Showing papers on "Line segment published in 1992"

An optimal algorithm for intersecting line segments in the plane

Abstract: The main contribution of this work is an O(n log n + k)-time algorithm for computing all k intersections among n line segments in the plane. This time complexity is easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.

Constructing stream surfaces in steady 3D vector fields

Abstract: A streamline is a curve which is everywhere tangent to a fluid velocity field. A stream surface is the locus of an infinite set of such curves, rooted at every point along a continuous originating line segment, or rake. A stream surface may be approximated by the triangular tiling of adjacent pairs of integrated streamlines. Such a surface may be refined by repeatedly splitting the widest of the ribbons by the insertion of new curves.A more efficient method begins with a discretization of the rake. These particles are repeatedly advanced a short distance through the flow field. New polygons are appended to the downstream edge of the surface. The spacing of the particles is adjusted to maintain an adequate sampling across the width of the growing surface. This approach more efficiently accesses the flow field volume data and produces a better distribution of points over the two dimensions of the stream surface.

Applications of parametric searching in geometric optimization

Abstract: We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include; (1) Finding the minimum Hausdorff distance in the Euclidean metric between two polygonal regions under translation; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem—given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, finding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solutions or are the first non-trivial solutions to these problems), our goal is to demonstrate the versatility of the parametric searching technique.

Method and system for specifying the arrangement of windows on a display

Abstract: A method and system for specifying the arrangement of windows on a display device [is provided]. [In a preferred embodiment of the present invention, a] A selection grid is displayed on the display device. The selection grid has a bounding rectangle which represents the bounds of the display device and has a plurality of lines extending vertically and horizontally across the bounding rectangle. A user selects which line segments should be removed from the selection grid. A line segment is defined by the intersection points of the vertical and horizontal lines. As the user selects a line segment, the line segment is removed from the selection grid. The line segments that are not selected define the arrangement for the windows. The computer system then arranges the windows on the display in accordance with the specified window arrangement.

A qualitative comparison study of data structures for large line segment databases

Abstract: A qualitative comparative study is performed of the performance of three popular spatial indexing methods - the R-tree, R+-tree, and the PMR quadtree-in the context of processing spatial queries in large line segment databases. The data is drawn from the TIGER/Line files used by the Bureau of the Census to deal with the road networks in the US. The goal is not to find the best data structure as this is not generally possible. Instead, their comparability is demonstrated and an indication is given as to when and why their performance differs. Tests are conducted with a number of large datasets and performance is tabulated in terms of the complexity of the disk activity in building them, their storage requirements, and the complexity of the disk activity for a number of tasks that include point and window queries, as well as finding the nearest line segment to a given point and an enclosing polygon.

A 3D world model builder with a mobile robot

Abstract: This article describes a system to incrementally build a world model with a mobile robot in an unknown environment. The model is, for the moment, segment based. A trinocular stereo system is used to build a local map about the environment. A global map is obtained by integrating a sequence of stereo frames taken when the robot navigates in the environment. The emphasis of this article is on the representation of the uncertainty of 3D segments from stereo and on the integration of segments from multiple views. The proposed representation is simple and very convenient to characterize the uncertainty of segment. A Kalman filter is used to merge matched line segments. An important characteristic of this integration strategy is that a segment observed by the stereo system corresponds only to one part of the segment in space, so the union of the different observations gives a better estimate on the segment in space. The authors have succeeded in integrating 35 stereo frames taken in their robot room.

Estimation of displacements from two 3D frames obtained from stereo

Abstract: A method for estimating 3D displacements from two stereo frames is presented. It is based on the hypothesize-and-verify paradigm used to match 3D line segments between the two frames. In order to reduce the complexity of the method, an assumption is made that objects are rigid. The formulate a set of complete rigidity constraints for 3D line segments and integrate the uncertainty of measurements in this formation. The hypothesize-and-verify stages of the method use an extended Kalman filter to produce estimates of the displacements and of their uncertainty. The algorithm is shown to work on indoor and natural scenes. It is also shown to be easily extended to the case in which several mobile objects are present. The method is quite robust, fast, and has been thoroughly tested on hundreds of real stereo frames. >

