Showing papers on "Line segment published in 1979"

Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering

Abstract: This paper describes a technique for transforming a twodimensional shape into a binary relation whose clusters represent the intuitively pleasing simple parts of the shape. The binary relation can be defined on the set of boundary points of the shape or on the set of line segments of a piecewise linear approximation to the boundary. The relation includes all pairs of vertices (or segments) such that the line segment joining the pair lies entirely interior to the boundary of the shape. The graph-theoretic clustering method first determines dense regions, which are local regions of high compactness, and then forms clusters by merging together those dense regions having high enough overlap. Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.

Geometric transforms for fast geometric algorithms

Abstract: Many computational problems are inherently geometrical in nature. For example, cluster analysis involves construction of convex hulls of sets of points, LSI artwork analysis requires a test for intersection of sets of line segments, computer graphics involves hidden line elimination, and even linear programming can be expressed in terms of intersection of half-spaces. As larger geometric problems are solved on the computer, the need grows for faster algorithms to solve them. The topic of this thesis is the use of geometric transforms as algorithmic tools for constructing fast geometric algorithms. We describe several geometric problems whose solutions illustrate the use of geometric transforms. These include fast algorithms for intersecting half-spaces, constructing Voronoi diagrams, and computing the Euclidean diameter of a set of points. For each of the major transforms we include a set of heuristics to enable the reader to use geometric transforms to solve his own problems.

A Generalized Line and Junction Labeling Scheme with Application to scene Analysis

Abstract: A line and junction labeling scheme is introduced that is valid for both planar and curved-surface bodies. Seven generalized junction types are defined and shown to cover all valid projections for a wide class of planar and curved-surface bodies. It is further shown that there are limitations on the permissible junction types as one moves from one end of a line segment to the other. The valid junction transitions provide 1) a new set of edge semantics for line labeling and 2) an ability to verify whether a given sequence of junctions forms a realizable configuration.

A concept of perceived orientation

Abstract: A great number of investigations have been made in an attempt to clarify and understand the visual perception of form, size, and location. Some neurophysiological models have been proposed to explain the basic experimental facts (Glezer, Doodkin, Cooperman, Levshina, Nevskaya, Podvigin, & Prazdnikova, 1975; Lindsay & Norman, 1972). The ability of man to assign orientation to objects has also drawn some attention, mainly in connection with the perception of form. A monograph has been published on this matter (Rock, 1973) which presents an excellent review of the studies made and the personal standpoint of the author. The essence of this standpoint seems to be that "the implicit cognitive description of a figure is a function of the figure's directions: whether a figure's long axis is 'vertical' or 'horizontal,' whether the figure rests on a base or stands on a point, whether it is symmetrical or not, and so forth. " However astonishing it may be, investigators usually are not concerned with the proper notion of the term "orientation." It is generally accepted that everybody knows what orientation is and therefore no special definition or more detailed discussion is needed. We feel that some attention must be paid to what we call perceived orientation and to the connection of our perception to the geometrical or other features of the objects. A clarification is also needed if we want to give a neurophysiological explanation of the findings or even to suggest some simple models. Let us stipulate, for discussion, only real twodimensional objects-figures, drawings, etc; visually perceived. What is the meaning of the questions: "What is the orientation of a contour drawing?" "What is the orientation of a combination of light and dark spots?" "What is the orientation of a cluster of dots?" If we have a line segment drawn on a sheet of paper, we may assume that the orientation of this simple object is given by the angle the segment forms with one of the existing real or imaginary lines, i.e., the edges of the sheet, the horizontal or the vertical line, some other lines drawn on the sheet, etc. In all cases, when we speak of perceived orientation of a line segment, it suffices to accept a convention for a real or imaginary line of reference and a direction for measurement of angles. The question of "orientation" for two-dimensional objects is far more complicated. Some conventions corresponding to our perception of simple figures might be accepted. The orientation of a rectangle may well be described by the angle between one of its longer sides and some other line. The orientation of an ellipse may be the corresponding angle for its longer axis. Such definitions will be in accordance with our perception of each figure. It is meaningless to assign orientation to some figures with more than one axis of symmetry. What should be the orientation of a circle, a square, or of an Archimede's . spiral? It seems clear that one may speak of perceived orientation of a figure only if there is a real or imaginary line segment defined by the figure that is perceivedeither as longer than all other such segments or as corresponding to some other salient principle. The essential point is that this segment should be unique. When there are more than one such segments (or lines) corresponding to the same principle, the assignment of orientation becomes ambiguous, difficult, and even impossible.

The range of values of a complex polynomial over a complex interval

Abstract: We discuss algorithms for the computation of the range of values of a complex interval polynomial over a complex interval. The mathematical results needed are based upon a result by Rivlin [7] valid for the range of values of a complex polynomial over the line segment [0, 1]. In the present work we extend his results to an arbitrary line segment in the complex plane. Based upon these results we then generate algorithms suitable for both line segments and rectangular regions in the complex plane executed in rectangular complex interval arithmetic. The algorithms are then tested on a variety of complex interval polynomials and compared both to the true range of values and to the values obtained by the Horner scheme.

