Showing papers on "Point (geometry) published in 2001"

Geometric approach to statistical analysis on the simplex

Abstract: The geometric interpretation of the expected value and the variance in real Euclidean space is used as a starting point to introduce metric counterparts on an arbitrary finite dimensional Hilbert space. This approach allows us to define general reasonable properties for estimators of parameters, like metric unbiasedness and minimum metric variance, resulting in a useful tool to better understand the logratio approach to the statistical analysis of compositional data, who's natural sample space is the simplex.

Spectral processing of point-sampled geometry

Abstract: We present a new framework for processing point-sampled objects using spectral methods. By establishing a concept of local frequencies on geometry, we introduce a versatile spectral representation that provides a rich repository of signal processing algorithms. Based on an adaptive tesselation of the model surface into regularly resampled displacement fields, our method computes a set of windowed Fourier transforms creating a spectral decomposition of the model. Direct analysis and manipulation of the spectral coefficients supports effective filtering, resampling, power spectrum analysis and local error control. Our algorithms operate directly on points and normals, requiring no vertex connectivity information. They are computationally efficient, robust and amenable to hardware acceleration. We demonstrate the performance of our framework on a selection of example applications including noise removal, enhancement, restoration and subsampling.

On a Coverage Process Ranging from the Boolean Model to the Poisson Voronoi Tessellation With Applications to Wireless Communications

Abstract: We define and analyze a random coverage process of the $d$-dimensional Euclidian space which allows one to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Johnson-Mehl model. Like for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidian space and a sequence of real valued random variables considered as marks of this point process. In this coverage process, the cell attached to a point is defined as the region of the space where the effect of the mark of this point exceeds an affine function of the cumulated effect of all marks. This cumulated effect is defined as the shot noise process associated with the marked point process. In addition to analyzing and visualizing this continuum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyze convergence properties of the coverage process using the framework of closed sets, and its differentiability properties using perturbation analysis. Our results require a pathwise continuity property for the shot noise process for which we provide sufficient conditions. The model in question stems from wireless communications where several antennas share the same (or different but interfering) channel(s). In this case, the area where the signal of a given antenna can be received is the area where the signal to interference ratio is large enough. We describe this class of problems in detail in the paper. The obtained results allow one to compute quantities of practical interest within this setting: for instance the \it outage probability is obtained as the complement of the volume fraction; the law of the number of cells covering a point allows one to characterize handover strategies etc.

Surface matching by 3D point's fingerprint

Abstract: This paper proposes a new efficient surface representation method for the application of surface matching. We generate a feature carrier for the surface point, which is a set of 2D contours that are the projection of geodesic circles onto the tangent plane. The carrier is named point's fingerprint because its pattern is similar to human fingerprint and discriminating for each point. Each point's fingerprint carries the information of the normal variation along geodesic circles. Corresponding points on surfaces from different views are found by comparing fingerprints of the points. This representation scheme includes more local geometry information than some previous works that only use one contour as the feature carrier. It is not histogram based so that it is able to carry more features to improve comparison accuracy. To speed up the matching, we use a novel candidate point selection method based on the shape irregularity of the projected local geodesic circle. The point's fingerprint is successfully used to register both synthetic and real 2 1/2 data.

Reconstructing surfaces using anisotropic basis functions

Abstract: Point sets obtained from computer vision techniques are often noisy and non-uniform. We present a new method of surface reconstruction that can handle such data sets using anisotropic basis functions. Our reconstruction algorithm draws upon the work in variational implicit surfaces for constructing smooth and seamless 3D surfaces. Implicit functions are often formulated as a sum of weighted basis functions that are radially symmetric. Using radially symmetric basis functions inherently assumes, however that the surface to be reconstructed is, everywhere, locally symmetric. Such an assumption is true only at planar regions, and hence, reconstruction using isotropic basis is insufficient to recover objects that exhibit sharp features. We preserve sharp features using anisotropic basis that allow the surface to vary locally. The reconstructed surface is sharper along edges and at corner points. We determine the direction of anisotropy at a point by performing principal component analysis of the data points in a small neighborhood. The resulting field of principle directions across the surface is smoothed through tensor filtering. We have applied the anisotropic basis functions to reconstruct surfaces from noisy synthetic 3D data and from real range data obtained from space carving.

