Showing papers on "Line segment published in 1987"

Efficient registration of stereo images by matching graph descriptions of edge segments

Abstract: We present a new approach to the stereo-matching problem. Images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours. The matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images, and is performed by an efficient prediction and propagation technique. This approach was tested on a variety of man-made environments, and it appears to be fast and robust enough for mobile robot navigation and three-dimensional part-positioning applications.

On some distance problems in fixed orientations

Abstract: In VLSI design, technology requirements often dictate the use of only two orthogonal orientations, determining both the shape of objects and the distance function, the $L_1 $-metric, to be used for wiring objects. More recent VLSI fabrication technology is capable of creating edges and wires in both the orthogonal and diagonal orientations.We generalize the distance concept to the case where any fixed set of orientations is allowed, and introduce a family of naturally induced metrics, and the subsequent generalization of geometrical concepts. A shortest connection between two points is in this case a path composed of line segments with only the given orientations. We derive optimal solutions for various basic planar distance problems in this setting, such as the computation of a Voronoi diagram, a minimum spanning tree, and the (minimum and maximum) distance between two convex polygons. Many other theoretically interesting and practically relevant problems remain to be solved. In particular, the new famil...

Routing method for use in wiring design

Abstract: A routing method for wiring design including a determining step for identifying, in one of the wiring sections where no wiring path is determined as yet, the direction of the line segment which is prohibited by an obstacle and accordingly determining a wiring path. The routing method also includes a generating step for generating, on a layer opposite to the layer on which one unprocessed line segment is present and in a position having the same plane coordinates as the line segment, an obstacle which prohibits only such line segments as are parallel in direction to the line segment, on the wiring path determined by the determining step.

An efficient new algorithm for 2-D line clipping: Its development and analysis

Abstract: This paper describes a new alorithm for clipping a line in two dimensions against a rectangular window. This algorithm avoids computation of intersection points which are not endpoints of the output line segment. The performance of this algorithm is shown to be consistently better than existing algorithms, including the Cohen-Sutherland and Liang-Barsky algorithms. This performance comparison is machine-independent, based on an analysis of the number of arithmetic operations and comparisons required by the different algorithms. We first present the algorithm using procedures which perform geometric transformations to exploit symmetry properties and then show how program transformation techniques may be used to eliminate the extra statements involved in performing geometric transformations.

Apparatus for recognition of drawn shapes or view types for automatic drawing input in CAD system

Abstract: An apparatus for recognition of shapes in drawings for automatic drawing input in a CAD system including a centerline extraction unit for extracting centerlines drawn in center positions of shapes from the line segments discriminated by a line segment discrimination unit, a symmetry determination unit for determining symmetry of shapes based on intersections between the extracted centerlines and straight lines between end points of contour lines, distances between the endpoints of contour lines and the intersections, angles between the centerlines and the straight lines between endpoints of contour lines, and a shape recognition unit for recognizing, using the result of determination of the symmetry determination unit, a shape, a length of line segment, and a position of line segment not indicated by deriving the shape, the length of line segment, and the position of line segment from a shape, a length of line segment, and a position of line segment indicated, and characters recognized by a character recognition unit. In connection with this shape recognition apparatus, an apparatus is provided for recognition of views in drawings for automatic drawing input. Also, shape recognition apparatuses are provided for setting dimensional values known in other views or derived dimension values calculated on the basis of known dimensional values to contour lines, and for adding line segments by producing a line segment based on a matching check.

A new efficient motion-planning algorithm for a rod in two-dimensional polygonal space

Abstract: We present here a new and efficient algorithm for planning collision-free motion of a line segment (a rod or a “ladder”) in two-dimensional space amidst polygonal obstacles. The algorithm uses a different approach than those used in previous motion-planning techniques, namely, it calculates the boundary of the (three-dimensional) space of free positions of the ladder, and then uses this boundary for determining the existence of required motions, and plans such motions whenever possible. The algorithm runs in timeO(K logn) =O(n 2 logn) wheren is the number of obstacle corners and whereK is the total number of pairs of obstacle walls or corners of distance less than or equal to the length of the ladder. The algorithm has thus the same complexity as the best previously known algorithm of Leven and Sharir [5], but if the obstacles are not too cluttered together it will run much more efficiently. The algorithm also serves as an initial demonstration of the viability of the technique it uses, which we expect to be useful in obtaining efficient motion-planning algorithms for other more complex robot systems.

