Showing papers on "Line segment published in 2009"

Geometric reasoning for single image structure recovery

Abstract: We study the problem of generating plausible interpretations of a scene from a collection of line segments automatically extracted from a single indoor image. We show that we can recognize the three dimensional structure of the interior of a building, even in the presence of occluding objects. Several physically valid structure hypotheses are proposed by geometric reasoning and verified to find the best fitting model to line segments, which is then converted to a full 3D model. Our experiments demonstrate that our structure recovery from line segments is comparable with methods using full image appearance. Our approach shows how a set of rules describing geometric constraints between groups of segments can be used to prune scene interpretation hypotheses and to generate the most plausible interpretation.

Path integral approach to eikonal and next-to-eikonal exponentiation

Abstract: We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.

Wide-baseline image matching using Line Signatures

Abstract: We present a wide-baseline image matching approach based on line segments Line segments are clustered into local groups according to spatial proximity Each group is treated as a feature called a Line Signature Similar to local features, line signatures are robust to occlusion, image clutter, and viewpoint changes The descriptor and similarity measure of line signatures are presented Under our framework, the feature matching is not only robust against affine distortion but also a considerable range of 3D viewpoint changes for non-planar surfaces When compared to matching approaches based on existing local features, our method shows improved results with low-texture scenes Moreover, extensive experiments validate that our method has advantages in matching structured non-planar scenes under large viewpoint changes and illumination variations

Transmission line directional awareness

Abstract: Coupling a charging station to a power line segment that is terminated at a first end by a charging terminal includes: sensing a communication signal propagating on the power line and being coupled from multiple taps connected to the power line segment, and determining if the communication signal is propagating on the power line segment in the direction from the first end to a second end of the power line segment or in the direction from the second end to the first end.

Automated Geospatial Conflation of Vector Road Maps to High Resolution Imagery

Abstract: As the availability of various geospatial data increases, there is an urgent need to integrate multiple datasets to improve spatial analysis. However, since these datasets often originate from different sources and vary in spatial accuracy, they often do not match well to each other. In addition, the spatial discrepancy is often nonsystematic such that a simple global transformation will not solve the problem. Manual correction is labor-intensive and time-consuming and often not practical. In this paper, we present an innovative solution for a vector-to-imagery conflation problem by integrating several vector-based and image-based algorithms. We only extract the different types of road intersections and terminations from imagery based on spatial contextual measures. We eliminate the process of line segment detection which is often troublesome. The vector road intersections are matched to these detected points by a relaxation labeling algorithm. The matched point pairs are then used as control points to perform a piecewise rubber-sheeting transformation. With the end points of each road segment in correct positions, a modified snake algorithm maneuvers intermediate vector road vertices toward a candidate road image. Finally a refinement algorithm moves the points to center each road and obtain better cartographic quality. To test the efficacy of the automated conflation algorithm, we used U.S. Census Bureau's TIGER vector road data and U.S. Department of Agriculture's 1-m multi-spectral near infrared aerial photography in our study. Experiments were conducted over a variety of rural, suburban, and urban environments. The results demonstrated excellent performance. The average correctness measure increased from 20.6% to 95.5% and the average root-mean-square error decreased from 51.2 to 3.4 m.

Undelayed initialization of line segments in monocular SLAM

Abstract: This paper presents 6-DOF monocular EKFSLAM with undelayed initialization using linear landmarks with extensible endpoints, based on the Plucker parametrization. A careful analysis of the properties of the Plucker coordinates, defined in the projective space ℙ5, permits their direct usage for undelayed initialization. Immediately after detection of a segment in the image, a Plucker line is incorporated in the map. A single Gaussian pdf includes inside its 2-sigma region all possible lines given the observed segment, from arbitrarily close up to the infinity range, and in any orientation. The lines converge to stable 3D configurations as the moving camera gathers observations from new viewpoints. The line's endpoints, maintained out of the map, are constantly retro-projected from the image onto the line's local reference frame. An extending-only policy is defined to update them. We validate the method via Monte Carlo simulations and with real imagery data.

Optimization Method for Highway Horizontal Alignment Design

Abstract: This research presents an optimization heuristic to solve the horizontal alignment of a highway segment. The iterative heuristic works in two stages. The first stage uses a neighborhood search approach to find a good piecewise linear line that approximates the highway alignment. The second stage further adjusts the alignment so that the external and code requirements are accurately satisfied. Both stages manipulate the piecewise linear line with a neighborhood search heuristic, and use a mixed integer program (MIP) to ensure that the piecewise linear line crosses the control areas and avoids the restricted ones. The optimal objective function value returned by the MIP is used to compare the quality between different piecewise linear lines. The lengths of each line segment are properly constrained in the MIP to ensure that curves can be correctly deployed. Starting from an initial feasible solution the process gradually improves the alignment through iterations. Computational examples are provided.

