Orthogonal Segments Research Articles

보행 시 노인의 상체 움직임에 대한 3차원적 분석

The purpose of this study was to investigate the kinematic variables of the upper part of the body for 8 elderly men during walking. For this study, kinematic data were collected using a six-camera (240Hz) Qualisys ProReflex system. The room coordinate system was right-handed and fixed in space, with righted orthogonal segment coordinate systems defined for the head, trunk, and pelvis. Based on a rigid body model, reflective marker triads were attached on the 3 segments. Three-dimensional Cartesian coordinates for each marker were determined at the time of recording using a nonlinear transformation(NLT) technique with ProReflex software (Qualisys, Inc.). Coordinate data were low-pass filtered using a fourth-order Butterworth with cutoff frequency of 6Hz. Three-dimensional angles of the head, trunk, and pelvis segment were determined using a Cardan method. On the basis of each segment angle, angle-angle plot used to estimated the movement coordinations between segments. The conclusions were as follows; (1) During the support phase of walking, the elderly people generally kept their, head the flexional and abductional posture. Particularly, the elderly displayed little internal/external rotation. (2) The elderly people showed extensional and external rotation postures in the trunk movement. Particularly, It showed the change from adduction into abduction at the heel contact event of the stance phase. (3) The elderly people showed almost same pelvis movement from the flexion into extension, from the abduction into adduction, and from internal rotation into external rotation at the mid stance and toe off of the stance phase.

Orthogonal segment stabbing

We study a class of geometric stabbing/covering problems for sets of line segments, rays and lines in the plane. While we demonstrate that the problems on sets of horizontal/vertical line segments are NP-complete, we show that versions involving (parallel) rays or lines are polynomially solvable.

Pattern Matching for Sets of Segments

In this paper we present algorithms for a number of problems in geometric pattern matching where the input consists of a collection of orthogonal segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration. We propose a new criterion for segment similarity called the coverage measure, and present efficient algorithms for maximizing it between sets of axis-parallel segments under translations. In the general case, we present a procedure running in time O(n3 log2 n), and for the case when all segments are horizontal, we give a procedure that runs in time O(n2 log2 n). Here n is the number of segments. In addition, we show that an ε-approximation to the Hausdorff distance between two sets of horizontal segments under vertical translations can be computed in time O(n3/2 max(poly(log M, log n, 1/ε))). Here, M denotes the ratio of the diameter to the closest pair of points in the sets of segments (where pairs of points lie on different segments). These algorithms are significant improvements over the general algorithm of Agarwal et al. that required time O(n4 log2

Orthogonal continuous segmentation polynomial

Operator of cyclic group is applied to divide the cyclic group space into orthogonal subspace. Function without symmetry (local defined polynomial) is expanded to function defined in the whole area by the cyclic group. Using the subspace of group to get the orthogonal segmentation polynomial.

Late Quaternary evolution of the San Antonio Submarine Canyon in the central Chile forearc (∼33°S)

Hydrosweep swath-bathymetry and seismic-reflection data reveal the morphology, sedimentary processes, and structural controls on the submarine San Antonio Canyon. The canyon crosses the forearc slope of the central Chile margin for more than 150 km before it empties into the Chile Trench near 33°S latitude. In its upper reaches, the nearly orthogonal segments of the San Antonio Canyon incise ∼1 km into thick sediment following underlying margin-perpendicular basement faults and along the landward side of a prominent margin-parallel thrust ridge on the outer mid-slope. At a breach in the outer ridge, the canyon makes a sharp turn into the San Antonio Reentrant. Resistance to erosion of outcropping basement at the head of the reentrant has prevented the development of a uniformly sloping thalweg, leaving gentle gradients (<2°) up-canyon and steep gradients (>6°) across the lower slope. Emergence of an obstruction across the head of the San Antonio Reentrant has trapped sediment in the mid-slope segments of the canyon. Presently, little sediment appears to reach the Chile Trench through the San Antonio Canyon. The development of the San Antonio Canyon was controlled by the impact of a subducted seamount, which formed the San Antonio Reentrant and warped the middle slope along its landward advancing path. Incision of the canyon landward of the outer mid-slope ridge may be ascribed to a combination of headward erosion and entrenchment by captured unconfined turbidity currents. Flushing of the canyon was likely enhanced during the lowered sea level of the last glaciation. Where the canyon occupies the triangular embayment of the reentrant at the base of the slope, sediment has ponded behind a small accretionary ridge. On the trench floor opposite the San Antonio Canyon mouth, a 200-m-thick levee–overbank complex formed on the left side of a distributary channel emanating from a breach in the accretionary ridge. Axial transfer of sediment was inhibited to the north of the San Antonio Canyon mouth, which left the trench to the north sediment starved. Between ∼32°40′S and 33°40′S, the Chile Trench axial turbidite channel deeply incises the San Antonio distributary complex. This entrenchment may have been initiated when the barrier to northward transport was eliminated.