Construction of line densities for parallel coordinate plots

Abstract: John J. MillerEdward J. WegmanCenter for Computational StatisticsGeorge Mason UniversityFairfax, VA 22030ABSTRACTThe graphical representation of high dimensional data may be accomplished by usingthe parallel coordinate plotting system. In such a representation points in Euclidian n-space aremapped into line segments in Euclidian 2-space by a projective transformation. Thisrepresentation preserves much of the geometric structure found in hyperspace but not easilyrepresentable by other methods. In large data set applications, the graphical displays may beheavily overplotted like ordinary scatterplots yielding uninterpretable displays. In this paper,we suggest replacing the raw data display with a density plot. In order to define densities forlines sensibly, we introduce the notion of line densities and develop their basic construction.We illustrate with theoretical parallel coordinate density plots for the normal and the uniformcases. Finally we illustrate sample density plots with 4-dimensional spheres.1. Introduction.The graphical display of high dimensional data is a challenging and difficult task. Anumber of interesting techniques including rotating three-dimensional scatterplots, thescatterplot matrix with brushing, the grand tour and other related graphical and computationalmethodologies have been invented with the ambition of seeing structural relationships amongrandom variables in three, four and more dimensions. One such technique is the parallelcoordinate display. This has been exposited by Inselberg (1985) as a tool for computationalgeometry and by Bolorforoush and Wegman (1988) and Wegman (1990) as a tool forexploratory data analysis. Recognizing the basic weakness of Cartesian plots as an inability tohave more than three orthogonal coordinate axes, the parallel coordinate idea is to give uporthogonality in favor of a system of parallel coordinate axes drawn in the 2-plane. Of course,as many parallel axes as one likes can be drawn in the 2-plane so that there is no inherentdimensionality limit. The idea then is to label each axis with an appropriate variable name andto connect points on adjacent axes with straight line segments. Figure 1.1 illustrates the basicidea.

Faster line segment intersection

Abstract: Publisher Summary This chapter presents an algorithm to determine whether two line segments in 2-D space intersect or not and to determine the point of intersection. Rapid calculation of line segment intersections is important because this function is often called a primitive many number of times in the inner loops of other algorithms. To develop the algorithm, it is convenient to use vector representation. The chapter describes C implementation as one that involves calculation of the intersection point coordinates where the segments are found to intersect. The C implementation uses integer arithmetic. Calculation of the intersection point involves operations that are cubic in the input coordinates so that the limitation to input coordinates in the range [0, 1023] or other similar-sized range avoids overflow on 32-bit computers. When line segments do not intersect, input coordinates in the range [0, 16383] can be handled.

Dynamic point location in general subdivisions

Abstract: The dynamic planar point location problem is the task of maintaining a dynamic set S of n non-intersecting, except possibly at endpoints, line segments in the plane under the following operations:•Locate(q point): Report the segment immediately above q, i.e., the first segment intersected by an upward vertical ray starting at q;•Insert(s segment): Add segment s to the collection S segments;•Delete(s segment): Remove segment s from the collection S of segments.We present a solution which requires space O(n), has query and insertion time O(log n loglog n) and deletion time O(log2 n). A query time below O(log2 n) was previously only known for monotone subdivisions and horizontal segments and required non-linear space.

Volume-based geometric modeling for radiation transport calculations.

Abstract: Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon's approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed.

Method for determining orientation of contour line segment in local area and for determining straight line and corner

Abstract: The present invention relates to a method for determining an orientation of a line segment in a contour in a local area of a binary contour image. The number of pixels having a predetermined value and located in each orientation in the local area, is obtained, and it is determined that a line segment exists in an orientation in which the number of pixels is large. Further, when it is determined that the number of pixels located in each of a plurality of orientations and having a predetermined value is greater than a sum of the numbers of pixels in orientations adjacent to said each orientation on both sides thereof, it is determined that a line segment exists in said each orientation. Two orientations in which large numbers of pixels are located are detected, and it is determined whether the point is a constituent of a line segment, a line segment of the sub-straight-line form, or a near-corner point, depending on angles made by the two orientations is equal to 180°, or a difference of the angles made by the two orientations from 180°. Contiguously arrayed pixels in the same orientation are detected as a line segment. A position and an orientation are obtained from points near a corner, and representative values of the positions and orientations of contiguously arrayed near-corner points are determined.

Method and apparatus for changing the perspective view of a three-dimensional object image displayed on a display screen

Abstract: An apparatus and method for rotating a perspective view of a three-dimensional object image displayed on a display screen from an original view point to a desired view point, and for moving the perspective view in a parallel manner from the original view point to the desired view point. When the perspective view is rotated, a circle is generated that has a first point corresponding to the desired view point. A line segment is generated from the first point to the center of the circle. A hemisphere is generated that has a top surface, a vertex, and the circle as a bottom surface. A second point on the top surface represents the first point projected to the top surface. The desired view point is a projection from the second point to the bottom surface of the hemisphere and the original view point is a projection from the vertex of the hemisphere. The perspective view displayed on the display screen is then changed to the desired view point. When the perspective view is moved in a parallel manner, a boundary is generated which represents a displayable range of the three-dimensional object image on the display screen. A line segment is generated from the current cursor position to the center of the boundary. The displayed perspective view is changed by moving the perspective view along the line segment by a distance equal to the length of the line segment.

