Showing papers on "Line segment published in 1993"

View variation of point-set and line-segment features

Abstract: The variation, with respect to view, of 2D features defined for projections of 3D point sets and line segments is studied. It is established that general-case view-invariants do not exist for any number of points, given true perspective, weak perspective, or orthographic projection models. Feature variation under the weak perspective approximation is then addressed. Though there are no general-case weak-perspective invariants, there are special-case invariants of practical importance. Those cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation. The variation with respect to view is studied for an important set of 2D line segment features: the relative orientation, size, and position of one line segment with respect to another. The analysis includes an evaluation criterion for feature utility in terms of view-variation. This relationship is a function of both the feature and the particular configuration of 3D line segments. The use of this information in objection recognition is demonstrated for difficult discrimination tasks. >

Range sensing by projecting multiple slits with random cuts

Abstract: A method for range sensing that projects a single pattern of multiple slits is described. Random dots are used to identify each slit. The random dots are given as randomly distributed cuts on each slit. Thus, each slit is divided into many small line segments. Segment matching between the image and the pattern is performed to obtain 3-D data. Using adjacency relations among slit segments, the false matches are reduced, and segment pairs whose adjacent segments correspond with each other are extracted and considered to be correct matches. Then, from the resultant matches, the correspondence is propagated by exploiting the adjacency relationships to get an entire range image. >

Iterated nearest neighbors and finding minimal polytypes

Abstract: We introduce a new method for finding several types of optimalk-point sets, minimizing perimeter, diameter, circumradius, and related measures, by testing sets of theO(k) nearest neighbors to each point. We argue that this is better in a number of ways than previous algorithms, which were based on high-order Voronoi diagrams. Our technique allows us for the first time to maintain minimal sets efficiently as new points are inserted, to generalize our algorithms to higher dimensions, to find minimal convexk-vertex polygons and polytopes, and to improve many previous results. We achieve many of our results via a new algorithm for finding rectilinear nearest neighbors in the plane in timeO(n logn+kn). We also demonstrate a related technique for finding minimum areak-point sets in the plane, based on testing sets of nearest vertical neighbors to each line segment determined by a pair of points. A generalization of this technique also allows us to find minimum volume and boundary measure sets in arbitrary dimensions.

Recovering 3D shape and motion from image streams using nonlinear least squares

Abstract: A shape and motion estimation algorithm based on nonlinear least squares applied to the tracks of features through time is presented. While the authors' approach requires iteration, it quickly converges to the desired solution, even in the absence of a priori knowledge about the shape or motion. Important features of the algorithm include its ability to handle partial point tracks and true perspective, its ability to use line segment matches and point matches simultaneously, and its use of an object-centered representation for faster and more accurate structure and motion recovery. >

Stereo matching, reconstruction and refinement of 3D curves using deformable contours

Abstract: The authors propose to replace a set of connected 3-D points or line segments with a 3-D formable curve, using weighted least-squares approximation. The parameters of the 3-D energy-minimizing curve are updated so that its 2-D projections on two or three stereoscopic images converge toward the corresponding image edges. Thus, a more realistic representation of the real non-polygonal world is obtained. The case where no initial 3-D information is provided is also considered. A novel approach is proposed to match a given 2-D curve in the first image to its corresponding position in the second image. The curve is tracked between the two images by a deformable curve constrained by a 2-D motion model. The position of the 2-D curve in the second image is then refined by relaxing the motion constraint. As a result, the correspondences between the curves of both images are known. An initial estimate of the 3-D curve can be recovered using the calibration parameters of the stereoscopic system. These approaches are illustrated by experimental results. >

Robust and efficient detection of convex groups

Abstract: An algorithm is presented that finds all convex sets of line segments in an image, such that the length of the line segments account for at least some fixed proportion of the length of the convex hull. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. An expected time analysis of the algorithm's performance is performed, together with experiments on real images that show that the algorithm is efficient and that tell when the groups found are unlikely to occur at random, and are likely to capture the underlying structure of a scene. >

Matching perspective views of coplanar structures using projective unwarping and similarity matching

Abstract: The problem of matching perspective views of coplanar structures composed of line segments is considered. Both model-to-image and image-to-image correspondence matching are given a consistent treatment. These matching scenarios generally require discovery of an eight-parameter projective mapping. When the horizon line of the object plane can be found in the image, which is accomplished in this case by using vanishing point analysis, these problems reduce to a simpler six-parameter affine matching problem. When the intrinsic lens parameters of the camera are known, the problem further reduces to four-parameter affine similarity matching. >

System and method of hybrid forward differencing to render bézier splines.

Abstract: A high speed and memory efficient system and method for rendering Bezier curves. The system utilizes a hybrid forward differencing function representing the Bezier curve defined by the Bezier control points and renders the curve with a small number of straight line segments. The system renders the curve in a manner that results in the same Bezier control points that are calculated using the prior art recursive subdivision techniques and rejects line segment approximations that would not be derived from recursive subdivision. The system can start at either end of a Bezier curve and will render the same approximation. The method is readily implemented on a computer and is applicable to Bezier curves of any order.

