Showing papers on "Line segment published in 1998"

Feature Extraction and Scene Interpretation for Map-Based Navigation and Map Building

Abstract: A scheme for extracting environment features from 1D range data and their interpretation is presented. Segmentation is done by deciding on a measure of model fidelity which is applied to adjacent groups of measurements. The extraction process is considered to include a subsequent matching step where segments which belong to the same landmark are to be merged while keeping track of those which originate from distinct features. This is done by an agglomerative hierarchical clustering algorithm with a Mahalanobis distance matrix. The method is discussed with straight line segments which are found in a generalized least squares sense using polar coordinates including their first-order covariance estimates. As a consequence, extraction is no longer a real time problem on the level of single range readings, but must be treated on the level of whole scans. Experimental results with three commercially available laser scanners are presented. The implementation on a mobile robot which performs a mapbased localization demonstrate the accuracy and applicability of the method under real time conditions. The collection of line segments and associated covariance matrices obtained from the extraction process contains more information about the scene than is required for map-based localization. In a subsequent reasoning step this information is made explicit. By successive abstraction and consequent propagation of uncertainties, a compact scene model is finally obtained in the form of a weighted symbolic description preserving topology information and reflecting the main characteristics of a local observation.

A unified factorization algorithm for points, line segments and planes with uncertainty models

Abstract: In this paper we present a unified factorization algorithm for recovering structure and motion from image sequences by using point features, line segments and planes. This new formulation is based on directional uncertainty model for features. Points and line segments are both described by the same probabilistic models and so can be recovered in the same way. Prior information on the coplanarity of features is shown to fit naturally into the new factorization formulation and provides additional constraints for the shape recovery. This formulation leads to a weighted least squares motion and shape recovery problem which is solved by an efficient quasi-linear algorithm. The statistical uncertainty model also enables us to recover uncertainty estimates for the reconstructed three dimensional feature locations.

Factorization methods for structure from motion

Abstract: In this article we present an overview of factorization methods for recovering structure and motion from image sequences. We distinguish these methods from general nonlinear algorithms primarily by their bilinear formulation in motion and shape parameters. The bilinear formulation makes possible powerful and efficient solution techniques including singular value decomposition. We show how factorization methods apply under various affine camera models and under the perspective camera model, and then we review factorization methods for various features including points, lines, directional point features and line segments. An extension to these methods enables them to segment and recover motion and shape for multiple independently moving objects. Finally we illustrate the generality of the factorization methods with two applications outside structure from motion.

Converting triangulations to quadrangulations

Abstract: We study the problem of converting triangulated domains to quadrangulations, under a variety of constraints. We obtain a variety of characterizations for when a triangulation (of some structure such as a polygon, set of points, line segments or planar subdivision) admits a quadrangulation without the use of Steiner points, or with a bounded number of Steiner points. We also investigate the effect of demanding that the Steiner points be added in the interior or exterior of a triangulated simple polygon and propose efficient algorithms for accomplishing these tasks. For example, we give a linear-time method that quadrangulates a triangulated simple polygon with the minimum number of outer Steiner points required for that triangulation. We show that this minimum can be at most ⌊ n 3 ⌋ , and that there exist polygons that require this many such Steiner points. We also show that a triangulated simple n-gon may be quadrangulated with at most ⌊ n 4 ⌋ Steiner points inside the polygon and at most one outside. This algorithm also allows us to obtain, in linear time, quadrangulations from general triangulated domains (such as triangulations of polygons with holes, a set of points or line segments) with a bounded number of Steiner points.

Polygonal approximation method and apparatus for use in a contour encoding system

Abstract: An apparatus polygonally approximates a contour of an object expressed in a digital video signal. First of all, the apparatus determines a pair of vertices on the contour. Then, a line segment connecting the pair of vertices is generated and widened to thereby produce a band segment. And, a contour segment corresponding to the line segment is detected and, subsequently, the band segment and the contour segment are matched. The band segment is widened to determine a new vertex located between the pair of vertices on the contour until the contour segment is completely covered by the widened band segment. During the band segment widening process, at least one contour pixel on the contour segment, wherein the detected contour pixels, if there are more than one, are last pixels being covered by the widened band segment, are determined and, among the detected contour pixels, a contour pixel, which is closest to a center of a straight line joining the pair of vertices, is determined as the new vertex. Based on the determined vertices, the apparatus recursively performs the above vertex detection process until all vertices on the contour are determined so that the contour is approximated by using the vertices.

