Showing papers on "Line segment published in 2001"

VRONI: an engineering approach to the reliable and efficient computation of voronoi diagrams of points and line segments

Abstract: We discuss the design and implementation of a topology-oriented algorithm for the computation of Voronoi diagrams of points and line segments in the two-dimensional Euclidean space The main focus of our work was on designing and engineering an algorithm that is completely reliable and fast in practice The algorithm was implemented in ANSI C, using standard floating-point arithmetic In addition to Sugihara and Iri's topology-oriented approach, it is based on a very careful implementation of the numerical computations required, an automatic relaxation of epsilon thresholds, and a multi-level recovery process combined with “desperate mode” The resulting code, named vroni , was tested extensively on real-world data and turned out to be reliable CPU-time statistics document that it is always faster than other popular Voronoi codes In our computing environment, vroni needs about 001n log 2 n milliseconds to compute the Voronoi diagram of n line segments, and this formula holds for a wide variety of synthetic and real-world data In particular, its CPU-time consumption is hardly affected by the actual distribution of the input data Vroni also features a function for computing offset curves, and it has been successfully tested within and integrated into several industrial software packages

On a common circle: Natural scenes and Gestalt rules

Abstract: To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.

Directional morphological filtering

Abstract: We show that a translation invariant implementation of min/max filters along a line segment of slope in the form of an irreducible fraction dy/dx can be achieved at the cost of 2+k min/max comparisons per image pixel, where k=max(|dx|,|dy|). Therefore, for a given slope, the computation time is constant and independent of the length of the line segment. We then present the notion of periodic moving histogram algorithm. This allows for a similar performance to be achieved in the more general case of rank filters and rank-based morphological filters. Applications to the filtering of thin nets and computation of both granulometries and orientation fields are detailed. Finally, two extensions are developed. The first deals with the decomposition of discrete disks and arbitrarily oriented discrete rectangles, while the second concerns min/max filters along gray tone periodic line segments.

Proximity Queries and Penetration Depth Computation on 3D Game Objects

Abstract: This paper discusses methods for performing proximity queries (collision detection, distance computation) and penetration depth computation on a large class of convex objects. The penetration depth of a pair of intersecting objects is the shortest vector over which one object needs to be translated in order to bring the pair in touching contact. The class of objects includes convex primitives such as polytopes (line segments, triangles, convex polyhedra) and quadrics (spheres, cones, cylinders), as well as shapes derived from these primitives by affine transformation and spherical expansion (inflating an object by a given offset).

Matching, reconstructing and grouping 3D lines from multiple views using uncertain projective geometry

Abstract: We present a geometric method for (i) matching 2D line segments from multiple oriented images, (ii) optimally reconstructing 3D line segments and (iii) grouping 3D line segments to corners. The proposed algorithm uses two developments in combining projective geometry and statistics, which are described in this article: (i) the geometric entities points, lines and planes in 2D and 3D and their uncertainty are represented in homogeneous coordinates and new entities may be constructed including their propagated uncertainty. The construction can be performed directly or as an estimation. (ii) relations such as incidence, equality, parallelism and orthogonality between points, lines and planes can be tested statistically based on a given significance level. Using these tools, the resulting algorithm is straightforward and gives reasonable results. It is only based on geometric information and does not use any image intensities, though it can be extended to use other information. The matching of 3D lines does not need any thresholds other than a significance value for the hypotheses tests.

Separating objects in the plane by wedges and strips

Abstract: In this paper we study the separability of two disjoint sets of objects in the plane according to two criteria: wedge separability and strip separability. We give algorithms for computing all the separating wedges and strips, the wedges with the maximum and minimum angle, and the narrowest and the widest strip. The objects we consider are points, segments, polygons and circles. As applications, we improve the computation of all the largest circles separating two sets of line segments by a logn factor, and we generalize the algorithm for computing the minimum polygonal separator of two sets of points to two sets of line segments with the same running time. ? 2001 Elsevier Science B.V. All rights reserved.