Significant line segments for an indoor mobile robot

Abstract: New algorithms for detecting and interpreting linear features of a real scene as imaged by a single camera on a mobile robot are described. The low-level processing stages are specifically designed to increase the usefulness and the quality of the extracted features for indoor scene understanding. In order to derive 3-D information from a 2-D image, we consider only lines with particular orientation in 3-D. The detection and interpretation processes provide a 3-D orientation hypothesis for each 2-D segment. This in turn is used to estimate the robot's orientation and relative position in the environment. Next, the orientation data is 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, a strong emphasis is placed on real-world applications and very fast processing with conventional hardware. Results of experimentation with a mobile robot under realistic conditions are given and discussed. >

Computing a face in an arrangement of line segments and related problems

Abstract: This paper presents a randomized incremental algorithm for computing a single face in an arrangement of n line segments in the plane that is fairly simple to implement. The expected running time of the algorithm is $O(n\alpha (n)\log n)$. The analysis of the algorithm uses a novel approach that generalizes and extends the Clarkson–Shor analysis technique [in Discrete Comput. Geom., 4 (1989), pp. 387–421]. A few extensions of the technique, obtaining efficient randomized incremental algorithms for constructing the entire arrangement of a collection of line segments and for computing a single face in an arrangement of Jordan arcs are also presented.

Calculation of the focusators into a longitudinal line-segment and study of a focal area

Abstract: Using an iterative method modernized with the adaptive subadjustment, we calculated phase functions of the focusators into a longitudinal axial line-segment, which is characterized by the constant light intensity along the line. Numerical studies were performed of a focal area: a character of variations of both the transverse diameter and the focusing efficiency along a line are reported.

A metric for line segments

Abstract: This correspondence presents a metric for describing line segments. This metric measures how well two line segments can be replaced by a single longer one. This depends for example on collinearity and nearness of the line segments. The metric is constructed using a new technique using so-called neighborhood functions. The behavior of the metric depends on the neighborhood function chosen. In this correspondence, an appropriate choice for the case of line segments is presented. The quality of the metric is verified by using it in a simple clustering algorithm that groups line segments found by an edge detection algorithm in an image. The fact that the clustering algorithm can detect long linear structures in an image shows that the metric is a good measure for the groupability of line segments. >

Structural description of line images by the cross section sequence graph

Abstract: In this paper, we propose the Cross Section Sequence Graph which describes line images in a simple and well structured form. It is composed of regular regions called cross section sequences and singular regions. A cross section sequence is a sequence of cross sections, each of which is constructed as a pair of boundary points almost perpendicular to the direction of the line. The sequence corresponds to a straight or curved line segment. The remaining regions are extracted as singular regions, each of which corresponds to an end point region, corner, branch, cross, and so on. The cross section sequence graph is useful for many kinds of feature extraction, especially for skeletonization since a singular region can be analyzed from adjacent regular regions. Experimental results show that the skeleton extracted from the cross section sequence graph is better than that of a pixel-wise skeletonization (thinning) in terms of both processing speed and the quality of the skeleton.

Vanishing Point Detection

Abstract: Commencing with a review of methods for vanishing point (VP) detection, a new approach is suggested. The proposed approach estimates the location of candidate vanishing points and provides probability measures which reflect the likelihood of those points being the VPs. This new approach allows VPs to be identified in less structured environments compared with its conventional counterparts.

Print control apparatus

Abstract: A print control apparatus for use with a printer for forming a print output based on command data generated by a computer. The print control apparatus includes a line segment data conversion unit for converting computer-generated command data to successive pieces of line segment data each having a position and a length in a raster direction, and a raster image data conversion unit for converting the line segment data to raster image data based on which printing is performed by the printer.

Active and intelligent sensing of road obstacles: Application to the European Eureka-PROMETHEUS project

Abstract: The authors address the problem of road obstacle detection. A sensor composed of an eyesafe laser range finder coupled with a charge coupled device (CCD) camera is proposed. This sensor is mounted in front of a vehicle. The basic idea is to first determine 2-D visual targets in intensity images of the camera. The range finder is then used not only to confirm or reject the real existence of the detected visual targets but also to acquire 3-D information of the confirmed visual targets. The central problem of this strategy is the method of detection of 2-D visual targets from intensity images of a road scene. In the method, line segments are considered as significant features. The concept of a line segment of interest and the concept of a dominant line segment are used. Two-imensional visual targets can be effectively determined with the help of the identification of the dominant line segments in an image. The range finder was used to confirm or reject a 2-D visual target. >

The complexity of detecting crossingfree configurations in the plane

Abstract: The computational complexity of the following type of problem is studied. Given a geometric graphG=(P, S) whereP is a set of points in the Euclidean plane andS a set of straight (closed) line segments between pairs of points inP, we want to know whetherG possesses a crossingfree subgraph of a special type. We analyze the problem of detecting crossingfree spanning trees, one factors and two factors in the plane. We also consider special restrictions on the slopes and on the lengths of the edges in the subgraphs.