Algorithms for line transversals in space

Abstract: Algorithms are developed for determining if a set of polyhedral objects in R3 can be intersected by a common transversal (stabbing) line. It can be determined in O(n) time if a set of n lines in space has a line transversal, and such a transversal can be found in the same time bound. For a set of n line segments, the complexity of finding such a transversal becomes O(nlogn). Finally, for a set of polyhedra with a total of n vertices, we give a O(n5) algorithm for determining the existence of, and computing, a line transversal. Helly-type theorems for lines and segments are also given. In particular, it is shown that if every six of a set of lines in space are intersected by a common transversal, then the entire set has a common transversal.

Computing simple circuits from a set of line segments is NP-complete

Abstract: Given a collection of line segments in the plane we would like to connect the segments by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon). However, there are collections of line segments where this cannot be done. In this note it is proved that deciding whether a set of line segments admits a simple circuit is NP-complete. Deciding whether a set of horizontal line segments can be connected with horizontal and vertical line segments to construct an orthogonal simple circuit is also shown to be NP-complete.

Line detection in digital pictures: a hypothesis prediction/verification pardigm

Abstract: We present an efficient method for detecting straight line segments in digital pictures using a hypothesis prediction/verification paradigm. In this paradigm, a straight line segment of predefined length is predicted to exist at some particular pixel location. The orientation of this predicted line segment is based on the edge orientation at the pixel location. This prediction is then verified against statistical tests performed on the line. As a result, the predicted line is either validated as being a line segment, or it is rejected. An extension of this algorithm for the detection of lines at different lengths is also presented, and a criterion is defined in order to evaluate the significance of the detected line segments.

Method of recognizing linear pattern

Abstract: A method of recognizing linear pattern contained in the video data stored in an original video memory. A memory region of the original video memory is divided into a plurality of regions, projective waveforms at a plurality of different projection angles are found out for each of the regions from the video data of the divisions, the projection waveforms are analyzed to determine the presence or absence of any linear pattern, direction () of line, line width (W) and line length (L) in each of the divisions, and a line segment corresponding to the linear pattern is picked up for each of the divisions based upon the results of determination.

Visual estimation of 3-D line segments from motion: a mobile robot vision system

Abstract: An efficient technique is presented for detecting, tracking and locating three-dimensional (3-D) line segments. The utility of this technique has been demonstrated by the SRI mobile robot, which uses it to locate features in an office environment in real time (one Hz frame rate). A formulation of Structure-from-Motion using line segments is described. The formulation uses longitudinal as well as transverse information about the endpoints of image line segments. Although two images suffice to form an estimate of a world line segment, more images are used here to obtain a better estimate. The system operates in a sequential fashion, using prediction-based feature detection to eliminate the need for global image processing.

Method for producing planar geometric projection images

Abstract: The lines representing each edge of each face of each object of a model for producing a multiple object image are segmented at line of sight intersections with other lines representing contour edges of visible faces. Each resulting edge line segment is checked against all visible faces to determine which are visible and which are invisible, and information on visibility is stored together with detailed information on each edge line segment for each object. The model is modified by changing the number of component objects and after each change checking the edge line segments for visibility only with respect to the changes associated with the changed component objects. This results in a substantial reduction in the required number of comparisons between segments and faces as compared to prior methods.

The Triangle: a Multiprocessor Architecture for Fast Curve and Surface Generation.

Abstract: : This paper describes the architecture and operation of the Triangle, a pipelined, parallel multiprocessor architecture for the computation and rendering of line segments, conic sections, spline curves, triangular patch surfaces, and tensor product surfaces. Based on a generalization of de Casteljau's algorithm for computing points on Bezier curves, the Triangle can be used as an accelerator to dramatically enhance the performance of standard graphics workstations. Although there is a wide spectrum of possible implementations, we estimate that a custom VLSI implementation that is currently being designed will be capable of peak rates well in excess of one million points of evaluation per second. Assuming a Motorola 68020 host, such a processor should be capable of completely recomputing 65 bicubic patches in real-time, at a density of 1,000 points per patch. Keywords: B-splines; Computer-aided geometric design; Curves and surfaces; Graphics hardware. (KR)

Locating polyhedral objects from edge point data

Abstract: A method is presented to locate a general polyhedron in space with six degrees of freedom. A light stripe sensor is assumed to be capable of providing three-dimensional data points on known edges of the polyhedron to within a known accuracy. A representation is found for all the ways three line segments of fixed length can fall between the edges of a polyhedron. This representation, called an edge interval, is used in a tree search to find the location of each data point to within an interval on the edge. The final location of the object is determined by a one-dimensional line search. The method is illustrated with simulated data from a unit tetrahedron and results from a computer implementation are presented. The tree search takes a negligible amount of time and the one-dimensional line search takes a small additional increment.