Method and system for representing and displaying digital ink

Abstract: A method and system for compressing and displaying a digital ink trace. Raw ink data is smoothed, and sharp points of the smoothed line are found. Curve-fitting is then used to generate a mathematical expression that defines the line segments between adjacent sharp points. The ink trace then is represented by a backbone spline that includes the sharp points and the mathematical expressions for the line segments. Thickness information, such as pressure or acceleration information, is combined with the backbone spline to provide a compressed ink file that represents a contour curve of the original ink trace. A display module uses an algorithm to separate the contour curve into a sequence of straight lines. A set of pixels is then generated for the display of each straight line using a novel antialiasing method. The pixels at the ends of adjacent straight lines are aligned using a weighting algorithm.

Digital lines and digital convexity

Abstract: Euclidean geometry on a computer is concerned with the translation of geometric concepts into a discrete world in order to cope with the requirements of representation of abstract geometry on a computer. The basic constructs of digital geometry are digital lines, digital line segments and digitally convex sets. The aim of this paper is to review some approaches for such digital objects. It is shown that digital objects share much of the properties of their continuous counterparts. Finally, it is demonstrated by means of a theorem due to Tietze (1929) that there are fundamental differences between continuous and discrete concepts.

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

Removal of line end shortening in microlithography and mask set for removal

Abstract: A mask set of two masks and a method of using these masks in a double exposure to avoid line shortening due to optical proximity effects is described. A pattern having pattern elements comprising a number of line segments, wherein each of the line segments has one or two free ends which are not connected to other mask pattern elements is to be transferred to a layer of resist. A first mask is formed by adding line extensions to each of the free ends of the line segments. A cutting mask is formed comprising rectangles enclosing each of the line extensions wherein one of the sides of said rectangles is coincident with the corresponding free end of said line segment. The first mask has opaque regions corresponding to the extended line segments. The cutting mask has transparent regions corresponding to the cutting pattern. In another embodiment a pattern having pattern openings comprising a number of line segments. In this embodiment the cutting pattern comprises rectangles having the same width as said line segments and add length to the line segments.

Method for finding contours in an image of an object

Abstract: A method is provided for robustly and efficiently identifying contours in an image of an object. Features are extracted from an image, typically using a Sobel edge detector or a set of large oriented filters, and are locally chained to form contour segments of particular character, such as line segments. A spatial hash table is used to access the contour segments according to the location of their endpoints. Candidate sets for joining to grow contours are reduced by considering only segments having ends in adjacent spatial hash bins. Contour constraints are applied to appropriately choose among the candidates to form contours. The method facilitates robust and efficient scratch detection of fiber-optic end faces, or of any surface that may have smoothly curved scratches.

Robust and efficient map-to-image registration with line segments

Abstract: This work investigates map-to-image registration for planar scenes in the context of robust parameter estimation. Registration is posed as the problem of estimating a projective transformation which optimally aligns transformed model line segments from a map with data line segments extracted from an image. Matching and parameter estimation is solved simultaneously by optimizing an objective function which is based on M-estimators, and depends on overlap and the weighted orthogonal distance between transformed model segments and data segments. An extensive series of registration experiments was conducted to test the performance of the proposed parameter estimation algorithm. More than 200 000 registration experiments were run with different objective functions for 12 aerial images and randomly corrupted maps distorted by randomly selected projective transformations.

A Soft k-Segments Algorithm for Principal Curves

Abstract: We propose a new method to find principal curves for data sets. The method repeats three steps until a stopping criterion is met. In the first step, k (unconnected) line segments are fitted on the data. The second step connects the segments to form a polygonal line, and evaluates the quality of the resulting polygonal line. The third step inserts a new line segment.We compare the performance of our new method with other existing methods to find principal curves.