3-D measurement of cutting tool wear

Abstract: The profile of a tool or other object having a flat reference plane is illuminated by interfering beams of coherent light to generate a striped light pattern which at any point deviates from straight lines as a function of the surface spacing from the reference plane. A camera image of the pattern taken at an angle to the beams is processed by an image analysis program which converts the stripes to lines corresponding to light peaks and valleys of the pattern. Tool wear or object profile is determined from the deviation of lines from straight reference lines. The program includes algorithms for identifying peak and valley line segments, determining the segments which are neighbors of other segments, and connecting lines according to a set of rules and constraints which use the data on neighbor segments and the proximity of segment end points.

Fully automated reconstruction of three-dimensional vascular tree structures from two orthogonal views using computational algorithms and productionrules

Abstract: A system for reconstructing 3-D vascular structures from two orthogonally projected images is presented. The formidable problem of matching segments between two views is solved using knowledge of the epipolar constraint and the similarity of segment geometry and connectivity. The knowledge is represented in a rule-based system, which also controls the operation of several computational algorithms for tracking segments in each image, representing 2-D segments with directed graphs, and reconstructing 3-D segments from matching 2-D segment pairs. Uncertain reasoning governs the interaction between segmentation and matching; it also provides a framework for resolving the matching ambiguities in an iterative way. The system was implemented in the C Ianguage and the C Language Integrated Production System (CLIPS) expert system shell. Using video images of a tree model, the standard deviation of reconstructed centerlines was estimated to be 0.8 mm (1.7 mm) when the view direction was parallel (perpendicular) to the epipolar plane. Feasibility of clinical use was shown using x-ray angiograms of a human chest phantom. The correspondence of vessel segments between two views was accurate. Computational time for the entire reconstruction process was under 30 s on a workstation. A fully automated system for two-view reconstruction that does not require the a priori knowledge of vascular anatomy is demonstrated.

Extraction and interpretation of semantically significant line segments for a mobile robot

Abstract: The authors describe algorithms for detecting and interpreting linear features of a real scene as images by a single camera on a mobile robot. The low-level processing stages were specifically designed to increase the usefulness and the quality of the extracted features for a semantic interpretation. The detection and interpretation processes provided a 3-D orientation hypothesis for each 2-D segment. This, in turn, was used to estimate the robot's orientation and relative position in the environment and to delimit the free space visible in the image. The orientation data was used by a motion stereo algorithm to fully estimate the 3-D structure when a sequence of images becomes available. From detection to 3-D estimation, an emphasis was placed on real-world applications and very fast processing with conventional hardware. >

The n‐line traveling salesman problem

Abstract: The special case of the Euclidean traveling salesman problem, where the n given points lie on a small number (N) of parallel lines in the plane, is solved by a dynamic programming approach in time nN, for fixed N, i.e., in polynomial time. This extends a result of Cutler (1980) for three lines. Such problems arise, for example, in the fabrication of printed circuit boards, where the distance traveled by a laser that drills holes in certain places of the board should be minimized. The parallelity condition can be relaxed to point sets that lie on N “almost parallel” line segments. We give a characterization of the allowed segment configurations by a set of forbidden subconfigurations.

New algorithms for minimum area k-gons

Abstract: Given a set P of n points in the plane, we wish to find a set Q ? P of k points for which the convex hull conv(Q) has the minimum area. We solve this, and the related problem of finding a minimum area convex k-gon, in time O(n2 log n) for fixed k, almost matching known bounds for the minimum area triangle problem. Our algorithm is based on finding a certain number of nearest vertical neighbors to each line segment determined by two input points. We use a classical result of Ramsey theory to prove that these nearest neighbors suffice to determine the minimum convex k-gon.