Multi-stage tessellation for graphics rendering

Abstract: This disclosure describes a multi-stage tessellation technique for tessellating a curve during graphics rendering. In particular, a first tessellation stage tessellates the curve into a first set of line segments that each represents a portion of the curve. A second tessellation stage further tessellates the portion of the curve represented by each of the line segments of the first set into additional line segments that more finely represent the shape of the curve. In this manner, each portion of the curve that was represented by only one line segment after the first tessellation stage is represented by more than one line segment after the second tessellation stage. In some instances, more than two tessellation stages may be performed to tessellate the curve.

A fast approach for geometry-adaptive block partitioning

Abstract: State-of-the-art video compression standards such as H.264 employ tree-structured motion compensation by splitting macro-blocks into fixed square or rectangular sub-blocks. Although, this approach leads to improved compression performance, recent studies have shown that further gain can be achieved via slicing blocks with arbitrary line segments to better match the boundaries between moving objects. However, finding the best partition remains an extremely computationally-intensive task. In this paper, we propose a fast method to identify efficient partitions using a two-step search of the radius and angle of the line segment. Experimental results show that this scheme is able to identify efficient motion boundaries using less iterations than existing techniques while maintaining comparable performance.

Information processing apparatus, processing method thereof, and computer-readable storage medium

Abstract: An information processing apparatus that calculates information on a position and an orientation of an image capture device relative to an object captured by the image capture device, holds three-dimensional information including a plurality of line segments that constitute the object, acquires an image of the object captured by the image capture device, detects an image feature indicating a line segment from the acquired image, calculates a position and orientation of the image capture device based on correspondence between the image feature indicating the detected line segment and the held line segment, and determines, for each of the held line segments, whether to use the line segment for the calculation of the position and orientation thereafter, based on at least one of a result of detection of the image feature, and information acquired in the calculation of the position and orientation.

Line Enhancement and Completion via Linear Left Invariant Scale Spaces on SE(2)

Abstract: From an image we construct an invertible orientation score, which provides an overview of local orientations in an image. This orientation score is a function on the group SE (2) of both positions and orientations. It allows us to diffuse along multiple local line segments in an image. The transformation from image to orientation score amounts to convolutions with an oriented kernel rotated at multiple angles. Under conditions on the oriented kernel the transform between image and orientation score is unitary. This allows us to relate operators on images to operators on orientation scores in a robust way such that we can deal with crossing lines and orientation uncertainty. To obtain reasonable Euclidean invariant image processing the operator on the orientation score must be both left invariant and non-linear. Therefore we consider non-linear operators on orientation scores which amount to direct products of linear left-invariant scale spaces on SE (2). These linear left-invariant scale spaces correspond to well-known stochastic processes on SE (2) for line completion and line enhancement and are given by group convolution with the corresponding Green's functions. We provide the exact Green's functions and approximations, which we use together with invertible orientation scores for automatic line enhancement and completion.

How to Recognize a Parabola

Abstract: Parabolas have many interesting properties which were perhaps more well known in centuries past. Many of these properties hold only for parabolas, providing a characterization which can be used to recognize (theoretically, at least) a parabola. Here, we present a dozen characterizations of parabolas, involving tangent lines, areas, and the well-known reflective property. While some of these properties are widely known to hold for parabolas, the fact that they hold only for parabolas may be less well known. These remarkable properties can be verified using only elementary techniques of calculus, geometry, and differential equations. A parabola is the set of points in the plane which are equidistant from a point F called the focus and a line / called the directrix. If the directrix is horizontal, then the parabola is the graph of a quadratic function p(x) = ax2 + sx + y. We will not distinguish between a function and its graph. A chord of a function f(x) is a line segment whose endpoints lie on the graph of the function. A chord of f(x) is a segment of a secant line to f(x). By the equation of a chord, we mean the equation of the corresponding secant line. Our first characterization of parabolas involves the area between a function and a chord having horizontal extent h.

VecSLAM: An Efficient Vector-Based SLAM Algorithm for Indoor Environments

Abstract: In this paper, we present an efficient SLAM (Simultaneous Localization and Mapping) algorithm named VecSLAM, which localizes and builds a vector map for mobile robots in indoor environments. Compared to grid-mapping approaches, vector-based mapping algorithms require a relatively small amount of memory. Two essential operations for successful vector mapping are vector merging and loop closing. Merging methods used by traditional line segment-based mapping algorithms do not consider the sensor characteristics, which causes additional mapping error and makes it harder to close loops after navigation over a long distance. In addition, few line segment-based SLAM approaches contain loop closing methodology. We present a novel vector merging scheme based on a recursive least square estimation for robust mapping. An efficient loop closing method is also proposed, which effectively distributes the resultant mapping error throughout the loop to guarantee global map consistency. Simulation studies and experimental results show that VecSLAM is an efficient and robust online localization and mapping algorithm.