3-D interpretation of single line drawings based on entropy minimization principle

Abstract: The human visual system can interpret two-dimensional (2-D) line drawings like the Necker cube as three-dimensional (3-D) wire frames On this human ability Thomas Marill presented two important papers First one proposed the 3-D interpretation model based on the principle to minimize the standard deviation of the angles between line segments in 3-D wire frame (MSDA), and reported the results of simulation experiments Second one proposed the principle to minimize the description length on the internal representation in visual system Motivated by Marill's principle to minimize the description length, we propose a principle to minimize the entropy of angle distribution between line segments in a 3-D wire frame (MEAD), which is more general than the MSDA one And we implement the principle MEAD using a genetic algorithm (GA) as a simulation program The results of simulation experiments show that the proposed principle of MEAD is more appropriate than the MSDA and another principle

Vapor phase etch trim structure with top etch blocking layer

Abstract: A blocking layer is formed on a hard mask having an initial thickness. Lines are fabricated by patterning the blocking layer and the hard mask to provide a line segment, the line segment having a first dimension measured across the line segment; reacting a surface layer of the line segment to form a layer of a reaction product on a remaining portion of the line segment; and removing the reaction product without attacking the remaining portion of the line segment and without attacking the blocking layer and the substrate to form the line segment with a second dimension across the line segment that is smaller than the first dimension. The blocking layer prevents the formation of reaction product on the hard mask so that the initial thickness of the hard mask is maintained. The blocking layer can also serve as an ARC layer for photoresist patterning so that the use of an additional film layer is not required.

Embroidery data generating apparatus

Abstract: A method for generating embroidery data based on an image including a plurality of pixels. A plurality of line segment data is generated for pixel groups, each pixel group including at least one pixel based therein. Each of the line segment data defines a line segment by an angle component in which the line segment extends, a length component indicating a length of the line segment and a color component indicating a color of the line segment. The embroidery data is generated based on the plurality of line segment data, so as to give embroidery stitches along the line segments.

Competitive Facility Location along a Highway

Abstract: We consider a competitive facility location problem with two players.Pla yers alternate placing points, one at a time, into the playing arena, until each of them has placed n points.The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins.W e present a winning strategy for the second player, where the arena is a circle or a line segment.

Online point location in planar arrangements and its applications

Abstract: Recently, Har-Peled [17] presented a new randomized technique for online construction of the zone of a curve in a planar arrangement of arcs. In this paper: we present several applications of this technique, which yield improved solutions to a variety of problems. These applications include: (i) an efficient mechanism for performing online point location queries in an arrangement of arcs; (ii) an efficient algorithm for computing an approximation to the minimum-weight Steiner-tree of a set of points, where the weight is the number of intersections between the tree edges and a given collection of arcs; (iii) a subquadratic algorithm for cutting a set of pseudo-parabolas into pseudo-segments; (iv) an algorithm for cutting a set of line segments (`rods') in 3-space so as to eliminate all cycles in the vertical depth order; and (v) a near-optimal algorithm for reporting all bichromatic intersections between a set R of red arcs and a set B of blue arcs, where the unions of the arcs in each set are both connected.

Process and structure for repairing defect of liquid crystal display

Abstract: A process for repairing defects applied in producing a liquid crystal display, wherein the liquid crystal display includes a pixel array formed by a plurality of scanning lines crossing with a plurality of data lines. The process includes steps of providing an essential repair line located on one side of the pixel array, welding a first intersection point of a defecting data line and the essential repair line and a second intersection point of a normal data line adjacent to the defecting data line and the essential repair line by a first laser to achieve electrical connection, and cutting a first breaking point and a second breaking point of the essential repair line by a second laser to achieve a broken circuit, wherein the first and second intersection points are located two sides of a line segment constructed by the first and second intersection points respectively.

Terrain decomposition and layered manufacturing

Abstract: We consider a problem that arises in generating three-dimensional models by methods of layered manufacturing: How does one decompose a given model P into a small number of sub-models each of which is a terrain polyhedron? Terrain polyhedra have a base facet such that, for each point of the polyhedron, the line segment joining the point to its orthogonal projection on the base facet lies within the polyhedron. Terrain polyhedra are exactly the class of polyhedral models for which it is possible to construct the model using layered manufacturing (with layers parallel to the base facet), without the need for constructing "supports" (which must later be removed). In order to maximize the integrity of a prototype, one wants to minimize the number of individual sub-models that are manufactured and then glued together. We show that it is NP-hard to decide if a three-dimensional model P of genus 0 can be decomposed into k terrain polyhedra. We also prove a two-dimensional version of this theorem, for the case in which P is a polygonal region with holes. Both results still hold if we are restricted to isothetic objects and/or axis-parallel layering directions.

