Showing papers on "Line segment published in 1989"
14 May 1989
TL;DR: The author describes a system for dynamically maintaining a description of the limits to free space for a mobile robot using a belt of ultrasonic range sensors and a Kalman filter update equation is developed to permit the correspondence of a line segment to the model to be applied as a correction to estimated position.
Abstract: The author describes a system for dynamically maintaining a description of the limits to free space for a mobile robot using a belt of ultrasonic range sensors. A model is presented for the uncertainty inherent in such sensors, and the projection of range measurements into external Cartesian coordinates is described. Line segments are then expressed by a set of parameters represented by an estimate and a precision. A process is presented for extracting line segments from adjacent collinear range measurements, and a fast algorithm is presented for matching these line segments to a model of the limits to free space of the robot. A side effect of matching observations to a local model is a correction to the estimated position of the robot at the time that the observation was made. A Kalman filter update equation is developed to permit the correspondence of a line segment to the model to be applied as a correction to estimated position. Examples of segment extraction, position correction and modeling are presented using real ultrasonic data. >
532 citations
TL;DR: It is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3D objects because few admissible hypotheses are retained from the interpolation of the three line segments.
Abstract: A method for finding analytical solutions to the problem of determining the attitude of a 3D object in space from a single perspective image is presented. Its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model, and on the search for the model attitude consistent with these projections. The geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight-degree equation in the general case. Using simple logical rules, it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3D objects because few admissible hypotheses are retained from the interpolation of the three line segments. Line matching by the prediction-verification procedure is thus less complex. >
493 citations
30 Oct 1989
TL;DR: For the first time it is shown how to reduce the cost of performing specific geometric constructions by using rounded arithmetic instead of exact arithmetic by exploiting a property of floating-point arithmetic called monotonicity.
Abstract: For the first time it is shown how to reduce the cost of performing specific geometric constructions by using rounded arithmetic instead of exact arithmetic. By exploiting a property of floating-point arithmetic called monotonicity, a technique called double-precision geometry can replace exact arithmetic with rounded arithmetic in any efficient algorithm for computing the set of intersections of a set of lines or line segments. The technique reduces the complexity of any such line or segment arrangement algorithm by a constant factor. In addition, double-precision geometry reduces by a factor of N the complexity of rendering segment arrangements on a 2/sup N/*2/sup N/ integer grid such that output segments have grid points as endpoints. >
61 citations
TL;DR: A modified Hough Transformation which performs contiguity check in a simple and efficient way is proposed and the area-time complexity of the proposed architecture is shown to be superior to the conventional sequential algorithm.
51 citations
TL;DR: Two experiments were conducted which tested the effect of two different types of cues on the allocation of attention in the visual field and the results are consistent with a simple spotlight theory in which spatial attention involves selecting a particular restricted area of theVisual field for which the perceptual efficiency is enhanced.
50 citations
Patent•
27 Nov 1989TL;DR: In this article, a graphics accelerator interface apparatus for receiving information to be displayed by a computer and the address of such information is presented. But it does not specify how to display such information.
Abstract: A graphics accelerator interface apparatus for receiving information to be displayed by a computer and the address of such information. Storing the addresses of vertices of a quadrilateral to be displayed by a computer, translating the addresses of vertices of a quadrilateral into signals representing the relations between each of such vertices and the others of the vertices, selectively decomposing a quadrilateral into line segment portions defining trapezoids which bound sets of scan lines, determining the coordinates of the end points of each scan line within such trapezoids, translating the coordinates of the end points into linear values for display, and storing such information for display on a computer output display.
49 citations
TL;DR: It is shown that any configuration consisting of a setV ofn points in general position in the plane and a set of 6n − 5 closed straight line segments whose endpoints lie inV, contains three pairwise disjoint line segments.
Abstract: Answering an old question in combinatorial geometry, we show that any configuration consisting of a setV ofn points in general position in the plane and a set of 6n ? 5 closed straight line segments whose endpoints lie inV, contains three pairwise disjoint line segments.
