Showing papers on "Line segment published in 1985"

Characterizing bar line-of-sight graphs

Abstract: Line-of-sight graphs were introduced by Garey, Johnson and So in connection with a circuit testing problem. A restricted version of the problem (using line segments and a single line-of-sight) is discussed and the associated graphs are characterized. Results for directed and weighted cases are also presented.

Method of pixel to vector conversion in an automatic picture coding system

Abstract: of the Disclosure An automatic picture coding system including a method for converting a bit-map image of the picture to vectors as the picture is being scanned. The bit map is delayed as it is being generated to form a series of tessellations or windows of data. The windows are propagated through a series of neighborhood-logic elements which perform data transformation operations such as growing, smoothing and thinning of the bit-map image. A bit stream output from the neighborhood logic which output includes only line and edge features of the original picture is transferred serially to a microcomputer where the features are parti-tioned into a plurality of line segments. Each line segment is chain coded and temporarily stored, as it is acquired, in a corresponding one of a plurality of lists, the lists being linked in an order corresponding with the order in which the segments are acquired. When the storage of each chain-coded segment is completed, the segment is converted to vectors and transmitted to a user device for display, storage, or further processing, the lists in which the converted segments were stored being unlinked and deallo-cated. The process is continued until the entire document has been scanned and converted to vectorial data.

Range searching in a set of line segments

Abstract: The range searching (or windowing) problem asks for an accommodation of a set of objects such that those objects that lie (partially) in a given axis-parallel rectangle can be reported efficiently. We solve the range searching problem for a set of n non-intersecting, but possibly touching, line segments in the plane and give a data structure that allows for range queries in O(k+ log2 n) time, where k is the number of reported answers. The structure is dynamic and allows for insertions and deletions of line segments in O(log2 n) time. The structure uses O(n log n) storage. The related problem of moving the window (range) parallel to one of the coordinate-axes, determining the first line segment that will become visible or stops being visible, is treated as well and similar bounds are obtained.

Distance problems in computational geometry with fixed orientations

Abstract: In computational geometry, problems involving only rectilinear objects with edges parallel to the x -and y-axes have attracted great attention. They are often easier to solve than the same problems for arbitrary objects, and solutions are of high practical value, for instance in VLSI design. This is because in VLSI design technology requirements often dictate the use of only two orthogonal orientations for the boundary edges of objects as well as wires.The restriction on the boundary edges motivates the study of rectilinear objects, while the restriction on wires brings the focus on the well-known L1-metric (the Manhattan distance). In short, given the two orthogonal orientations, both the shape of objects and the distance function are determined in a natural way.More recent VLSI fabrication technology is capable of creating edges and wires in both the orthogonal and diagonal orientations. This motivates us to study more general polygons, and to generalize the distance concept to the case where any fixed set of orientations is allowed. We 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 family of metrics may help bridge the gap between the L1- and the L2-metrics, as those are the limiting cases for two and infinitely many regularly distributed orientations.

Bounds for partitioning rectilinear polygons

Abstract: We study the problem of partitioning a rectilinear polygon with interior points into rectangles by introducing a set of line segments. All points must be included in at least one of the line segments introduced and the objective function is to introduce a set of line segments such that the sum of their lengths is minimal. Since this problem is computationally intractable, we present efficient approximation algorithms for its solution. The solutions generated by our algorithms are guaranteed to be within a fixed constant of the optimal solution value. Even though the constant approximation bound is not so small, we conjecture that in general the solutions our algorithms generate are close to optimal.

A unified approach to interference problems using a triangle processor

Abstract: Triangulation is an efficient way to simplify and unify interference problems, such as hidden line and surface elimination and Boolean shape operations in solid modeling. Almost all of the processing relevant to a triangle can be performed by computing some 4 x 4 determinants. The author proposes a hardware processor (TRIANGLE PROCESSOR) that quickly intersects a triangle with a point, a line segment, or another triangle. Various applications of the TRIANGLE PROCESSOR are explained in this paper, including applications to face and volume triangulations.The author stresses that the triangulation approach and the TRIANGLE PROCESSOR simplify, speed up and unify various types of processing relating to interference.