Dipmeter processing technique

Abstract: A process for processing a dipmeter curve is shown in the preferred embodiment. In a curve, line segments are drawn between curve minima, a second set of line segments are drawn between minima in the first segments, and this is repeated to desired number of levels. When finished, line segments are numbered and become a branched tree. This tree is reorganized to form an event tree which is easily converted into a stored digital value and is processed for correlation with other curves.

Lumber cutting system

Abstract: A system for maximizing the board width fitting to a flitch wherein grade lumber rules permit a designated percentage of wane area. The side edges of the minor face of the flitch are assumed to be straight edge line segments. Each line edge segment is established at designated vertical distances. The beginning and end of each line edge segment is thus determined and the relative longitudinal and lateral positions as between the beginning and end of each line segment determines a rectangular area that is assumed to be half surface area and half wane area. The side edge of a board is then computed to include the allowable wane area. Boards may also be force fit from visual examination by designation of the board width that will separate the flawed portion from the non flawed portion.

Technical note It doesn't make me nearly as CROSS Some advantages of the point-vector representation of line segments in automated cartography

Abstract: The point-vector representation for line segments offers several advantages over other more familiar representations for lines and line segments, such as the point-slope form, the slope-intercept form and the two-point form. With the point-vector form, line segment intersection routines and related cartographic computations, such as point-in-polygon routines and detection of near-intersections, can be streamlined, simplified and more easily understood geometrically. The point-vector segment representation retains information on the line segment and not just the line. Special case handling for vertical lines is not necessary as with some other representations and several computational short cuts can be derived directly from the segment end-point coordinates.

Shape Matching Of Two-Dimensional Occluded Objects

Abstract: Recognition of partially occluded object is a desirable function in a computer vision system, especially one employed in an industrial automation environment. In this controlled environment, the objects to be recognized can be constrained to a relatively flat region (plane of image), and thus be easily modelled by polygons. This paper studies issues in such a computer vision system and presents algorithms for the various processes involved in occluded polygon matching and recognition. The recognition process is carried out by model matching. The scene may contain unknown model objects which may overlap or touch each other, giving rise to partial occlusion. Both the model and the scene objects are represented by their polygon approximations. Features used for matching are extracted from line segments connecting all possible pairs of vertices in the polygon. They are: vertex types at two ends of line segment, angles of these vertices, line type, and line length. A polygon clipping algorithm based on geometrical properties is used to determine the types of line segments. We also develop a context-free grammar for recognizing line types. To speed up the recognition process, only priority features are used in the initial matching. The priority features are identified after some analysis of the geometrical properties of polygons with occlusion. A consistency check also reduces the pool of candidates for matching. The matching algorithm superposes the model object on the scene along line segments in sequence and checks the dissimilarity between the region enclosed by the scene polygon and the region enclosed by the model polygon appearing in the scene. A dissimilarity measure based on the phenomenon of light illumination and the theory of fuzzy subset has been designed to measure the edge consistency between the scene and candidate model to select the best possible fit.

Drawing recognizing device

Abstract: PURPOSE: To detect a line cut part and to connect it by obtaining the candidate of the line cut part on a shape line beforehand, discriminating it from a line segment with characteristics for the shape line, and performing a labeling and a propagation processing. CONSTITUTION: Two opening end points to approximate in a prescribed distance are detected, a linear element to be connected to them is registered as the shape line cut candidate, and a shape line cut candidate label is added. Next, the linear element obviously different from the shape line is extracted, and a non-shape line label is added. Next, the processing to propagate the non-shape line label for the linear element to which the label is not added is performed, thereafter, the processing to propagate the shape line cut candidate label for the linear element, to which the label is not added, is performed. Further, based on the characteristics on the lines which the shape line and the non-shape line, the shape line is extracted. Finally, trailing is started from the linear element which is obviously not the shape line, and the linear element to constitute the respective types of symbols is extracted, and the symbol composed of the series of the linear elements which have been extracted is recognized. COPYRIGHT: (C)1989,JPO&Japio

Closed graphic identifier

Abstract: PURPOSE:To eliminate the disagreement between a graphic and loop information and to speed up processing by applying thinned and broken lines to an image so as to make graphic information into a table and detecting the loop by a retrieval operation on the table. CONSTITUTION:An open arc reducing mechanism P1 reads and checks information on the end points of a line segment as for each arc in an arc table M2 out of a broken line data memory. If it is zero, the mechanism P1 sets a disuse flag to the line segment. A vector retrieval mechanism P2 selects a nonopen arc in the table M2, and sets its segment line number to a register R1. An angle difference computing mechanism P3 calculates the angle difference between the vector with a number previously set and the vector with a number currently set, and stores the sum of this angle difference and the old one. A directional flag is added to the line segment to be processed. The mechanism P2 retrieves the line segment clockwise. If the total sum of the angle differences comes to 2pi or returns to the initial state, a loop is closed. At that time a loop data generating mechanism P4 adds an ID to the loop, and registers its line segment group in a loop data memory.