Vector display scope

Abstract: A cathode-ray oscilloscope controlled by a circuitry receiving four (4) voltage inputs representative of the Cartesian coordinates of endpoints of two (2) vectors, for visually displaying the vectors in the form of a dashed line segment and a solid line segment. The circuity responds to operator input for generating display signals to rotate the two displayed vectors with respect to the CRT screen and responds to internal control for blinking the display of either of the vectors according to a preset vector magnitude limit.

On The Inference Of Crack Statistics From Observations On An Outcropping

Abstract: It is difficult to examine the cracks in a three-dimensional body; one is usually limited to observations on an outcropping, a cut, or a plane obtained by sectioning a sample. This paper considers two problems. The direct problem is to find the distribution of line segments in a plane section when the three-dimensional distribution of cracks is homogeneous, isotropic, and exponential. This distribution can be expressed in closed form by means of Hankel functions. It is shown that the distribution in a plane section is qualitatively different from the three-dimensional distribution in having a peak for a finite value of segment length, i.e., there is a most probable (non-zero) segment length. It is also concluded that the mean segment size in the plane is ..pi../2 times the mean crack diameter in three dimensions. This result is consistent with the well-known observation that small cracks have a lower probability of being intercepted by a plane than larger cracks. The number density of line segments is finally expressed in terms of the Hankel function of order zero. The indirect problem is to infer the three-dimensional distribution of cracks from the distribution on a section, which could be, for example, an outcropping. Thismore » problem is solved by deriving an integral equation relating the three-dimensional distribution of cracks and the distribution of line segments in a plane, and showing that it can be solved for an arbitrary distribution of segments on the out-cropping. The special case of the Hankel distribution leads to the exponential distribution in three dimensions; thus, thesolution method is verified. 3 figures.« less

Display system for displaying maps having two-dimensional roads

Abstract: Method and apparatus for displaying maps on which the roads have width as well as length. The input to the system is a list of end points of line segments. The system operates upon this list to create a new set of line segment end points, defining two line segments for each one of the input line segments. The new line segments define roads having a predetermined width.

Rectangular routeing in Smeed's city

Abstract: A rectangular system of roads is examined in a simple circular city where homes and workplaces are uniformly and independently distributed. Expressions for the number of vehicles crossing a given line segment are derived.

Decomposition ofTwo-Dimensional Shapesby Graph-Theoretic Clustering

Abstract: This paperdescribes atechnique fortransforming atwo- dimensional shapeintoabinary relation whoseclusters represent the intuitively pleasing simple parts oftheshape. Thebinary relation can bedefined onthesetofboundary points oftheshape oronthesetof linesegments ofapiecewise linear approximation totheboundary. Therelation includes allpairs ofvertices (orsegments) suchthatthe line segment joining thepairlies entirely interior totheboundary of theshape.Thegraph-theoretic clustering methodfirst determines denseregions, whicharelocal regions ofhighcompactness, andthen formsclusters bymerging together thosedenseregions having high enoughoverlap. Usingthisprocedure onhanddrawn colonshapes copied fromanX-rayandonhandprinted characters, theparts deter- minedbytheclustering oftencorrespond welltodecompositions that ahumanmight make. IndexTerms-Clustering, graph-theoretic clustering, relation cluster- ing, shape, shape decomposition, shape matching. I.INTRODUCTION

Line recognizing method of pattern recognition unit

Abstract: PURPOSE: To make it possible to recognize automatically a pattern drawn by broken lines or chain lines by detecting terminal-point coordinates of another line segment residing in an extremely small area centering basic-point coordinates and then by regarding the coordinates as expected coordinates. CONSTITUTION: Photoelectric converter 2 binary-codes video information on drawing 1 and stores it in picture memory 3 temporarily. Next, solid-line path recognition unit 4 extracts feature points of a solid line from the information in memory 3 and then stores it in feature-point storage memory 5. Next, contiguous expectation limiting circuit 7 regards terminal-point coordinates of a specific segment in memory 5 as basic-point coordinates and finds distances between respective line segments and respective terminal points centering on the coordinates. When the distance is less than a threshold level, the coordinates are transferred to connection expectation memory 8 as contiguous expectation. Next, direction deciding circuit 9 finds the angle of the vector, etc., of the segment, to which basic-point coordinates belong, to a reference vector from coordinates stored in memory 8, and decides whether the angle is less than the reference value. Thus, connection deciding circuit 10 judges whether both segments should be connected. COPYRIGHT: (C)1981,JPO&Japio

An algorithm to compute the eigenvalues/functions of the laplacian operator within a region containing a sharp corner

Abstract: An algorithm to compute the eigenvalues/functions of the Laplacian operator within a region with a sharp corner or line segment is given. Point matching is used around the boundary and the algorithm is based on the Dew and Scraton (1973) method. It is shown that the numerical solution is an exact solution of a perturbed form of the problem and error estimates are obtained. A transformed problem, which eliminates the zero eigenvalue, is used for the Neumann problem.

Three-Dimensional Perception of Planar Line Segments

Abstract: Two-dimensional line drawings can be perceived as three-dimensional images if they are viewed through a grating of parallel lines placed a short distance above the drawing. The position in space of the images is a function of the angle between the lines in the drawing and those in the viewer grating.