Production of extrusion die

Abstract: PURPOSE: To obtain the necessary bearing length and the inclined angle of a back reliefing part by deciding the point to subdivide a taper tape shape, by forming the aggregation of small line segments by connecting the subdivided point thereof with a straight line and by controlling by deciding the average inclined angle on each small line segment. CONSTITUTION: The point to subdivide the shape relating to the taper tape shape is decided so that the difference in the ideal inclined face 6 of the back reliefing part and the inclined face 6 of the back relief part to be formed actually concerning the necessary taper tape shape comes within the allowable error range virtually in the case of the shape of the bearing aperture of an extrusion die being the circle of the radius R 0 and the bearing length L and inclined angle T of the back relief part varying gradually. The aggregation of the small line segments is formed by connecting with a straight line the subdividing point thereof. the control value of the inclination inside each small line segment is decided based on the angle made by the direction concerning the small line segment thereof and the tangent line direction in the shape of the bearing aperture. COPYRIGHT: (C)1987,JPO&Japio

Detector for circular body

Abstract: PURPOSE:To obtain data on an independent circle and an arc by picking up an image of plural bodies whose contours are arcuate or enveloped with an arc, making a raster scan and converting data into binary data, and operating a scanning segment terminal part and the overlap state of segments. CONSTITUTION:An image 12 of the plural circular bodies 11 on a background 10 is picked up while they overlap one another. The video signal obtained by making the raster scan on the image is converted 13 into a binary signal to obtain a picture as shown in a figure 24. This information is written in a picture memory in DMA mode by a picture information input circuit 14 which includes the picture memory and a picture feature extraction part. A connectivity analyzing part 15 detects 16 boundary points on the basis of line segment information (coordinates and length of segment terminal part and whether the segment overlaps an adjacent segment or not) on the binary-coded picture from the feature extraction part, and carries out the trace arithmetic 17 of inner and outer circumferential points, arithmetic 18 of arcuate parts, arithmetic 19 of estimated circles, and output 20 of detection results to constitute body circle detection data. Consequently, the positions, sizes, and number of overlapping circles are detected.

Object retrieval system

Abstract: PURPOSE: To reduce the number of collation times with a cubic dictionary and to attain a quick retrieval even if the direction of an input object is unknown by providing an appearance dictionary. CONSTITUTION: An observation circuit 1 projects an unknown object at two-dimensional coordinates, and a line drawing extraction circuit 2 extracts a line segment corresponding to the ridge line of the object and stores said segment in a picture memory 3. A collation circuit 7 refers to the line drawing read out of the memory 3 and plural line drawings stored in the appearance dictionary 8, and selects candidates whose polygonal shape and connection relation are the same as appearance. A projection conversion circuit 5 reads areas corresponding to the appearance candidates out of the dictionary 8, and projects three-dimensional data stored in the cubic dictionary 6 on a two-dimensional plane corresponding to these areas. A collation circuit 4 collates the two-dimensional projected image read out of the memory 3 with that outputted from the circuit 5. If they are equal, they are unsidered to be a category which the dictionary 6 has to retrieve, and additional information is outputted. COPYRIGHT: (C)1987,JPO&Japio

Improved computer graphics 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, the edge line segments are checked for visibility only with respect to the changes associated with the changed component objects. This results is a substantial reduction in the required number of comparisons between segments and faces as compared to prior methods.

The Accuracy of the Digital Representation of a Straight Line

Abstract: Both in Image Processing and in Computer Graphics digital straight line segments play a role as the simplest way to connect pixels. But while in Computer Graphics the emphasis is on the generation of these lines, given the parameters intercept and slope, the focus in Image Processing is on measuring the parameters, given the lines. Aspects of this analysis are the so-called linearity conditions (specifying the necessary and sufficient conditions for a set of points to be a digitized straight line segment) and the accuracy of the representation (specifying how accurately a given digitized straight line segment describes the underlying continuous reality). Both aspects have been investigated in depth [1]–[9]. The question of accuracy has recently been solved completely, when mathematical expressions were given for the set of all continuous line segments that could have generated a given digital straight line segment [8]. These expressions are in fact the formulas for the inversion of the digitization process. As such, they are also interesting for Computer Graphics.