Image display device

Abstract: PROBLEM TO BE SOLVED: To provide an image display device that can display an image, in a way such that the positional relations between an entire screen and selected screens can be easily confirmed SOLUTION: This image display device is provided with a display means, that applies transparent conversion to a virtual three-dimensional space in which a single or a plurality of virtual planes with images pasted on them are placed with respect to a view point placed in the virtual three-dimensional space and displays the result on a display screen and with an image layout means that lays out a 1st virtual plane with images pasted thereon in the virtual three-dimensional space, in a way such that the front side of the 1st virtual plane is directed front with respect to the view point, pastes the images pasted to selected areas of the 1st virtual plane to a 2nd virtual plane different from the 1st virtual plane, when the part areas of the 1st virtual plane are selected, and lays out the 2nd virtual plane at a position nearer to the view point than the 1st virtual plane in the virtual three-dimensional space and at the position, at which the 2nd virtual plane is displayed smaller than the entire size of the 1st virtual plane, when the display means applies transparent conversion to the virtual three-dimensional space, in which the 1st and 2nd virtual planes are placed so that the front side of the 1st virtual plane is directed toward the front with respect to the viewpoint

Efficient Generation of High-Quality Unstructured Surface and Volume Grids

Abstract: Procedures are presented for efficient generation of high-quality unstructured surface and volume grids. The overall procedure is based on the well proven Advancing Front/Local-Reconnection (AFLR) method. The AFLR triangular/tetrahedral grid generation procedure is a combination of automatic point creation, advancing type ideal point placement, and connectivity optimization schemes. A valid grid is maintained throughout the grid generation process. This provides a framework for implementing efficient local search operations using a simple data structure. It also provides a means for smoothly distributing the desired point spacing in the field using a point distribution function. This function is propagated through the field by interpolation from the boundary point spacing or by specified growth normal to the boundaries. Points are generated using either advancing- front type point placement for isotropic elements, advancing-point type point placement for isotropic right angle elements, or advancing-normal type point placement for high-aspect-ratio elements. The connectivity for new points is initially obtained by direct subdivision of the elements that contain them. Local-reconnection with a min-max type (minimize the maximum angle) type criterion is then used to optimize the connectivity. The overall procedure is applied repetitively until a complete field grid is obtained. An advancing-normal procedure is coupled with AFLR for anisotropic tetrahedral and pentahedral element grids. Advancing along prescribed normals from solid boundaries generates layers of anisotropic elements. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be directly recovered. The AFLR surface grid procedure uses an approximate physical space grid to define the surface during grid generation. The mapped space coordinates are mapped back to the actual surface at completion. Multiple surface definition patches are grouped into a single surface. A global mapping transformation is generated for the single surface using the grouped surface connectivity. The mapping coordinates are obtained by solving a coupled set of Laplacian equations. The overall procedure has been applied to a wide variety of configurations. Selected results are presented which demonstrate that high-quality unstructured grids can be efficiently and consistently generated for complex configurations.

Simultaneous partitions of measures by K-fans

Abstract: A k-fan is a point in the plane and k semilines emanating from it. Motivated by a neat question of Kaneko and Kano, we study equipartitions by k-fans of two or more probability measures in the plane, as well as partitions in other prescribed ratios. One of our results is: for any two measures there is a 4-fan such that one of its sectors contains two-fifths of both measures, and each of the the remaining three sectors contains one-fifth of both measures.

A complete distance field representation

Abstract: Distance fields are an important volume representation. A high quality distance field facilitates accurate surface characterization and gradient estimation. However, due to Nyquist's Law, no existing volumetric methods based on the linear sampling theory can fully capture surface details, such as corners and edges, in 3D space. We propose a novel complete distance field representation (CDFR) that does not rely on Nyquist's sampling theory. To accomplish this, we construct a volume where each voxel has a complete description of all portions of surface that affect the local distance field. For any desired distance, we are able to extract a surface contour in true Euclidean distance, at any level of accuracy, from the same CDFR representation. Such point-based iso-distance contours have faithful per-point gradients and can be interactively visualized using splatting, providing per-point shaded image quality. We also demonstrate applying CDFR to a cutting edge design for manufacturing application involving high-complexity parts at un-precedented accuracy using only commonly available computational resources.

Device and method for determining the orientation of an eye

Abstract: In a device or a method for determining the direction of vision of an eye, a starting point or a final point of a light beam reflected by a part of the eye and detected by a detector system, or of a light beam projected by a projection system onto or into the eye two-dimensionally, describes a pattern of a scanning movement in the eye. The inventive method uses a displacement device that guides the center of the pattern of movement into the pupil or macula center of the eye, and a determination device that uses the pattern of movement of the scanning movement to determine the pupil center or macula center.

Regular and non-regular point sets: Properties and reconstruction

Abstract: In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of r-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed conditions based on properties of the underlying continuous shapes. Indeed, contrary to previous sampling criteria, our regularity condition can be checked on the basis of the samples alone and can be turned into a provably correct curve and surface reconstruction algorithm. Our reconstruction methods can also be applied to non-regular and unorganized point sets, revealing a larger part of the inner structure of such point sets than past approaches. Several real-size reconstruction examples validate the new method.

