Showing papers on "Line segment published in 1996"

3D Model Acquisition from Extended Image Sequences

Abstract: A method for matching image primitives through a sequence is described, for the purpose of acquiring 3D geometric models. The method includes a novel robust estimator of the trifocal tensor, based on a minimum number of token correspondences across an image triplet; and a novel tracking algorithm in which corners and line segments are matched over image triplets in an integrated framework. The matching techniques are both robust (detecting and discarding mismatches) and fully automatic.

Distributed algorithms for formation of geometric patterns with many mobile robots

Abstract: We discuss a method for controlling a group of mobile robots in a distributed manner. The method is distributed in the sense that all robots, or most of the robots in some cases, plan their motion individually based upon the given goal of the group and the observed positions of other robots. We illustrate the method by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. We also show how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. Finally, we show how the robots can be divided into two or more groups. It turns out that in many cases most robots execute an identical, simple algorithm. The performance of the method is demonstrated by simulation. © 1996 John Wiley & Sons, Inc.

Robust and efficient detection of salient convex groups

Abstract: This paper describes an algorithm that robustly locates salient convex collections of line segments in an image. The algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. We give an expected case analysis of the algorithm performance. This demonstrates that salient convexity is unlikely to occur at random, and hence is a strong clue that grouped line segments reflect underlying structure in the scene. We also show that our algorithm run time is O(n/sup 2/log(n)+nm), when we wish to find the m most salient groups in an image with n line segments. We support this analysis with experiments on real data, and demonstrate the grouping system as part of a complete recognition system.

Approximation of polygonal curves with minimum number of line segments or minimum error

Abstract: We improve the time complexities for solving the polygonal curve approximation problems formulated by Imai and Iri. The time complexity for approximating any polygonal curve of n vertices with minimum number of line segments can be improved from O(n2log n) to O(n2). The time complexity for approximating any polygonal curve with minimum error can also be improved from O(n2log2n) to O(n2log n). We further show that if the curve to be approximated forms part of a convex polygon, the two problems can be solved in O(n) and O(n2) time respectively for both open and closed polygonal curves.

Longest line method and apparatus for fingerprint alignment

Abstract: A non-minutia method and apparatus for comparing a reference fingerprint image to a candidate fingerprint image are disclosed. During enrollment of a reference image, a unique reference set of data is generated in a reference coordinate system by placing a group of line segments on the reference image. A collection of constraints is used for defining the subspace for each line of the reference group. A similar set of candidate line segments is constructed on the candidate fingerprint image in a candidate coordinate system. A candidate set of data is determined and then compared with the reference set of data using translation and rotation of the coordinate systems. Tolerances of the comparison are also provided for.

External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

Abstract: In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient new external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red-blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems, the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting informationfrom them.

An optimal algorithm for the (<= k)-levels, with applications to separation and transversal problems.

Abstract: This paper gives an optimal O(n log n + nk) time algorithm for constructing the levels 1,...,k in an arrangement of n lines in the plane. This algorithm is extended to compute these levels in an arrangement of n unbounded x-monotone polygonal convex chains, of which each pair intersects at most a constant number of times.These algorithms can be used to solve the following separation and transversal problems. For a set of n blue points and a set of n red points, find a line that separates the two sets in such a way that the sum, m, of the number of red points above the line and the number of blue points below the line is minimized. Such an optimal line can be found in O(nm log m + n log n) time. For a set of nline segments in the plane, find a line that intersects the maximum number of the line segments. Such an optimal line can be found in O(nm log m + n log n) time for vertical segments and in O((nm log m + n log2n) α(n)) expected time for arbitrary line segments, where m denotes the number of line segments not intersected by the optimal line.

An optimal algorithm for computing (≤k)-levels, with applications

Abstract: This paper gives an optimal O(n log n+nk) time algorithm for constructing the levels 1,…, k in an arrangement of n lines in the plane. This algorithm is extended to compute these levels in an arrangement of n unbounded x-monotone polygonal convex chains, of which each pair intersects at most a constant number of times. We then show how these results can be used to solve several geometric optimization problems including the weak separation problem for sets of red and blue points or polygons, the maximum line transversal problem for sets of line segments, the densest hemisphere problem for sets of points on a sphere and the optimal corridor problem for sets of points in the plane. All of the algorithms are quality-sensitive; they run faster if the optimal solution is a good one.