44 citations
Patent•
14 Jun 1989TL;DR: In this paper, the authors present a mapping circuit of a CRT display device in accordance with the present invention, where vertex calculating means (2 and 3) evaluates corresponding relations between vertexes of a three-dimensional polygon and vertices of a two-dimensional polygone, and inclination calculating means calculates inclination of the line segments connecting the respective vertexes connecting the vertexes and inclinations of the lines connecting the vertices connecting the 2D and 3D polygones.
Abstract: In a mapping circuit of a CRT display device in accordance with the present invention, vertex calculating means (2 and 3) evaluates corresponding relations between vertexes of a three-dimensional polygon and vertexes of a two-dimensional polygon and inclination calculating means (4 and 5) calculates inclination of the line segments connecting the respective vertexes of the three-dimensional polygon and inclinations of the line segments connecting the vertexes of the two-dimensional polygon. Vertexes interpolating means (6 and 7) performs interpolation between the respective vertexes of the three-dimensional polygon and also performs interpolation between the respective vertexes of the two-dimensional polygon. Then, using the interpolated points as start points or end points, start and end points interpolating means (9, 10, 11 and 12) performs interpolation between the respective start points and end points. A picture pattern on the coordinates of each interpolated point is read out by a pixel array memory control portion (14) and using the coordinates of each interpolated point as an address, the picture pattern is written in a frame memory (17), so that the picture pattern is displayed on a CRT display (18). Consequently, a host computer does not need to perform coordinate transformation in pixel units.
41 citations
04 Jun 1989
TL;DR: An efficient method for finding straight lines in edge maps is described, based on a pyramid structure, which has an attractive architecture which is suitable for parallel implementation.
Abstract: An efficient method for finding straight lines in edge maps is described. The algorithm is based on a pyramid structure. At the bottom level of the pyramid, short line segments are detected by applying a Hough transform to small subimages. The algorithm proceeds, bottom up, from this low-level description by grouping line segments within the local neighborhoods into longer lines. Line segments which have local support propagate up the hierarchy and take part in grouping at higher levels. The length of a line determines approximately the level in the pyramid to which it propagates, and a hierarchical description of the line segments in a scene is obtained. The line-segment-grouping process is also based on a Hough transform. The method is quite efficient and has an attractive architecture which is suitable for parallel implementation. >
39 citations
Journal Article•
38 citations
TL;DR: It is proved that deciding whether a set of line segments admits a simple circuit is NP-complete, and the NP-completeness proof relies on the fact that line segments may intersect at their endpoints.
Abstract: Given a collection of line segments in the plane, the segments are connected 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. The NP-completeness proof relies on the fact that line segments may intersect at their endpoints. 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.
TL;DR: In this paper, the authors considered the one-dimensional case of estimating the length of a line segment by counting the number of points that happen to fall within the segment and showed that if the points are equidistantly located, the variance of the estimate is a strictly periodic function of the length.
Abstract: SUMMARY
After listing some general formulae for sampling in n-dimensional space, the author considers the one-dimensional case: the estimation of the length of a line segment by counting the number of points that happen to fall within the segment. If the points are equidistantly located, the variance of the estimate is a strictly periodic function of the length of the segment. This systematic sample has a higher efficiency than simple and stratified random samples of the same intensity.
With some modifications, the results carry over to the two-dimensional case: the estimation of the area of a plane figure by counting the number of sample points falling inside the figure. However, the strict periodicity of the variance in the one-dimensional systematic case is replaced by a ‘Zitterbewegung’. The magnitude of this oscillation is seen to be very different for figures of different shapes.
Some results are presented also for the estimation of areas by line transects, and for the estimation of volumes by aid of lattices of points in R3, and R4. Some comments are also given on the practical implications of the results for sampling in the plane.
01 Mar 1989
TL;DR: An efficient parallel algorithm is given for constructing the arrangement of n line segments in the plane, i.e., the planar graph determined by the segment endpoints and intersections, which runs in O(logn) time using O(n logn / k) processors.