A minimal lamination of the unit ball with singularities along a line segment

Abstract: We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis, extending from the origin. We further study the transversal structure of the minimal limit lamination and find removable singularities along the line segment and a non-removable singularity at the origin. This extends a result of Colding and Minicozzi where they constructed a sequence with curvatures blowing up only at the center of the ball, Dean’s construction of a sequence with curvatures blowing up at a prescribed discrete set of points, and the classical case of the sequence of re-scaled helicoids with curvatures blowing up along the entire vertical axis.

On the generation of nearly optimal, planar paths of bounded curvature and bounded curvature gradient

Abstract: We present a numerically efficient scheme to generate a family of path primitives that can be used to construct paths that take into consideration point-wise constraints on both the curvature and its derivative. The statement of the problem is a generalization of the Dubins problem to account for more realistic vehicle dynamics. The problem is solved by appropriate concatenations of line segments, circular arcs and pieces of clothoids, which are the path primitives in our scheme. Our analysis reveals that the use of clothoid segments, in addition to line segments and circular arcs, for path generation introduces significant changes on issues such as path admissibility and length minimality, when compared with the standard Dubins problem.

Trajectory Voting and Classification Based on Spatiotemporal Similarity in Moving Object Databases

Abstract: We propose a method for trajectory classification based on trajectory voting in Moving Object Databases (MOD). Trajectory voting is performed based on local trajectory similarity. This is a relatively new topic in the spatial and spatiotemporal database literature with a variety of applications like trajectory summarization, classification, searching and retrieval. In this work, we have used moving object databases in space, acquiring spatiotemporal 3-D trajectories, consisting of the 2-D geographic location and the 1-D time information. Each trajectory is modelled by sequential 3-D line segments. The global voting method is applied for each segment of the trajectory, forming a local trajectory descriptor. By the analysis of this descriptor the representative paths of the trajectory can be detected, that can be used to visualize a MOD. Our experimental results verify that the proposed method efficiently classifies trajectories and their sub-trajectories based on a robust voting method.

Robust and precise circular arc detection

Abstract: In this paper we present a method to robustly detect circular arcs in a line drawing image. The method is fast, robust and very reliable, and is capable of assessing the quality of its detection. It is based on Random Sample Consensus minimization, and uses techniques that are inspired from object tracking in image sequences. It is based on simple initial guesses, either based on connected line segments, or on elementary mainstream arc detection algorithms. Our method consists of gradually deforming these circular arc candidates as to precisely fit onto the image strokes, or to reject them if the fitting is not possible, this virtually eliminates spurious detections on the one hand, and avoiding nondetections on the other hand.

Range pattern definition of susceptibility of layout regions to fabrication issues

Abstract: A memory is encoded with a data structure that represents a pattern having a range for one or more dimensions and/or positions of line segments therein. The data structure identifies two or more line segments that are located at a boundary of the pattern. The data structure also includes at least one set of values that identify a maximum limit and a minimum limit (i.e. the range) between which relative location and/or dimension of an additional line segment of the pattern in a portion of a layout of an integrated circuit (IC) chip, represents a defect in the IC chip when fabricated. In most embodiments, multiple ranges are specified in such a range defining pattern for example a width range is specified for the width of a trace of material in the layout and a spacing range is specified for the separation distance between two adjacent traces in the layout.

A discrete spherical x-ray transform of orientation distribution functions using bounding cubes

Abstract: We investigate a cubed sphere parametrization of orientation space with the aim of constructing a discrete voxelized version of the spherical x-ray transform. For tracing the propagation of a unit great circle through the partition subsets, the frustums of the cubed sphere, a fast procedure is proposed. The circle's parts in each frustum are gnomonically mapped into line segments inside the bounding cubes. The line segments constitute a convex polygon with vertexes indicating frustum exit–entry points. Thus the problem of system matrix calculation is reduced to the tracing of line segments within rectangular voxel arrays partitioning the bounding cubes. Hence algebraic reconstruction techniques can be used in a comprehensive way for orientation distribution function estimation from diffraction data.

Viewpoint invariant features from single images using 3D geometry

Abstract: In this paper we present a novel approach for generating viewpoint invariant features from single images and demonstrate their application for robust matching over widely separated views. The key idea consists of retrieving building structure from single images and then utlising the recovered 3D geometry to improve the performances of feature extraction and matching. Urban environments usually contain many structured regularities, so that the images of those environments contain straight parallel lines and vanishing points, which can be efficiently exploited for 3D reconstruction. We present an effective scheme to recover 3D planar surfaces using the extracted line segments and their associated vanishing points. The viewpoint invariant features are then computed on the normalized front-parallel views of the obtained 3D planes. The advantages of the proposed approach include: (1) the new feature is very robust against perspective distortions and viewpoint changes due to its consideration of 3D geometry; (2) the features are completely computed from single images and do not need information from additional devices (e.g. stereo cameras, or active ranging devices). Experiments are carried out to demonstrate the proposed scheme ability to effectively handle very difficult wide baseline matching tasks in the presence of repetitive building structures and significant viewpoint changes.