Linear interpolation circuit

Abstract: In a CRT display unit coordinates of start and end points P0, P1 of a line on the screen of the CRT are provided from a controller 11 and stored in a register 12. A line information calculating portion 13 calculates information necessary for linear interpolation based on the stored start and end point coordinates and the line segment information thus obtained is stored in a register 14. Based on the stored line segment information, a coordinates interpolating portion 15 calculates base line and supplement line data comprising a plurality of dots for constituting a straight line connecting the start and end points, which data are stored in a frame memory transfer register 16, A, B, C, prior to transfer to a frame memory. Thus, base and supplement line data are simultaneously transferred for linear interpolation and at the same time, information of the subsequent line segment is calculated so that the processing time for linear interpolation can be made short.

Algorithms for Mathematical Morphological Operations with Flat Top Structuring Elements

Abstract: The mathematical morphological operations on grey scale images require the selections of the minimum or the maximum value within the windows set by structuring elements. This paper deals with the structuring elements which are three dimensional with flat top and infinite height. The flat top region can be various shapes of one or two dimensions such as line segment, hexagon, octagon or circle. This paper describes the optimal implementation of the morphological operations with such structuring elements, an iterative method which combines controlled image shiftings and comparisons between the original and shifted images. It is an effective image processing method without a cytocomputer architecture [1,2].

The Use Of Natural Constraints In Image Segmentation

Abstract: Current edge detection techniques are often insensitive to some perceptually significant edges in an image. Similarly, segmentation techniques do not always segment an image into perceptually meaningful regions. Edge detection and segmentation algorithms can be improved by incorporating the natural constraints used by humans in the perception of line drawings. To uncover some of these natural constraints, psychophysical experiments were performed. The results show that the perceptibility of individual lines in a drawing depends upon the presence of particular local features. First, short lines appear to have lower contrast than long lines. Second, there is a hierarchy of three types of connections between the ends of line segments, and the perceived contrast of a line increases by different amounts, depending upon which types of end connections are present. The natural constraints uncovered in the psychophysical experiments were incorporated into a computer vision module which selectively enhances and segments line drawings. The in-put to the module is a drawing containing straight and/or curved lines, and the output is an enhanced and segmented version of the line drawing. The computations in the module are local and can be performed in parallel. They are efficient because of the simplicity of the operations involved, and because they are performed just once-no iterative relaxation is required. The use of natural constraints results in lines being enhanced in accordance with their perceptual significance. For example, lines which are part of the outer contours of objects are enhanced more than other lines, while lines that are part of object edges are enhanced more than lines which form part of textures or noise. In addition, when one object occludes another, the object in the foreground is enhanced versus the occluded object. When objects are accidentally aligned, the segmentation computed by the module agrees with the segmentation used by humans. By using the natural constraints, many tasks which previously had been thought to require domain dependent knowledge, can be performed using data driven, bottom-up processing.

System for detecting robot interference in teaching of cooperation work

Abstract: PURPOSE:To improve the accuracy of detection of interference of robot hands by correcting a parameter only with the interference of links at the outermost tip of the robot in comparing the shortest distance between two line segments with a predetermined parameter. CONSTITUTION:In expressing each link of the robot as a center line segment, equations of straight line segments including end points A, B and C, D of each line segment are expressed by parameters at first. Then the shortest distance between robots is obtained and the minimum distance (d) smallest in them is obtained, it is compared with an interference parameter (c) and it is discriminated that an interference exists with d<=c. Since the discrimination of interference is not accurate because of a semi-sphere at end points caused inevitably attended with the discrimination of the distance between center lines when the interference between robots takes place between hands, one of semi-spheres is eliminated to avoid the effect of the semisphere not existing actually in order to prevent it and it is corrected as an interference parameter ch.

Correspondence processing method of stereophonic image

Abstract: PURPOSE:To obtain securely execution information on a feature line by coordinating stable connection line component or line segments which are hardly influenced by noise according to all their features, and coordinating respective points on the basis of the result. CONSTITUTION:Original image input devices 21 and 22 each consist of a TV camera, AD converter, and frame memory in combination, and line drawing extracting circuits 23 and 24 performs threshold processing of results based upon Laplacean to perform binary coding processing. A parallax offset detecting circuit 25 calculates the quantity of shifting so that the mutual correlation between a right and a left original image is maximum. It is considered that line segments at segment extracting circuits 26 and 27 are between terminal points, branch points, or maximum points of a line component of 1 in thickness. A feature point coordinating circuit 29 coordinates singular points of the same height among feature points on single segments or composite segment of the coordinated right and left images. A depth calculating circuit 30 calculates the depth corresponding to the coordinated feature points and identifies the body.