Abstract: An efficient parallel algorithm is given for constructing the arrangement of n line segments in the plane, i.e., the planar graph determined by the segment endpoints and intersections. This algorithm is efficient relative to three efficiency measures--it is an NC algorithm, it has a small time-processor product, and it is output-size sensitive. In particular, it runs in O(logn) time using O(n logn / k) processors, where k is the size of the output (which is (n2) in the worst case). The algorithm does not receive the value of k as input, it determines it on-line. A method for solving an important special case of the segment arrangement problem is also shown, namely, when each input segment is parallel to one of the coordinate axes (i.e., iso-oriented). The algorithm for this problem runs in O(log n) time using an optimal O(n+ k/log n) processors. The model of computation is the CREW PRAM model, where processor allocation must be explicit and global.
TL;DR: An Ω(n log n) fixed order algebraic decision tree lower bound for determining the existence of a line stabber for a family of n line segments in the plane is presented and it is shown that this problem is equivalent to determining if the width of a set of points is less than or equal to w.
TL;DR: If a segment of a line differs in luminance or color from the rest of the line, three illusory phenomena may be perceived: a reduction in contrast of theline segment relative to the background, subjective contours running perpendicularly to the ends of theLine segment, and spread of color or brightness surrounding the line segment.
01 Dec 1989
TL;DR: The role of vision for the task of robot mobility is discussed, and an efficient technique is presented for detecting, tracking, and locating three-dimensional line segments.
Abstract: The role of vision for the task of robot mobility is discussed. An efficient technique is presented for detecting, tracking, and locating three-dimensional 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 (3-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 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. >
Patent•
10 Mar 1989TL;DR: In this article, an apparatus and method for discriminating the linearity of a line segment in an image processing system consisting of elements for extracting and tracking a train of points from a high contrast portion of a video image and determining whether the position of one ofthe points exceeds a predetermined threshold value representative of a condition which defines the end of the linearness of the train.
Abstract: An apparatus and method for discriminating the linearity of a line segment in an image processing system consisting of elements for extracting and tracking a train of points from a high contrast portion of a video image and for determining whether the position of one ofthe points exceeds a predetermined threshold value representative of a condition which defines the end of the linearity of the train of points.
Patent•
13 Nov 1989
TL;DR: In this paper, at least two line segments forming part of a line of discrete elements are aligned to form a line and each line segment is collected by a light sensitive sensor array (2, 3) having a number of light sensitive cells forming a segment vector.
Abstract: At least two line segments of discrete elements forming part of a line of discrete elements are aligned to form a line. Each line segment is collected by a light sensitive sensor array (2, 3) having a number of light sensitive cells forming a segment vector (80). Each sensor array (2, 3) has a total visional field which is divided into an active visional field and a visional field edge, that aligning means, present in the coinciding visual field of two sensor arrays are imaged by initialization in at least one cell in the segment vector (80). The active visional fields of the sensory arrays are determined in dependence on the position of the aligning means in the segment vector (80). The line is joined by the cells (84) of the segment vectors, which cells (84) represent the active visional field, while the cells (82) representing the visional field edge are skipped.
TL;DR: A relaxation algorithm without a parameter for shape matching of partially occluded two-dimensional objects is described, based on a relaxation labelling process of Rosenfeld et al.
04 Jun 1989
TL;DR: Methods and algorithms for recovering planar, cylindrical, conical, and spherical surfaces are described, and some test results are presented.
Abstract: An intermediate representation of stereo image data in terms of 3D line segments is used to extract visible surfaces and their parameters. Methods and algorithms for recovering planar, cylindrical, conical, and spherical surfaces are described, and some test results are presented. The essence of the approach is testing of small sets of 3D line segments for compatibility with a particular surface type. Maximal sets of segments of supporting different surface are then identified. Some of the algorithms involve a novel use of the dual space representation. In the domain of polyhedral scenes initially restricted to blocklike objects and spaces, the planar surfaces are combined, using connectivity, to create 3D boxes, that correspond either to simple (i.e. convex) objects or spaces, or to convex parts, which are further combined to create composite objects and spaces. >
13 Dec 1989
TL;DR: In this article, an efficient, robust algorithm for determining the best transformation, meaning either a similarity or a congruence, between a point set and a model consisting of line and circle segments, assuming the desired transformation is small.