Polygon offsetting using a Voronoi diagram and two stacks

Abstract: The generation of the trimmed offset of a simple polygon is a conceptually simple but important and computationally non-trivial geometric problem for many applications. This article presents a linear time algorithm to compute a trimmed offset of a simple polygon consisting of arcs as well as line segments in a plane. Assuming that a Voronoi diagram of the polygon is available, the algorithm uses two stacks: T-stack and C-stack. The T-stack contains intersections between an offset and Voronoi edges, and the C-stack contains an offset chain which is a part of the trimmed offset. The contents of both stacks are pushed into and popped from the stacks in a synchronized fashion depending on the events that occur during the offsetting process.

Method and apparatus for graphics scaling

Abstract: A method and apparatus for scaling graphics data is begins by retrieving a line segment of graphics data from a frame buffer, or memory, which stores the graphics data in lines. Once the line segment of a current line has been retrieved, a corresponding line segment of another line is retrieved from a line buffer. The two line segments are then blended together to produce blended pixel information. The blended pixel information is then scaled and subsequently stored to produce a resulting graphics output. After the corresponding line segment has been retrieved from the line buffer, it is overwritten with the currently retrieved line segment.

Sliced configuration spaces for curved planar bodies

Abstract: We present the first practical, implemented configuration-space computation algorithm for a curved, planar object translating and rotating amidst stationary obstacles. The bodies are rigid, compact, regular, and bounded by a finite number of rational parametric curve segments. The algorithm represents the three-dimensional configu ration space as two-dimensional slices in which the moving object has a fixed orientation. It discretizes the configuration space into in tervals of equivalent slices separated by critical slices. The output is topologically correct and accurate to within a specified toler ance. We have implemented the algorithm for objects bounded by line segments and circular arcs, which is an important class for applications. The program is simple, fast, and robust. The slice representation is a natural and efficient abstract data type for geo metric computations in robotics and engineering.

A robust Hough transform technique for description of multiple line segments in an image

Abstract: The process of using the Hough transform (HT) to detect lines in an image involves the computation of the HT for the entire image, accumulating votes in an accumulator array and searching the array for peaks which hold information of potential lines present in the input image. The process of peak formation generates a butterfly shaped spread of votes in the accumulator array. The authors have used this property to adaptively define windows of interest around a detected peak to facilitate the description of multiple line segments within an image in terms of the coordinates of their end points. The developed technique has been employed to test several images composed of multiple line segments and the results in terms of accuracy of the determination of line segment mid points are presented. While most methods which employ the HT to detect line segments cannot handle the case of separate line segments formed by a colinear set of points, it is shown that the developed method can successfully do so. This algorithm would find applications in different areas of machine vision like robotics and manufacturing systems. Results of the application of the developed method, to detect lane markers and curve signs from a road scene captured by a CCD camera, to aid in the maneuvering of autonomous vehicles are presented.

Approximation in Line Space — Applications in Robot Kinematics and Surface Reconstruction

Abstract: Combining classical line geometry with techniques from numerical approximation, we develop algorithms for approximation in line space. In particular, linear complexes, linear congruences and reguli are fitted to given sets of lines or line segments. The results are applied to computationally robust detection of special robot configurations and to reconstruction of fundamental surface shapes from scattered points.

Rounding Arrangements Dynamically

Abstract: We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene7 and Hobby,11 it rounds the endpoints and intersections of all line segments to representable points, but in a way that is globally topologically consistent. The algorithm is dynamic because, following Mulmuley,16 it uses a randomized hierarchy of vertical cell decompositions to make locating points, and inserting and deleting line segments, efficient. Our algorithm is novel because it marries the robustness of the Greene and Hobby algorithms with Mulmuley's dynamic algorithm in a way that preserves the desirable properties of each.

