to recent advances in high-speed 3D laser-scanning technologies, the set of dense points collected from the external boundary surface of a physical object, often referred to as the point cloud data, is emerging as a new representation format of 3D shapes. A typical point cloud data set contains millions of coordinate data points, and this leads to significant computational challenges for the subsequent data processing tasks in practical applications. This paper presents a new point cloud simplification algorithm to reduce the number of data points scanned from a mechanical part, in which the boundary surfaces often contain sharp edges. Because of the distinct feature represented by data points located on or near the sharp edges (edge points), these points should always be retained by the simplification process. The proposed algorithm thus identifies these edge points first and then progressively removes the least important data point until the specified data reduction ratio is reached. The quantification of a point’s importance is based on points in its neighborhood and corresponds to the point’s contribution to the representation of local surface geometry. The effectiveness of the proposed algorithm is demonstrated through the simplification results of several practical point cloud data sets.

Simplified TBA equations of the AdS_5 x S^5 mirror model

Abstract: We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS_5 x S^5 mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies.

Optimal dynamic vertical ray shooting in rectilinear planar subdivisions

Abstract: We consider the dynamic vertical ray shooting problem against horizontal disjoint segments, that is, the task of maintaining a dynamic set S of n nonintersecting horizontal line segments in the plane under a query that reports the first segment in S intersecting a vertical ray from a query point. We develop a linear-size structure that supports queries, insertions, and deletion in O(log n) worst-case time. Our structure works in the comparison model on a random access machine.

Automated pavement distress detection using advanced image processing techniques

Abstract: In this paper, a novel, fast and self-adaptive image processing method is proposed for the extraction and connection of break points of cracks in pavement images. The algorithm first finds the initial point of a crack and then determines the crack's classification into transverse, longitudinal and alligator types. Different search algorithms are used for different types of cracks. Then the algorithm traces along the crack pixels to find the break point and then connect the identified crack point to the nearest break point in the particular search area. The nearest point then becomes the new initial point and the algorithm continues the process until reaching the end of the crack. The experimental results show that this connection algorithm is very effective in maximizing the accuracy of crack identification.

Counting Triangulations of Planar Point Sets

Abstract: We study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of $43^n$ for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, we derive new upper bounds for the number of planar graphs ($o(239.4^n)$), spanning cycles ($O(70.21^n)$), and spanning trees ($160^n$).

Experimental study of energy-minimizing point configurations on spheres

Abstract: In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.

Swing analyzer and golf club shaft selecting system

Abstract: A measuring device includes a strain gauge, a processing unit calculating an expected bending point value corresponding to a bending point position, and a display unit capable of displaying an output value from the processing unit. The processing unit calculates the expected bending point value based on a measured value of strain gauge at a first time point during a swing of the user and a measured value of strain gauge at a second time point closer to an impact time point than the first time point. The processing unit stores in advance conversion data for converting the expected bending point value to recommended kick point output value indicating kick point, and the processing unit outputs the recommended kick point output value corresponding to the calculated expected bending point value to the display unit.

Approximation algorithms for the Euclidean traveling salesman problem with discrete and continuous neighborhoods

Abstract: In the Euclidean traveling salesman problem with discrete neighborhoods, we are given a set of points P in the plane and a set of n connected regions (neighborhoods), each containing at least one point of P. We seek to find a tour of minimum length which visits at least one point in each region. We give (i) an O(α)-approximation algorithm for the case when the regions are disjoint and α-fat, with possibly varying size; (ii) an O(α3)-approximation algorithm for intersecting α-fat regions with comparable diameters. These results also apply to the case with continuous neighborhoods, where the sought TSP tour can hit each region at any point. We also give (iii) a simple O(log n)-approximation algorithm for continuous non-fat neighborhoods. The most distinguishing features of these algorithms are their simplicity and low running-time complexities.

An algorithmic approach for maintenance management based on advanced state space systems and harmonic regressions

Abstract: Point mechanisms are special track elements which failures results in delays and increased operating costs. In some cases such failures cause fatalities. A new robust algorithm for fault detection of point mechanisms is developed. It detects faults by comparing what can be considered the ‘normal’ or ‘expected’ shape of some signal with respect to the actual shape observed as new data become available. The expected shape is computed as a forecast of a combination of models. The proposed system deals with complicated features of the data in the case study, the main ones being the irregular sampling interval of the data and the time varying nature of the periodic behaviour. The system models are set up in a continuous-time framework and the system has been tested on a large dataset taken from a point mechanism operating on a commercial line.

A modified Q4/Q4 element for topology optimization

Abstract: Design variable and displacement fields are distinct. Thus, their respective material and finite element meshes may also be distinct, as well as their actual location of nodes for the two fields. The proposed Q4/Q4M element possesses design variable nodes and displacement nodes which are not coincident. The element has been implemented using different approaches, including continuous approximation of material distribution and nodal approaches. The results obtained demonstrate that the element is effective in generating structural topologies with high resolution. From a numerical point of view, mesh independent solutions can be obtained by means of projection.

Toward automatic reconstruction of interiors from laser data

Abstract: So far, realistic models of interiors have always been designed manually with the help of dedicated software packages. However, the demand for indoor models for different purposes has recently increased, thus a higher degree of automation could better satisfy different applications and speed up the processes. We present a technique for the fully automated modelling of indoor environments from a three dimensional point cloud. The results we achieve are very promising and the method suggested may provide completion to the actual standard for 3D city modelling. Our approach is based on a plane sweep algorithm for the segmentation of a point cloud in order to recognize the planar structures of a room. At first the 3D points that belong to the horizontal structures are tagged by sweeping a virtual plane along the vertical direction and thresholding the distances of each point to the plane. All the points that are not chosen as either floor or ceiling are labelled as potential wall points and are being considered in the following segmentation step to detect the vertical faces. Finally, the floor plan of the room is estimated by intersecting the directions of the walls and finding the vertices that constitute the ground shape. The result generated is a 3D model in CAD format, which perfectly fits the original point cloud.

Point process diagnostics based on weighted second-order statistics and their asymptotic properties

Abstract: A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.

Method, system and computer program product for targeting of a target with an elongate instrument

Abstract: An embodiment is directed to a method and a system for assisting the targeting of a target with an elongate instrument, wherein the instrument is to be inserted into a living object's body part along a predetermined trajectory extending between an entry point of said instrument into said body part and a target point associated with said target. The method comprises an instrument directing assisting step for generating and displaying an image allowing a user to assess to which extend the longitudinal axis of the instrument is aligned with the vector connecting the target point and the tip portion of said instrument. Also, the method comprises an instrument guiding assisting step of generating and displaying an image allowing a user to assess to which extent the instrument motion during insertion thereof coincides with the predetermined trajectory.

Multiple object speed tracking system

Abstract: A multiple object speed tracking system that can provide data related to the rate of travel of each object in a set of multiple objects as each object is traveling either toward or away from a predetermined point.