Abstract: A description is given of an efficient, robust algorithm for determining the best transformation, meaning either a similarity or a congruence, in two or three dimensions, between a point set and a model consisting of line and circle segments, assuming the desired transformation is small. Although convergence to a correct match cannot be guaranteed, several figures of merit for the congruence allow wrong convergences to be detected. The image and the model are constructed of different elements, i.e. points versus line and circle segments, which is well suited for the applications discussed. If this feature is undesirable, however, the algorithm can be adapted to match two sets of segments or two sets of points. Experimental results are presented for the case of a similarity in 2D using line segments only. >
22 Nov 1989
TL;DR: A binocular-stereo-matching algorithm, based on a line matching method, which does not require the horizontal epipolar line constraint, which can be a useful tool for solving the correspondence problem in 3D computer vision.
Abstract: A binocular-stereo-matching algorithm, based on a line matching method, which does not require the horizontal epipolar line constraint is presented. The method makes use of the line searching window determined by the epipolar lines of the extreme pixels of a given line segment and two circles whose radius is equal to the maximum possible disparity. The proposed algorithm was implemented on the KAISION-I system, designed for real-time image processing, and has been tested with various types of real scenes. The experimental results show that the proposed algorithm can be a useful tool for solving the correspondence problem in 3D computer vision. >
20 Mar 1989
TL;DR: In this paper, the authors examined different constraints which can be used to find the correspondences between line segments in an image sequence and presented an algorithm for matching line segments when the motion of the camera is approximately known.
Abstract: The author examines different constraints which can be used to find the correspondences between line segments in an image sequence. These constraints are imposed by the continuity of the 3-D motion and also by certain types of motions. The author derives simple equations which relate corresponding tokens in three consecutive images when the 3-D motion is a translation. Next, he describes an algorithm for matching line segments when the motion of the camera is approximately known and presents some experimental results. If a camera moving in a stationary environment is considered, an image motion is related to the location of the corresponding object in space with respect to the instantaneous axis of translation. The author performs a geometrical analysis of this relationship and introduces concepts for this analysis. It is noted that this relationship is useful for tracking objects in the field of view. >
21 Mar 1989
TL;DR: A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with an innovative, efficient edge detection scheme that is being incorporated into a distributed robot control system.
Abstract: A highly structured and compact algebraic representation of grey-level images is expanded Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme The major advantage of this feature extractor is its general, object-independent nature Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching The feature extractor and model matcher are being incorporated into a distributed robot-control system
Patent•
11 Jan 1989
TL;DR: In this paper, the authors propose to automatically delete a part impossible to be worked by extracting a neighboring line segment and a tangent line vector in a dividing line side, extending and interpolating a straight line segment to the divide line side when both are almost opposite.
Abstract: PURPOSE:To automatically delete a part impossible to be worked by extracting a neighboring line segment and a tangent line vector in a dividing line side, extending and interpolating a straight line segment to the dividing line side when both are almost opposite. CONSTITUTION:When an inside closed graphic 2 is displayed to a display 20, an electronic computer 10 divides the closed graphic 2, at first, by a dividing line 4 to pass through one of line segments to constitute the inside closed graphic from the one point of an outside closed graphic 2. When the presence of a part impossible to be worked is known, an operator activates a means 11. The means 11 successively removes the respective line segments of a straight line and a circular arc and a tangent line vector in a tangent line part is computed. When the tangent line vectors are almost opposite, such as the relations between a tangent line vector 33V and 35V and between 34V and 36V, is decided, the means 11 instructs the matter to a means 12, a line segment to be circular arc part is deleted out of the tangent line vectors by the means 12. Then, line segments 37 and 38 are obtained in the opposite side of a dividing line 4 and extended to the dividing line 4 side and the line segment is interpolated.