Composite halftone screens with stochastically distributed clusters or lines

Abstract: A method and system of designing a digital halftoning screen for forming images on output sheets according to a set of image signals. The method generates a halftone line screen having multiple levels, each level having multiple line segments, each line segment having an equal pre-determined number of elements. The method stochastically assigns threshold values to pixels corresponding to a first element within the multiple line segments of a first level and assigns a same threshold value to a pixel corresponding to a single level to create a first element stochastic fill sequence. The method then assigns threshold values to pixels corresponding to a first element within the multiple line segments of the remaining levels of the halftone line screen according to the first element stochastic fill sequence.

Straight line detecting method

Abstract: A straight-line detecting method for detecting a straight line in an image by using a combinatorial Hough transform at a high speed by restricting a voting area to assure detection of a short line segment without decreasing a processing rate, which method comprises the steps of: determining parameters of Hough transform of a straight line passing a remarkable edge point (x1, y1) and another edge point (x2, y2) in a X-Y plane according to the transform equations θ=-a tan{(x1-x2)/(y1-y2)} and ρ=x1 cos θ+y1 sin θ; voting of pixels corresponding to parameters (θ, ρ); and detecting a straight line existing in the X-Y plane by the number of votes in a plane of ρ-θ parameters and which is characterized in that another edge point (x2, y2) is a point existing in any of specified neighboring areas positioned at right and left and above and below from a center area where the remarkable edge point (x1, y1) is located.

Triangle rendering using adaptive subdivision

Abstract: Based on the error analysis of line segment rendering, we propose a new approach to piecewise linear approximation that proves significantly more efficient than previous solutions and allows the maintenance of any degree of accuracy. The major idea uses triangle subdivision versus scanline subdivision, computing the number of subtriangles based on the ratio of homogeneous coordinates. We show that it is possible to reduce the number of divisions by several orders of magnitude and still maintain high-quality rendering.

Non-volatile ferroelectric memory with section plate line drivers and method for accessing the same

Abstract: A ferroelectric memory device with plate line segments free from the capacitive plate line segment coupling in a read/write operation, and a method of accessing the memory device. The memory device includes a floating protection circuit for protecting unselected plate line segments from being floated during a read/write operations. The floating protection circuit prevents data disturbance due to the capacitive plate line segment coupling. In a data write method of the memory device, a sense amplifier corresponding to a bit line is activated after a voltage corresponding to a data bit to the bit line is applied. In a data read method of the memory device, the sense amplifier is activated and then a column gate corresponding to the bit line is selected.

Fast algorithms for clipping lines and line segments in E 2

Abstract: 2 are presented. The suggested algorithms are based on a technique of coding the line direction together with the end points of the clipped line segment. They solve all cases more effectively. The algorithms are convenient for clippings lines or line segments by rectangle. Theoretical considerations and experimental results are also presented.

Optimal piecewise linear image coding

Abstract: Piecewise linear (PL) image coding proceeds in three steps: 1) a digital image is converted into a 1D-signal using a scanning procedure, for example by scanning lines in a zig- zag or Hilbert order. 2) The signal is approximated by the graph of a piecewise linear function, which consists of a finite number connected line segments. 3) Entropy encoding of the sequence of the segment end points. In this step differential coding can be used for one or both coordinate sequences of the end points. In this step differential coding can be used for one or both coordinate sequences of the end points. To ensure a desired approximation quality a constraint is imposed, e.g., on the root-mean-square error of the PL signal. In this paper we consider uniform approximation. Two problems are addressed: first, an optimal PL approximation in the sense of a minimal number of segments is to be obtained. Second, when entropy coding of the segments is used, how can one jointly optimize the variable length code and the PL approximation yielding a better or even minimal rate without violating the uniform error bound. The first problem is solved by dynamic programing, the second is approached by using Huffman coding and an annealing procedure in which the design of the Huffman tables and the dynamic programming is alternately iterated using a cost function that reflects the codework lengths of the current variable length code. This algorithm is guaranteed to converge to a minimum length code. We describe the algorithms, implementation issues, compare two different scanning procedures, the zig-zag line scan and the Hilbert scan, and report results for encoding various test images.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Kit of elements and a method of using the kit for flashing a roof-penetrating element