Range finding and feature extraction by segmentation of images for mobile robot navigation

Abstract: This paper describes techniques to identify various features in a scene using a laser range finding sensor, scanning horizontally in one dimension. The authors describe the optical and electronic properties of the sensor, together with the distributed processing hardware. The authors present a method to recognise and parameterise straight lines and ellipses occurring together in ID range images. In particular, the authors: (1) Present a line fitting system which recursively fits points to line segments, given range and bearing information, and correctly accounts for the sensors error sources. This system also passes on unfitted points to the ellipse fitter. (2) Extend Rothwell and Zisserman's improvements to the Bookstein algorithm to determine ellipse parameters from few observed points which lie over a small angular excursion of the ellipse, for example a pipe in an industrial environment. (3) Discuss the problems of outliers, and develop methods of recognising and rejecting them, including the use of intensity as well as range data. The authors show solutions to these problems on real data, and finally discuss further methods they might use to improve the ellipse fitting.

Interactive drawing recognition processing method and apparatus thereof

Abstract: A drawing is read by a scanner to create raster data. A labeling process is executed for the data to extract a contour line for each pattern element resultant from the labeling process to produce contour line data and region data to manage, in a tree structure, information related to a circumscribed rectangle of each line segment of the contour line. When the operator picks by a pointing device a predetermined region on the screen of a display and a pair of line segments for recognition, there is retrieved region data corresponding to the specified region. After extracting contour line data associated with the retrieved region data, a center line creation process is executed according to the extracted contour line data.

Systems and methods for wrapping a closed polygon around an object

Abstract: A system and methods for wrapping a closed polygon around an object represented in a computer system, where the closed polygon is substantially adjacent to the object without intersecting or clipping the object. The system and methods are especially useful for fitting text close to the object in a word processor or page layout system. The method involves dividing the object into a number of horizontal threshold bands. Four points are sequentially positioned within each threshold band along the edge of the object in the band. The first and last points are located proximate to the object on the horizontal boundaries of the threshold band, but do not intersect the object. The middle points are located at the intersections of three defined lines. In this configuration, line segments between any of the four points do not and cannot intersect the object. The step of placing four points along the side of the object within a threshold band is repeated within each of the threshold bands along both sides of the object to form a set of polygon points. This set of polygon points is then sequentially connected to form the closed polygon that wraps around the object. Text can then be flowed around the object without any clipping of the object.

Line detection algorithm

Abstract: In this paper, a simple and efficient approach in the line segment detection algorithm, which employs the properties of digital line segment, is proposed. In discrete domain, a continuous line can be considered as combination of sets of pattern in the quantized direction of edge pixels (i.e. 0/spl deg/, 45/spl deg/, 90/spl deg/, 135/spl deg/) with approximately equal number of pixels. Based on this characteristic, the boundary convergence of discrete line is derived. According to this convergence property, a simple and efficient line detection algorithm is proposed. Due to its simplicity and efficiency, real-time line detection can be achieved.

Algorithms for generalized halfspace range searching and other intersection searching problems

Abstract: In a generalized intersection searching problem, a set S of colored geometric objects is to be preprocessed so that, given a query object q, the distinct colors of the objects of S that are intersected by q can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and have many applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the color classes satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving objects that are not necessarily iso-oriented. These problems include: generalized halfspace range searching in R d , for any fixed d ≥ 2, and segment intersection searching, triangle stabbing, and triangle range searching in R 2 for certain classes of line segments and triangles. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.

Segmentation of planar curves into circular arcs and line segments

Abstract: In many applications, like shape analysis, it is necessary to decompose an object contour into straight-line segments and circular arcs, because many man-made objects (especially machined parts) are composed of these two types of geometric entities. This paper presents a procedure for segmenting a planar curve into lines and arcs, in which the number of entities (or break points) of the curve is given. This procedure can be divided into two stages: (1) to obtain a starting set of break points, and determine the approximation functions (lines and arcs) for the data intervals that are separated by the break points; and (2) to adjust the break points until the error norm is locally minimized. The first stage is based on the detection of significant changes in curvature using the chain-code and differential chain-code techniques, and the second stage is an optimization curve/line fitting scheme. A computational comparison with a modified dynamic programming (MDP) approach shows that the proposed procedure obtains near optimal solutions (relative errors less than 1%) for all the test problems, and requires less than 1.2% of the computational time needed by the MDP approach.

Incremental update of the visibility map as seen by a moving viewpoint in two dimensions

Abstract: Consider the following problem: A viewpoint moves amongst a set of line segments in the plane and it is desired to maintain the sequence of lines visible from the viewpoint at every increment in its position. The sequence of visible lines is identical for most increments in the position of the viewpoint. It is different only when the viewpoint crosses a visual discontinuity line. Our objective is to be able to quickly report whether the sequence of visible lines needs to be updated and perform the update quickly in that case. We propose an algorithm that satisfies both criteria while using space linear in the number of visual discontinuity lines. This last condition is important because constructing the arrangement of these lines would take space quadratic in their number.

Extremal Properties of Vertices on Special Polygons, Part I

Abstract: Summary. First, extremal properties of endpoints of line segments in n-dimensional Euclidean space are discussed. Some topological properties of line segments are also discussed. Secondly, extremal properties of vertices of special polygons which consist of horizontal and vertical line segments in 2-dimensional Euclidean space, are also derived.