A hybrid approach to RBPF based SLAM with grid mapping enhanced by line matching

Abstract: In this paper, we present a novel data structure representing the environment with occupancy grid cells while each grid map is associated with a set of line features extracted from laser scan points. Due to the fact that line segments are principal elements of artificial environments, they provide considerable geometric information about the environment which can be used for enhancing the accuracy of localization. Orthogonal characteristic of line features is the key issue to guarantee the consistency of the SLAM algorithm by allowing us to deal with lines that are parallel or perpendicular to each other. This behavior allows us to sample robot poses more correctly. As a result, the proposed algorithm can close bigger loops with the same number of particles. Experimental results are carried out using SICK LMS-100 laser scanner which has a maximum range of 20m and Pioneer 3DX mobile robot mapping an indoor environment with the size of 40m × 47m.

Simultaneous multi-line-segment merging for robot mapping using Mean shift clustering

Abstract: Line segment based representation of 2D robot maps is known to have advantages over raw point data or grid based representation gained from laser range scans. It significantly reduces the size of the data set. It also contains higher geometric information, which is necessary for robust post processing. The paper describes an algorithm to convert global 2D robot maps to line segment representation, using a pre-aligned set of point-based single scans as input. Mean-shift clustering on the set of all line segments is utilized to merge perceptually similar segments to single instances: locally linear features in the environment are unambiguously represented by single line segments in the final global map. Apart from a scaling parameter, the approach is parameter free. Experiments on real world data sets prove its applicability in the field of robot mapping.

On Modem Illumination Problems

Abstract: In this paper we review recent results on a new variation of the Art Gallery problem. A common problem we face nowadays, is that of placing a set of wireless modems in a building in such a way that a computer placed anywhere within the building receives a signal strong enough to connect to the Web. In most buildings, the main limitation for this problem is not the distance of a computer to a wireless modem, but rather the number of walls that separate them. We study variations of the following problem: Let P be a simple polygon with n vertices. How many points p1, . . . , pk (representing wireless modems) are always sufficient such that for any other point p in P, there is a pi such that the line segment joining p to pi crosses at most k edges of P? The parameter k represents the strenght of the signal emited by the modems. We study variations of this problem for families of line segments, families of lines, orthogonal polygons, and sets of horizontal or vertical disjoint segments, or sets of lines.

Control device, laser irradiation device, optimization font data database, recording method, and computer-readable storage medium

Abstract: A control device controls a laser irradiation device to record visible information on a medium by irradiation of a laser beam. The control device includes a drawing information storage unit which stores drawing information of line segments contained in line images of characters, numbers, and symbols. A drawing information acquiring unit acquires drawing information of a line image as an object to be drawn. A thickness information acquiring unit acquires thickness information which specifies a thickness of each line segment. An overlapping line segment detecting unit detects a pair of line segments drawing ranges of which, inclusive of the line segment thickness, overlap each other, based on the thickness information and the drawing information. A line dividing/shortening unit divides or shortens at least one of the pair of line segments so that the drawing ranges of the pair of line segments do not overlap each other.

Data processing from a Laser Range Finder sensor for the construction of geometric maps of an indoor environment

Abstract: In this paper we propose a methodology to detect lines or edges for a later construction of geometric maps using a URG-04LX Laser Range Finder from Hokuyo Automatic, Co. First, the algorithm decodes the raw data from the sensor, using URG series, into a list of points in polar coordinates. Afterward, it converts to x-y coordinates in order to have the first image. The list of points is reduced using sub sampling, and then it applies Hough Transform to obtain line segments. The Hough Transform is applied in several cycles, using masks to erase lines already found and detect new lines segments. At the end, the algorithm is able to group up to 90.32% of the points in the original image.

Quality assessment of linear data

Abstract: This paper presents methods to evaluate the geometric quality of spatial data. Firstly, a point‐based method is presented, adapting conventional assessment methods whereby common points between datasets are compared. In our approach, initial matches are established automatically and refined further through interactive editing. Second, a line‐based method which uses correspondences between line segments is proposed. Here, the geometry of line segments in vector is transformed into a set of rasterized values so that their combination at each pixel can restore their original vector geometry. Matching is performed on rasterized line segments and their matching lengths and displacements are measured. Experimental results show that the line‐based approach proposed is efficient to evaluate the geometric quality of spatial data without requirements of topological relationships among line features.