Abstract: The kit is made from sheet material for flashing a quadrangular roof-penetrating element, for instance a window ( 4 ), in an inclined roof ( 5 ) with a substantially plane surface, which material comprises a first element ( 1 ) with two through cuts ( 6 ) extending convergingly from the ends of a first line segment (L 1 ) to an edge ( 7 ) of this element ( 1 ), a second element ( 2 a ) with two through cuts ( 11, 12 ), which cuts extend from each end of a second line segment (L 2 ) obliquely to an edge ( 13 ) of the element ( 2 a ) under formation of an acute angle (V 21 ) with the line segment (L 2 ) and obliquely or straight to an edge ( 14 ) of the element ( 2 a ) under formation of an obtuse or straight angle (V 22 ) with the line segment (L 2 ), respectively, an element ( 2 b ) mirror-inverted relative to the second element ( 2 a ), a third element ( 3 ) with two through cuts ( 19 ), which elements extends from each end of a third line segment (L 3 ) extends to each their respective edge ( 20 ) of the element ( 3 ) under formation of an obtuse or straight angle (V 3 ) with the line segment (L 3 ).

Exact region of interest cone beam imaging using 3D backprojection

Abstract: A scanning and data acquisition method and apparatus for three dimensional (3D) computerized tomography (CT) imaging of an object, wherein a plurality of line integral derivatives for a respective plurality of line segments L formed in cone beam projection data acquired on a detector at a plurality of source positions, are calculated. The extent of line segments L in the data acquired at each of the source positions is determined by a mask formed by cone beam projections onto the plane of the detector of portions of the source scan path that are above and below the source position that acquired the cone beam data in which the line integral derivatives for line segments L are being calculated. The line integral derivatives calculated for a plurality of the line segments L are then backprojected onto a 2D space corresponding to the plane of the detector. Finally, the results of the 2D backprojecting step are 3D backprojected into a 3D space, thereby reconstructing a 3D image of the object.

E-mail signature block segmentation

Abstract: A technique for segmenting a loosely constrained text block, such as an e-mail signature block into sub-blocks by performing line segment extraction and connected component analysis on the foreground characters and background characters and recursively repeating connected component analysis on both the foreground and background characters and line segment extraction on the background characters until a text output includes no mixed reading blocks. A technique for correcting over segmentation errors in a line of text from a loosely constrained text block which has undergone geometrical analysis.

Mask plotting data generating method

Abstract: PROBLEM TO BE SOLVED: To prevent mask accuracy from being adversely influenced even when plotting a fine pattern by correction of an optical proximate effect by simplifying a graphic included in data over a range with an allowable dimensional error for the pattern. SOLUTION: A graphic group (a) is simplified. As a result (b) obtained by resolving the graphic group (a) to counterclockwise oriented line segments, the line segments 3, 7, 10, 14, 20, 24, 26, 28 and 30 which are not axially parallel are so short that they are replaced with the axial parallel pattern for simplification. In the case of the line segment 20, an angle formed by the line segments 19 and 21 connected to the line segment 20 is 90°. In such a case, the intersection of the line segments 19 and 20 is set as a new apex. In the case of the line segment 14, two line segments connected to the line segment 14 are in parallel with the X-axis, so that the apex of the coordinates of a start point and an end point (x1, y1) and (x2, y2) is eliminated and the apex of ((x1+x2)/2 y1) and ((x1+x2)/2 y2) is newly added. The same processing is performed to the other diagonal lines (c). COPYRIGHT: (C)2000,JPO

Image processing apparatus and method

Abstract: An image processing apparatus includes an image input unit that receives time-series images, and a candidate area tracking unit that extracts a line segment in a specific direction, sets an obstacle candidate area in a vicinity of the detected line segment, and searches the vicinity of the line segment extracted in each frame, thus tracking the obstacle candidate area with low computational cost. Using the tracking result of tracking a group of three or more candidate areas, a plane assumption verifier determines to which of the preset planes these candidate areas belong. On the basis of the result by the plane assumption verifier, an obstacle detector detects an obstacle and estimates the position of the obstacle.

Embeddings of curves in the plane

Abstract: In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of $C^2$) polynomials whose Newton polygon is either a triangle or a line segment. Our classification has several applications to the study of embeddings of algebraic curves in the plane. In particular, we show that for any $k \ge 2$, there is an irreducible curve with one place at infinity, which has at least $k$ inequivalent embeddings in $C^2$. Also, upon combining our method with a well-known theorem of Zaidenberg and Lin, we show that one can decide "almost" just by inspection whether or not a polynomial fiber is an irreducible simply connected curve.