Cartographic indexing into a database of remotely sensed images

Abstract: The paper aims to develop simple statistical methods for indexing line patterns. The application vehicle used in this study involves indexing into an aerial image database using a cartographic model. The images contained in the database are of urban and semi urban areas. The cartographic model represents a road network known to appear in a subset of the images contained within the database. There are known to be severe imaging distortions present and the data cannot be recovered by applying a simple Euclidean transform to the model. We effect the cartographic indexing into the database using pairwise histograms of the angle differences and the cross ratios of the lengths of line segments extracted from the raw aerial images. We investigate several alternative ways of performing histogram comparison. Our conclusion is that the Matusita and Bhattachargya distances provide significant performance advantages over the L/sub 2/ norm employed by M. Swain and D. Ballard (1990). Moreover, a sensitivity analysis reveals that the angle difference histogram provides the most discriminating index of line structure; it is robust both to image distortion on to the variable quality of input line segmentation.

Dynamical morphological processing: a fast method for base line extraction

Abstract: In most document analysis and recognition systems, straight lines are considered as one of the basic elements that should be located and eliminated to simplify the process of document analysis and recognition. The superposition or the intersection of different objects of interest found in the same area makes the process of detecting and extracting these line segments a non-trivial task to pursue, especially, if the method should preserve the valuable objects of interest that intersect with these lines. In this paper, we present a new and effective approach that detects the existence of line segments and eliminates them with the challenge of preserving the valuable information that intersects these line segments. The new approach makes use of the well-known morphological processing technique of the closing operation, that uses a fixed structuring element, towards the use of a dynamic structuring element. The purpose of the new dynamic structuring element is to detect and preserve the valuable objects intersecting the line segments that should be eliminated regardless of the different orientations with which the objects intersect these line segments.

Supercover 3D polygons

Abstract: A new discrete 3D polygon called Supercover Polygon is introduced. The polygon is a tunnel free plane segment defined by vertices and edges. An edge is a 3D line segment. Two different polygons can share a common edge and if they do, the union of both polygons is tunnel free. This is definition of discrete polygons that has the “most” properties in common with the continuous polygon. It seems particularly interesting for modelization of discrete scenes by way of digitization.

Maintaining Visibility of a Polygon with a Moving Point of View

Abstract: The following problem is studied in this paper: Given a scene with an n-vertex simple polygon and a trajectory path in the plane, construct a data structure for reporting the perspective view from a moving point along the trajectory. We present conceptually simple algorithms for the cases of this problem in which the trajectory path consists of several line segments or of a conic curve that contains the polygon. Our algorithms take O(n log n) time and O(n) space. We also prove that the problem of reporting perspective views from successive points along a trajectory path takes Ω(n log n) time in the worst case in the algebraic computation tree model. Our data structure reports the view from any query point on the trajectory in O(k + log n) time for a view of size k.

Method and apparatus for parametric signature verification

Abstract: A signature verification method operates by comparing the numerical values of parameters evaluated on a trial signature with stored reference data derived from previously entered reference signatures. The parameters include global features of the signature, and also include a stroke-direction code (SDC) of the signature. An SDC is derived by subdividing the signature into a sequence of time-ordered, spatially oriented line segments, each segment extending between a pair of discrete points along the signature. Each line segment has a stroke-direction value. The SDC is the ordered sequence of these stroke-direction values.

Algorithms for generalized halfspace range searching and other intersection searching problems

Abstract: In a generalized intersection searching problem, a set S of colored geometric objects is to be preprocessed so that, given a query object q, the distinct colors of the objects of S that are intersected by q can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and have many applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the color classes satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving objects that are not necessarily iso-oriented. These problems include: generalized halfspace range searching in R d , for any fixed d ≥ 2, and segment intersection searching, triangle stabbing, and triangle range searching in R 2 for certain classes of line segments and triangles. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.

Method for mapping line segment intersections to machine representable points

Abstract: The present invention provides a technique for mapping the intersections of line segments to machine representable points in a tiled plane. The technique provides for two mapping rules with respect to intersections that result in dividing an original line segment into a number of line segment fragments, each of which is an output machine representable line segment. The mapping rules are designed to minimize the fragmentation of an output set of machine representable line segments while still maintaining their topological consistency and geometric accuracy (i.e., closeness) with respect to the corresponding set of original input line segments. The technique provides a way for operations that manipulate line segments to be implemented in a simple manner assuming a finite precision model of computer arithmetic. Such techniques have numerous applications in the field of computer graphics including, but not limited to, hidden surface elimination, set operations on polygons, and the decomposition of complex polygons into simpler components, such as triangles, trapezoids, or monotone regions.