Reconstruction of General Curves, Using Factorization and Bundle Adjustment

Abstract: In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.

OmniVista:an application for isovist field and path analysis

Abstract: This paper briefly describes the software application OmniVista written for the Apple MacintoshPlatform. OmniVista is essentially an isovist generating application, which uses the 2d planof a building or urban environment as input data, and then can be used in one of threemodal ways. Firstly, point isovists can be generated by ‘clicking’ onto any location in theenvironment. Secondly, all navigable space can be flood-filled with points, which may then beused to generate a field of isovists. Finally, a path of points can be used to examine howisovist properties vary along the path - the results of this can either be output as numericaldata, or exported as a series of pictures, which may be combined to form an animation of thevarying isovists along the route. This paper will examine all three modes of use in turn,starting from the simplest (point) to the more complex (the path). A description and equationfor all isovist measures used in the application will also be given as an appendix to thepaper.

Systems and methods for generating string correlithm objects

Abstract: In one aspect of the invention, a system for processing data includes a memory operable to store a plurality of correlithm objects. Each correlithm object includes a plurality of values defining a point in a particular space. The particular space is defined by a plurality of dimensions and includes a plurality of points. The system also includes a processor operable to generate the values in at least a portion of the correlithm objects. A distance between a first point associated with one of the correlithm objects and each of the plurality of points in the particular space defines a distribution having a mean and a standard deviation such that a ratio of the mean to the standard deviation increases with the number of dimensions of the particular space. A distance between the first point and a second point associated with another of the correlithm objects is substantially larger than the mean of the distribution.

Experimental comparisons of space vector neutral point balancing strategies for three-level topology

Abstract: The three-level neutral point clamp topology has attracted applications in medium-voltage high-power drive systems in recent years. Since the topology utilizes a neutral point voltage to achieve half bus voltage withstanding of power devices and three-level output voltage delivery, it is critical to balance the neutral point voltage in occasions of disturbed or even continuous unbalance load conditions. This paper proposes a couple of balancing techniques based on space vector modulation principle and experimentally compares their effectiveness against the existing method.

Optimality conditions in non-convex set-valued optimization

Abstract: The notion of radial epiderivative is introduced and then a necessary and sufficient condition for a point to be a weak minimal solution (weak-efficient solution) for a non-convex set-valued optimization problem is derived. Such a condition subsumes various necessary and/or sufficient conditions found in the literature for single-valued convex/non-convex mappings.

An enhanced thinning algorithm using parallel processing

Abstract: A thinning algorithm is a very important factor in recognizing the characters, figures and drawings. Until comparatively lately, various methods have been proposed for the thinning algorithm. We ascertain the point at issue of ZS, LW and WHF algorithms that are parallel thinning algorithms. The parallel thinning algorithm means that the first processing does not have to influence the second processing. the ZS algorithm has a problem that loses pixels in slanting lines and the LW algorithm does not have one pixel width in slanting lines. We propose an enhanced parallel thinning algorithm that connects the pixels to each other and preserves the end point.

Method and system for 3-D content creation

Abstract: The present invention provides a method and system for generation of 3-D content from 2-D sources In particular, the present invention provides a method for determining a point cloud from one or more 2-D sources The method of the present utilizes a search process for locating a point of maximal crossing of line segments, wherein each line segment line is generated for each possible point match between an image point in a first 2-D scene data source and an image point in a second 2-D scene data source The search is performed over all possible camera rotation angles The point cloud solution generated by the methods of the present invention may then be utilized as input to perform texture mapping or further 3-D processing

A practical method for estimation of point light-sources

Abstract: We introduce a general model for point light-sources and show how the parameters of a source at finite distance can be estimated by shading on an object with known geometry and Lambertian reflectance. The parameters we estimate include not only the direction but also the location of the source. Furthermore, we argue that the system introduced here can be used in arbitrarily complex background illumination, provided one can switch on and off the light-source that is to be estimated.

Building 3-D Human Face Models from Two Photographs

Abstract: This paper presents a working system for building 3-D human face models from two photographs. Rather than using expensive 3-D scanners, we show that frontal face models can be faithfully reconstructed from two photographs taken by consumer digital cameras in a totally non-invasive setup. We first rectify the image pair so that corresponding epipolar lines become coincident, by computing a dual point transformation. We then address the correspondence problem by converting it into a maximal surface extraction problem, which is then solved efficiently. The method effectively removes local extrema. Finally, a Euclidean reconstruction is achieved with the help of a novel factorization method for perspective cameras. Most of the computational steps are conducted in projective space. Euclidean information is introduced only at the last stage. This sets apart our system from the traditional ones which begin with metric information by using carefully calibrated cameras. We have collected a bank of face pairs to test our system, and are satisfied with its performance. Results from this image database are demonstrated.