Chopping system of figure

Abstract: PURPOSE:To chop only an object figure even if a object to be chopped in the figure is brought into contact with the other object by chipping only the neighborhood figure coupled to a skeletal line CONSTITUTION:An input figure signal 10-1 is line-thinned, and a skeletal line figure (b) can be obtained Coordinate points aligning is executed by using a space between feature points on the skeletal line figure as one skeletal line segments, and a table C of a coordinate points aligned line is generated Out of skeletal line segments in the table C, those having the geometric property to satisfy a certain reference are registered in a table (d) In case they cannot be listed up because their exceptional properties cannot satisfy said reference, skeletal line segments are specified by a man-machine mode and listed up With respect to skeletal line segments selected in such a way, a figure (e) is reproduced by figuring of the coordinate points aligned line Finally, a figure (f) is chopped out by figure chopping processing to chop only a neighborhood figure on the figure coupled to the skeletal line figure (e)

Method for identifying projected and recessed polygon in graphic processing

Abstract: PURPOSE:To attain ease of identification of projected/recessed polygons by using a line segment of the polygon as a reference, measuring a cross angle of an adjacent line segment connected to the said reference line segment sequentially and applying decision that it is a projected polygon when all angles are smaller or larger than 180 deg and it is a recessed polygon when not CONSTITUTION:When a controller 12 gives a command to a direction to be measured by a measuring direction indicating section 121 that an apex angle coordinate of a polygon is measured clockwise or an internal angle formed by both adjacent lines is measured counter clockwise, it is discriminated by a measuring direction discriminating section 122 and the result of measurement is decided by a decision section 123 while 180 deg is taken as a reference When all measured angles are smaller or larger than 180 deg, it is decided as a projected polygon and decided as a recessed polygon when not Thus, the identification of the projected/recessed polygon is attained easily without noticing inner/outer angle formed by two line segments

Quantizing method of hand-written character and graphic

Abstract: PURPOSE:To enable quantization free from a character fluctuation and an inclination by extracting a temporary segment from inputted coordinate information and by considering the synthesization of adjacent temporary segments as one temporary segment if the difference in the temporary directional code of the adjacent temporary segments. CONSTITUTION:Coordinate information (a) obtained from a coordinate input device 1 is inputted to a temporary segmenting processing part 2, a candidate considered to be the segment is extracted and set to temporary segment information (b), which is inputted to a temporary directional code generating part 3. In accordance with the direction of the temporary segment, temporary directional code information (c) in 32 directions is generated and inputted to a segment synthesization processing part 4, which synthesizes the segment if necessary by utilizing the temporary directional code information (c) and outputs the final segment information (d). A directional code generating part 5 outputs directional code information (e) in eight objective directions in accordance with the direction of the segment. Provided that when directional codes of adjacent two segments are equal, they are synthesized in order to be one line segment, and one directional code shall be given.

Smear-out device of picture

Abstract: PURPOSE:To complete smear out of a picture with one main scanning by tracing respectively a closed polygonal shape picture clockwise and counter-clockwise, generating an initial point group of smear out and inputting/outputting the point group while referencing a profile line. CONSTITUTION:A profile line generating means 215 traces an apex of a closed polygonal picture representing the content of a polygonal storage means 200 and writes a value 1 to a picture element to which a line segment deciced by two apexes among picture elements of a profile line storage means 245. Then a forward inner line generating means 205 and a reverse inner line generating means 210 trace respectively an apex of the closed polygonal picture to calculate a vector of each side, traces forward or reverse a vector group, finds out a vector whose y-axis component is negative and writes a value 1 to the picture element. A summing point group generating means 230 writes a value 1 to a region storage means 235 when any of picture elements is 1. A condition transfer means 240 traces picture elements in the x direction, references the content of the profile line storage means 245 to decide the content of the region storage means 235.