17 Aug 1989
TL;DR: In this paper, a parallel algorithm for constructing the Voronoi diagram of a polygonal scene was given, i.e., a set of line segments in the plane such that no two segments intersect except possibly at their endpoints.
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 in O(log2n) time using O(n) processors in the CREW PRAM model.
Patent•
02 Mar 1989
TL;DR: In this article, the line segment is extracted for each range of a certain line-thinned density value, and the line segments can be extracted separately for a part, in which an edge is made clear, and a part in which the edge is not made clear.
Abstract: PURPOSE: To efficiently extract a line segment constituting an objective body from a density picture, where brightness and darkness is not made clear, by executing line thinning according to the density value of each picture element to the density edge picture and extracting the line segment for each range of a certain density value. CONSTITUTION: The line thinning is executed according to the density value of each picture element in an edge detection part 5 to the density edge picture, to which differentiation processing is executed. Then, since the line segment is extracted for each range of a certain line-thinned density value, the line segment can be extracted separately for a part, in which an edge is made clear, and a part in which the edge is not made clear. After the line segment is extracted in a line segment extraction part 6 concerning all points having a value more than a threshold value on a Hough plane after Hough transform, it is judged in a line thinning integration processing part 8 whether the line segment can be regarded same or not. Accordingly, the line segment corresponding to a point near the maximum point on the Hough plane can be extracted as well. Thus, even when the brightness and darkness is not made clear in the density picture, the line segment can be satisfactorily extracted. COPYRIGHT: (C)1990,JPO&Japio
Patent•
26 Oct 1989
TL;DR: In this paper, a long line segment obtained with coupling the line segments including distortion, etc., by integrating the line segment at a distance = the prescribed threshold is extracted, and the intersection coordinates of the intersection between a line segment integrated by a furcating point extract processing part 7 and the other line segment are obtained.
Abstract: PURPOSE:To automatically extract a long line segment obtained with coupling the line segments including distortion, etc., by integrating the line segments at a distance = the prescribed threshold. Next, the coordinates of the starting point and end point of the line segment integrated by a starting point/end point extract processing part 6 are obtained, the coordinates of the intersection between the line segment integrated by a furcating point extract processing part 7 and the other line segment are obtained, and they are outputted as straight line segment data 8. The plural line segments connected in such a way can be automatically extracted as the integrated long line segment.
23 May 1989
TL;DR: It is proposed that the medial axis transformation (MAT), being an invertible transformation, has value in lossless data compression, and, since the MAT conveys the line structure of an image, that it is also useful for vector conversion.
Abstract: It is proposed that the medial axis transformation (MAT), being an invertible transformation, has value in lossless data compression, and, since the MAT conveys the line structure of an image, that it is also useful for vector conversion. To this end, some properties of the MAT are established and then exploited to devise a specialized chain-code representation. This MAT-based chain-code language captures any binary image but is particularly suited to line drawings. An extension of the language that can express chain-code sequences as linear and quadratic line segments under tunable error tolerance is described. The representation has achieved acceptable lossless data compression and significant additional compression for line drawings when vectorization is employed. As the error tolerance is increased, the amount of compression increases together with distortion. Thus, the method can be used to obtain a rate/distortion curve for binary images. >
05 Jun 1989
TL;DR: The maximum-weight matching problem is considered, and algorithms of complexities of complexities are obtained for the convex and the nonconvex case, respectively.
Abstract: An O(n3/2√a(n)) time algorithm is presented for finding a minimum-weight matching of a set of 2n points lying on the boundary of a convex polygon, where a(n) is the functional inverse of the Ackerman's function. Generalizing this result, we obtain an O(n3/2 logn√a(n)) time algorithm for the minimum-weight matching of points lying on the boundary of a simple nonconvex polygon, where we require that the line segments joining the matched pairs be contained within the polygon. We also consider the maximum-weight matching problem, and obtain algorithms of complexities O(n) and O(n log n) for the convex and the nonconvex case, respectively. By contrast, finding a weighted matching of an arbitrary set of points takes O(n5/2 log4n) time [Vaidya 1987].