Wiring editing method, for semiconductor package, capable of easily editing offset of wiring pattern

Abstract: A wiring editing method for a semiconductor package of this invention includes the steps of assuming virtual circular arcs R 1 to R 4 in consideration of a clearance round a predetermined via 11 a in a designated area on a virtual plane, drawing a regular polygon 12 circumscribing the virtual circular arcs R 1 to R 4, drawing a tangent from a crossing via 11 to the virtual circular arcs R 1 to R 4 and connecting to the regular polygon 12 to thereby form a wiring pattern 13 when the virtual circular arcs R 1 to R 4 cross any of the vias 11, and moving or omitting the line segment forming the regular polygon 12 in the wiring pattern 13 to change a wiring route when an offset occurs in the wiring pattern 13 passing between the vias 11 inside the designated area.

Peripheral object confirming device

Abstract: PROBLEM TO BE SOLVED: To enable the accurate driving operation by accurately detecting position of an object existing in the periphery of the own-vehicle, and displaying a map to a driver when parking. SOLUTION: Distance and direction to the object existing in the periphery of the own-vehicle obtained by a distance measuring device 4 such as a laser radar is stored in a distance data memory unit 5 in order as a data point sequence with position of the own-vehicle obtained by an own-vehicle position detecting device 1. An object position judging unit 8 judges the positional condition of the peripheral object on the basis of a residual line segment, which is obtained by eliminating a line segment out of the nearly horizontal or nearly vertical angle relation in relation to the reference direction obtained by a reference direction computing unit 3 when the own-vehicle straightly travels, from the line segment, which is obtained by computing a linear approximation in a linear approximation unit 6 on the basis of the data point sequence, in a noise eliminating unit 7. Arrangement of the peripheral object is displayed in a display unit 10 by a map generating unit 9. COPYRIGHT: (C)2002,JPO

Clock synchronization with removal of clock skews through network measurements in derivation of a convext hull

Abstract: A method, computer program product, and data processing system for estimating and correcting the amount of clock skew in end-to-end network timing measurements is disclosed. Measured delays are combined with their time of measurement to create ordered pairs. These ordered pairs represent points within a Cartesian plane. The convex hull of these points is determined, and an optimal line segment from the resulting polygon is selected and extrapolated to create an affine function estimating clock skew over time. The optimal line segment of the polygon is one that optimizes a selected objective function. The objective function is selected so as to be an appropriate measurement of the accuracy of the resulting linear function as an estimate of the actual clock skew.

Segmentation of text lines in digitized images

Abstract: A method for locating symbols arranged in one or more rows in an image includes smearing the image, and fitting line segments through edge points of features in the smeared image. A group is found of the line segments that are in mutual proximity and are mutually substantially parallel. A region of the image that contains the group of the line segments is identified as a possible location of the symbols.

Online Point Location in Planar Arrangements and Its Applications

Abstract: Recently, Har-Peled [HP2] presented a new randomized technique for online construction of the zone of a curve in a planar arrangement of arcs. In this paper we present several applications of this technique, which yield improved solutions to a variety of problems. These applications include: (i) an efficient mechanism for performing online point-location queries in an arrangement of arcs; (ii) an efficient algorithm for computing an approximation to the minimum weight Steiner tree of a set of points, where the weight is the number of intersections between the tree edges and a given collection of arcs; (iii) a subquadratic algorithm for cutting a set of pseudo-parabolas into pseudo-segments; (iv) an algorithm for cutting a set of line segments (``rods'') in 3-space to eliminate all cycles in the vertical depth order; and (v) a near-optimal algorithm for reporting all bichromatic intersections between a set R of red arcs and a set B of blue arcs, where the unions of the arcs in each set are both connected.