The complexity of computing simple circuits in the plane

Abstract: As far back as Euclid's ruler and compass constructions, computation and geometry have been domains for the exploration and development of fundamental mathematical concepts and ideas. The invention of computers has spurred new research in computation, and now with a variety of applications couched in the fundamentals of Euclidean geometry, the study of geometric algorithms has again become a popular mathematical pursuit. In this thesis, the computational aspects of a fundamental problem in Euclidean geometry is examined. Given a set of line segments in the Euclidean plane, one is asked to connect all the segments to form a simple closed circuit. It is shown that for some sets of line segments it is impossible to perform this task. The problem of deciding whether a set of line segments admits a simple circuit is proved to be NP-complete. A restriction of the class of permissible input allows a polynomial time solution to the simple circuit decision problem. It is also shown that a polynomial solution can be realized by restricting the class of simple circuit in the output. All the polynomial time decision algorithms exhibited deliver a simple circuit if one exists. Furthermore, in all cases the simple circuit obtained can be optimized with respect to area or perimeter.

Free Positioned And Oriented Focal Lines From Computer-Generated Holograms

Abstract: Focal lines of arbitrary position and orientation even parallel to the optical axis may be used in a variety of situations, such as display of 3-D images, contouring of inclined surfaces and holographic optical elements. A synthetic generation using a computer is promising because of the flexibility. Then, the wave propagation has to be simulated. We present a calculation by use of the stationary phase method and show the analogy to the solution of the wave equation. A cube composed of line segments is recorded in a hologram and reconstructed optically. For each line segment, a second line foci occurs in the Fourier plane of the hologram which causes irritation when the image is visually observed. Superposition of a slight random phase variation removes the ambiguity and allows secure accomodation. Intensity variations along the line segment can be introduced by superposition of several distributions which reconstruct the same line segment. A further generalization may be achieved to reconstruct nonstraight focal lines in 3-D.

A Model-Based System For Object Recognition In Aerial Scenes

Abstract: Preliminary results of a system that uses model descriptions of objects to predict and match features derived from aerial images are presented. The system is organized into several phases: 1) processing of image scenes to obtain image primitives, 2) goal-oriented sorting of primitives into classes of related features, 3) prediction of the location of object model features in the image, and 4) matching image features to the model predicted features. The matching approach is centered upon a compatibility figure of merit between a set of image features and model features chosen to direct the search. The search process utilizes an iterative hypothesis generation and verication cycle. A "search matrix" is con-structed from image features and model features according to a first approximation of compatibility based upon orientation. Currently, linear features are used as primitives. Input to the matching algorithm is in the form of line segments extracted from an image scene via edge operatiors and a Hough transform technique for grouping. Additional processing is utilized to derive closed boundaries and complete edge descriptions. Line segments are then sorted into specific classes such that, on a higher level, a priori knowledge about a particular scene can be used to control the priority of line segments in the search process. Additional knowledge about the object model under consideration is utilized to construct the search matrix with the classes of line segments most likely containing the model description. It is shown that these techniques result in a, reduction in the size of the object recognition search space and hence in the time to locate the object in the image. The current system is implemented on a Symbolics LispTM machine. While experimentation continues, we have rewritten and tested the search process and several image processing functions for parallel implementation on a Connection Machine TM computer. It is shown that several orders of magnitude faster processing rates are achieved, as well as the possibility of entirely new processing schemes which take advantage of the unique Connection Machine architecture.

Extraction system for bending point of hand-written picture input device

Abstract: PURPOSE:To precisely detect a bending point by extracting a typical point, removing a display point including noise and detecting a partial curve based on a change in an angle between typical points. CONSTITUTION:A display point extraction part 12 extracts a few display point strings practically following the drawn line of a hand-written picture from an inputting coordinate string followed by the input of the hand-written picture. A typical point extraction part 14 extracts a typical point through the use of a recursive typical point extraction system with respect to the display point string. First two end points of the picture are defined as typical points, then a display point farthest from a line segment connecting two end points among display points lying between the first two end points is selected, and a changing angle between two line segments connecting the display point and two end points is investigated. If the valve exceeds the prescribed threshold (1st threshold S1), the display point is extracted as a typical point. A critical point extraction part 16 sequentially connects the typical points by line segments. If the changing angle between adjacent line segments exceeds the prescribed threshold (2nd threshold S2), its in-between typical point is extracted as a critical point.