Structure and motion from line segments in multiple images

Abstract: An approach for recovering the structure of a rigid scene composed of straight line segments and the pose of moving camera from multiple images under perspective projection is presented. Recovery is formulated as minimizing the total squared image distance between measured segments and the projection of the reconstructed infinite lines with respect to structural and motion parameters. An efficient algorithm for minimizing this nonlinear objective function is presented. The approach can be directly used for accurately locating correspondences in multieyed stereo, as well as for pose estimation from landmarks. Its effectiveness is demonstrated quantitatively through simulation and qualitatively with a real image sequence. >

Online approximate Cartesian path trajectory planning for robotic manipulators

Abstract: To achieve online Cartesian space trajectory planning, the authors present methods for approximating Cartesian paths by recursive joint trajectories. Systematic procedures are proposed for approximating an arbitrary smooth Cartesian path by concatenated line segments and for selecting intermediate knot points along the line segments. Two recursive joint trajectory planning algorithms are derived using quartic spline interpolation. The proposed approach is illustrated by a numerical example. >

On a counterexample to a conjecture of Mirzaian

Abstract: Let L = { l 1 , l 2 ,…, l n } be a set of n pairwise disjoint line segments on the plane. A simple polygon Q is a circumscribing polygon of L if the vertices of Q are endpoints of segments in L and every segment in L is either an edge or an internal diagonal of Q . A Mirzaian conjectured that any L has a circumscribing polygon. In this note we present a counterexample to this conjecture.

Thinning and segmenting handwritten characters by line following

Abstract: This article presents a new thinning algorithm particularly well suited to handwriting characters or engineering drawing images. The line following scheme is used with major improvements to reduce the distortion at intersections. The new algorithm uses a thinning window to detect the shape and type of each intersection it is about to thin. This added information allows for a much more accurate thinning process. The algorithm also segments the skeleton into line segments as it is generated. These lines correlate partly with the strokes that produced the image. To analyze the performance of the new algorithm, a comparative study of the skeletons is performed over speed and quality criteria. This study shows that the algorithm reduces the distortion at the line intersections while remaining fast.

Detecting and decomposing self-overlapping curves

Abstract: A curve is self-overlapping if it can be divided by nontrivial line segments into simple curves. We show how to test whether a given curve is self-overlapping, and also how to construct sets of line segments that demonstrate that the curve is self-overlapping. We also describe several interesting topological properties of self-overlapping curves.

Reinforcement of linear structure using parametrized relaxation labeling

Abstract: The problem of reinforcing local evidence of linear structure while suppressing unwanted information in noisy images is considered, using a modified form of relaxation labeling. The methodology is based on parametrizing a continuous set of orientation labels via a single vector and using a sigmoidal thresholding function to bias neighborhood influence and ensure convergence to a meaningful stable state. Label strength and label/no-label decisions are incorporated into a single functional. Optimal points of the functional represent the cases where as many pixels (objects) as possible have achieved the desirable linear-structure-reinforced and noise-suppressed labelings. Three different linear structure reinforcement tasks are considered within the general framework: edge reinforcement, edge reinforcement with thinning, and bar (line segment) reinforcement. Results from several image data sets are presented. This approach can directly handle continuous feature information from low-level image analysis operators, and the computational complexity of labeling is reduced. >

System and method for generating a trimmed parametric surface for display on a graphic display device

Abstract: A method and system for representing an arbitrary parametric surface having one or more trimming polylines applied thereto. A quadrilateral mesh coextensive with the parametric surface is generated. The quadrilateral mesh has a plurality of edges and vertices coinciding with the line segments and points of the trimming polylines. In order to generate the quadrilateral mesh, a two-dimensional array of U,V values is defined, wherein points in the array are adjusted to include the points of the trimming polylines. After all of the points needing adjustment are adjusted, the points in the array are evaluated, thereby creating geometric coordinate values for each point in the array.

Use of the Hough transform to separate merged text/graphics in forms

Abstract: Presents a new method for the separation of merged text/form-structure components in forms. The technique described uses a modified version of the Hough transform to detect the structure of the form. The closed contours of the connected components are approximated by piecewise linear line segments. The parameters of the Hesse normal form of each line segment serve as input for the Hough transform. Compared to the vectorized boundary of characters, the lines of the form structure consist of appreciable more line segments with the same orientation and distance. So, the problem of the form structure detection in the database of line segments can be reduced to the detection of local peaks in the Hough space. Subsequent processing steps reconstruct the remaining contour fragments to characters. >

Computing shortest transversals of sets

Abstract: Given a family of objects in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(n log n) time algorithms for computing a shortest transversal of a family of n lines, a family of n line segments, and a family of convex polygons with a total of n vertices. In general, finding a line transversal for a family of n objects takes Ω(n log n) time. This time bound holds for a family of n line segments as well as for a family of convex polygons with a total of n vertices. Hence, our shortest transversal algorithms for these families are optimal.