The number of two-dimensional maxima

Abstract: Let n points be placed uniformly at random in a subset A of the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for large n and for many sets A, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.

The Basics of Diffusion

Abstract: The concept of diffusion may be viewed naively as the tendency for a group of particles initially concentrated near a point in space to spread out in time, gradually occupying an ever larger area around the initial point. Herein the term “particles” refers not only to physical particles, but to biological population individuals or to any other identifiable units as well. Furthermore, the term “space” does not refer only to ordinary Euclidean space but can also be an abstract space (such as ecological niche space).

Ball-point pen

Abstract: A spring ( 5 ) for pressing a ball ( 23 ) forward is disposed within a tip body ( 2 ) and a holder ( 3 ). The spring ( 5 ) includes a straight part ( 6 ) and a coil part ( 7 ). The straight part ( 6 ) is inserted into the tip body ( 2 ), and the coil part ( 7 ) is disposed within the holder ( 3 ). A protrusion ( 4 ) is provided on the inner surface of the holder ( 3 ). The coil part ( 7 ) climbs over the protrusion ( 4 ) and its engagement and stopping are set up.

Electric appliance with information display device and device for moving information display device

Abstract: PROBLEM TO BE SOLVED: To make possible for anybody having a different point of sight in height to easily watch the display of an information display device attached to various devices including electric appliances. SOLUTION: A user X stands in front of the door 2 of a refrigerator main body 1. A distance from a camera 4 to the user X is set to be L1, and a photographing angle by the camera 4 is set to be θ. The photographing angle is set so that the center of user's eyes is positioned at the center of the image photographed by the camera 4. The height of use's eye is calculated by the distance L1 and the angle α. Provided that the height H is positioned downward by L2 from the camera in the vertical direction, the distance L2 is obtained by calculating an equation, L2=L1cosθ. The moving distance of the image display device is calculated by calculating a difference between H and the height of the center of the image display device in the vertical direction on an image display device mounting member 5 at the time. COPYRIGHT: (C)2003,JPO

Tight error bounds of geometric problems on convex objects with imprecise coordinates

Abstract: We study accuracy guaranteed solutions of geometric problems denned on convex region under an assumption that input points are known only up to a limited accuracy, that is, each input point is given by a convex region that represents the possible locations of the point. We show how to compute tight error bounds for basic problems such as convex hull, Minkowski sum of convex polygons, diameter of points, and so on. To compute tight error bound from imprecise coordinates, we represent a convex region by a set of half-planes whose intersection gives the region. Error bounds are computed by applying rotating caliper paradigm to this representation.

Development of a Robust Algorithm for Transformation of a 3D Object Point onto a 2D Image Point for Linear Pushbroom Imagery

Abstract: expressed in a rigorous mathematical form (Kim, 2000). Further A powe$ul and robust algorithm for the Indirect Method, i.e., studies are required for the understanding of the geometry of the transformation of a 30 object point onto a 2D image point linearpushbroomimages. for linear pushbroom imagery, is proposed. This algorithm This paper addresses the problem of rectification of linear solves the transformation iteratively with an initial estimate pushbroom images so that the images can be geometrically ref- of the 20 image point coordinates. However, this algorithm erenced. There can be two ways to solve this problem. The first does not require any sophisticated procedures to determine a one is referred to as the Direct Method, which solves the prob- "good" initial estimate and it always converges to the correct lem by projecting an image point in two-dimensional (zD) solution. This algorithm works using the following procedures: image coordinates onto an object point in three-dimensional first, with an (random) initial estimate of the 20 image point (3D) object coordinates. A technique called Ray-Tracing coordinates, calculate the attitude of the camera platform; (O'Neilland Dowman, 1988) was developed to solve the prob- second, with the given attitude, calculate the position of the lem by the Direct Method. The other one is referred to as the camera platform and the 20 image point; and third, update Indirect Method, which solves the problem the other way the estimate with the calculated 2D image point coordinates around, i.e-9 by projecting a 3D object point onto a zD image and then go back to the first procedure and continue iteration point. It is known that the Indirect Method has many advan- until the estimated and calculated image point coordinates tages overthe Direct Method (Mayrand Hei~ke, 1988). In Par- converge. Results of the experiment show that this algorithm ticular~ it reduce sthe processing time and amount of memory converges very fast even when the initial estimate has a required for image resampling. huge error. However, a robust numerical solution of the Indirect Method for linear pushbroom images has so far not been devel-