Quantized projecting method

Abstract: PURPOSE:To obtain quantized projection with high accuracy in a short time by applying operation to a projected point until both end points of a divided line segment have the contiguous performance, and writing the end points to a coordinate plane. CONSTITUTION:An operation section 1 executes a series of a processings. A projection quantizing section 2 operates functions g(t), h(t) of a curve set externally in response to a specified variable tn or the like to output a quantized coordinate of an end point Pn. An adjacency check section 3 discriminates the contiguous performance based on the coordinate of the end point Pn from the projection quantizing section 2. An intermediate point generating section 4 calculates the variable of the intermediate point based on the result of check of contiguous performance from the adjacency check section 3. A stack memory 5 stores variables t1, t2 of the end point of each line segment, and the end point Pn from the projection quantized section 2 is written in the memory 6 corresponding to the quantized coordinate plane PLN. Variables t1, t2 of the points P1, P2 of a line segment l1 are set initially to a stack memory 5.

Method for checking relation of graphic for lots of graphic data

Abstract: PURPOSE:To check relation of a graphic in high speed with less meaningless check as to lots of drawing data including slants by processing all areas being a check object while dividing the area into parallel area of a prescribed size and processing each parallel area while dividing the parallel area into slits only when slants exist. CONSTITUTION:A trapezoid decided by coordinates (X1, Y1)-(X4, Y4) is used as a basic graphic, all areas Z including all graphic data being a check object at first are sectioned into plural parallel regions (hereinafter called page) P prolonged in the X coordinate decided optionally and the right side and left side of the trapezoid existing in the page P are extracted respectively as two line segments. In a page where a slant line segment 7 exists in the page P, the page P is divided minutely into plural parallel slit areas. A rectangular region 11 taking a slant line segment 7r as a diagonal line is assumed, end points 71, 72, 81, 82, 91 and the line segment 7r of the line segments 7r, 8, 9 existing in the area 11 offer a cross point 92, slit areas S, S are sectioned by using each line in parallel with the X coordinate passing through the said point as a boundary so as to attain division with the required minimum value. This is registered in the order of magnitude of components.

On-line recognition device of hand written graphic

Abstract: PURPOSE:To allow on-line recognition independent of inclination of a graphic a stroke order and the number of strokes and to enhance operability of a machine by dividing graphic automatically and limiting a stroke order, the number of strokes and inclination of a graphic in one graphic CONSTITUTION:A distance between coordinate points is set to a threshold value, and a coordinate point string D1 from a tablet 100 is stored in a memory 300 as coordinate point data D2 by sampling A range of coordinate point data D2' from pendown to penup stored in the memory 300 are converted into line segment data D3 which are converted into straight line or curve data D4 according to an angle change in ranging two line segments Angles at starting and end points of each line segment of the data D4 are qunatized by 32 direction code CD, thereby obtaining data D5 Then connecting relation between respective line segments in said converted data D4 is investigated A direction code string D6 is made which is arranged in the one direction from the line segment quantized data D5 and a list 1 By comparing the direction code string D6 with a reference figure GST, similarity degree F is calculated The similarity degree obtained in such a way is compared with a threshold F0(=10) set beforehand When F

Approximating method of polygonal line of line figure

Abstract: PURPOSE:To obtain a polygonal line approximating system of a line figure which can repeats an area by cutting a line segment becoming an arbitrary pair and setting each line segment to a new pairs of start points CONSTITUTION:A point P3 is selected, distances from the bending point P3 to respective apexes P7, P8, P9, and P10 of the inner circumference are calculated and the apex P7 nearest to the bending point P3 is decided as a corresponding point With respect to bending point P4 its corresponding point P8 is decided in the same manner, a T5 and a cutting point T6 are generated from a middle point of the bonding points P3 and P4 that of the apexes P7 and P8, respectively, and a closed area E is cut at the line segments T5 and T6 In such cutting the bending point P4 and the apex P8 are set to a start point of a line segment with respect to the start points T5 and T6 by using cutting points T5 and T6 of each line segment to be an object as a new start point, and the bending point P5 and the apex point P9 are made to an end point with respect to the start points P4 and P8 by using the bending point P4 and the apex point P8 as a pair of start points