System and method for rendering bezier splines

Abstract: A high speed and memory efficient system and method for rendering Bezier curves. The system utilizes a hybrid forward differencing function representing the Bezier curve defined by the Bezier control points and renders the curve with a small number of straight line segments. The system renders the curve in a manner that results in the same Bezier control points that are calculated using the prior art recursive subdivision techniques and rejects line segment approximations that would not be derived from recursive subdivision. The system can start at either end of a Bezier curve and will render the same approximation. The method is readily implemented on a computer and is applicable to Bezier curves of any order.

Geometric Pattern Matching Under Euclidean Motion.

Abstract: Given two planar sets A and B, we examine the problem of determining the smallest ϵ such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance ϵ of some member of B. We establish upper bounds on the combinatorial complexity of this subproblem in model-based computer vision, when the sets A and B contain points, line segments, or (filled-in) polygons. We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion.

Constructing the Voronoi diagram of a set of line segments in parallel

Abstract: In this paper we give a parallel algorithm for constructing the Voronoi diagram of a polygonal scene, i.e., a set of line segments in the plane such that no two segments intersect except possibly at their endpoints. Our algorithm runs inO(log2n) time usingO(n) processors in the CREW PRAM model.

Hologram information forming method

Abstract: A hologram surface to express a phase distribution, a visual field in which a solid image can be seen; and a stereoscopic display limit are set in a virtual space. A target to be stereoscopically displayed is subsequently expressed in the virtual space by a set of micro polygons. A plurality of slice planes which are parallel with the horizontal plane are set into the virtual space including the target. The line segments which intersect the polygons are obtained for every slice plane. The detected line segment is divided or clipped as necessary and is finally divided into the portion which can be always seen from the whole region of the visual field and a portion which is obstructed by another line segment and can be seen from only a part of the visual field, thereby extracting the line segment. In the calculation of a phase distribution, sampling points are set onto the extracted line segment, a 1-dimensional hologram phase distribution on the hologram surface is calculated for every sampling point, and the calculated 1-dimensional hologram phase distributions are added to every slice plane.

Weaving patterns of lines and line segments in space

Abstract: Aweaving W is a simple arrangement of lines (or line segments) in the plane together with a binary relation specifying which line is “above” the other. A system of lines (or line segments) in 3-space is called arealization ofW, if its projection into the plane isW and the “above-below” relations between the lines respect the specifications. Two weavings are equivalent if the underlying arrangements of lines are combinatorially equivalent and the “above-below” relations are the same. An equivalence class of weavings is said to be aweaving pattern. A weaving pattern isrealizable if at least one element of the equivalence class has a three-dimensional realization. A weaving (pattern)W is calledperfect if, along each line (line segment) ofW, the lines intersecting it are alternately “above” and “below.” We prove that (i) a perfect weaving pattern ofn lines is realizable if and only ifn ≤ 3, (ii) a perfect m byn weaving pattern of line segments (in a grid-like fashion) is realizable if and only if min(m, n) ≤ 3, (iii) ifn is sufficiently large, then almost all weaving patterns ofn lines are nonrealizable.

Robust polygon modelling

Abstract: The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance s of the original line segment. If the curve is implicit, s is bounded by a small multiple of the rounding unit. If the curves are explicit, the bound on s may grow with the number of curves. One can mix implicit and explicit representations to suit the application.

Generalized Zone Plates Focusing Light into Arbitrary Line Segments

Abstract: A new computer-generated generalized zone plate is proposed, which is able to concentrate the incident beam into a line segment of various length and arbitrary inclination to the optical axis, as well as unrestricted distribution of the longitudinal intensity. The approach is based on the energy conservation principle and equations of the paraxial ray tracing, both considered in the cartesian coordinate system. Hyberbolic, elliptic, linear, and conical zone plates are shown to be limiting cases of the proposed element. Other specific cases, e.g. a new element focusing into a segment of the optical axis, are also derived.

Compact hardware realization for Hough based extraction of line segments in image sequences for vehicle guidance

Abstract: Important key symbols used in many image processing applications are straight line segments of edges and contours. The real-time determination of straight line symbols in video sequences requires high computational rates which call for application-specific integrated circuits (ASICs). For a vision-based vehicle guidance system a compact image processing unit has been developed which extracts straight lines as symbols for the street boundaries. This unit consists of two specially designed ASICs for the segmentation of symbols and a general programmable microcontroller for high-level processing. The implemented pipeline of the algorithm comprises gradient operation, edge thinning line verification, and Hough transformation. Although the image processing unit was originally developed for vehicle guidance the hardware can be used for other industrial and robotic applications as well. >