Area-efficient algorithms for straight-line tree drawings

We investigate several straight-line drawing problems for bounded-degree trees in the integer grid without edge crossings under various types of drawings: (1) upward drawings whose edges are drawn as vertically monotone chains, a sequence of line segments, from a parent to its children, (2) order-preserving drawings which preserve the left-to-right order of the children of each vertex, and (3) orthogonal straight-line drawings in which each edge is represented as a single vertical or horizontal segment. Main contribution of this paper is a unified framework to reduce the upper bound on area for the straight-line drawing problems from O(n logn) (Crescenzi et al., 1992) to O(n loglogn) . This is the first solution of an open problem stated by Garg et al. (1993). We also show that any binary tree admits a small area drawing satisfying any given aspect ratio in the orthogonal straight-line drawing type. Our results are briefly summarized as follows. Let T be a bounded-degree tree with n vertices. Firstly, we show that T admits an upward straight-line drawing with area O(n loglogn) . If T is binary, we can obtain an O(n loglogn) -area upward orthogonal drawing in which each edge is drawn as a chain of at most two orthogonal segments and which has O(n/ logn) bends in total. Secondly, we present O(n loglogn) -area (respectively, -volume) orthogonal straight-line drawing algorithms for binary trees with arbitrary aspect ratios in 2-dimension (respectively, 3-dimension). Finally, we present some experimental results which shows the area requirements, in practice, for (order-preserving) upward drawing are much smaller than theoretical bounds obtained through analysis.

Segmentation and recognition of dimensioning text from engineering drawings

Recognition of dimensioning text in engineering drawings is an essential part of the drawing understanding process, as this text provides the exact dimensions and tolerances of the object described in the drawing. We consider engineering drawings produced according to either ISO or ANSI drafting standards. Text segmentation and recognition are preceded by orthogonal zig-zag vectorization, arc segmentation, and arrowhead pair recognition. Initial textbox extraction is done by a region growing process, performed on text-wire candidates. On the basis of textbox context (neighboring annotation wires) the drafting standard is detected. Raw textboxes are divided into logical textboxes, which are further decomposed into basic textboxes. A neural network based OCR algorithm is applied to each basic textbox. Finally, the OCR recognition results are verified by using contextual information and comparing the results with the measurements made directly on the drawing.

Experiments on the practical I/O efficiency of geometric algorithms: Distribution sweep versus plane sweep

We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation are our implementations of distribution sweep and three variations of plane sweep. Distribution sweep is specifically designed for the situations in which the problem is too large to be solved in internal memory, and theoretically has optimal I/O cost. Plane sweep is a well-known and powerful technique in computational geometry, and is optimal for this particular problem in terms of internal computation. The three variations of plane sweep differ by the sorting methods (external versus internal sorting) used in the preprocessing phase and the dynamic data structures (B-tree versus 2-3-4-tree) used in the sweeping phase. We generate the test data by three programs that use a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million segments. The experiments provide detailed quantitative evaluation of the performance of the four algorithms, and the observed behavior of the algorithms is consistent with their theoretical properties. This is, to the best of our knowledge, the first experimental algorithmic study comparing the practical performance between external-memory algorithms and conventional algorithms with large-scale test data.

Constitutive equations of thermoelastovisco-plastic processes of material deformation along three-dimensional load paths with orthogonal segments

Constitutive equations of thermoelastovisco-plastic processes of material deformation along three-dimensional load paths with orthogonal segments

Inhibition of Return without Visual Awareness

When a cue and a target are successively presented at the same location, reaction times to discriminate the location of the target are longer than when they are at different locations (inhibition of return: IOR). We found that visual awareness of the cue was not necessary for IOR to occur. Both eyes dichoptically viewed 9 × 9 scattered arrays of vertical or horizontal line segments. To avoid effects of eye dominance and binocular rivalry, cue displays were presented briefly (33, 50, or 200 ms). Three types of cue displays were randomised: (i) no cue: horizontal segments for the left (right) eye and vertical segments for the right (left) eye; subjects perceived scattered binocularly-combined crosses, (ii) binocular (fusible) cue: displays for both eyes had cue elements (a horizontal or vertical segment popping out among orthogonal background segments) and identical interocularly; subjects easily perceived the cue; (iii) dichoptic cue: displays for both eyes had cues at the same location, but all the segments were interocularly orthogonal. Here, because of the brief presentation that horizontal and vertical segments were just combined binocularly, and subjects could see only scattered crosses. Thus, they could not be aware of the cue, which exists at the monocular level. After the cue display disappeared, the target displays [same as the cue display in (ii), but with an independent location of the pop-out target] were presented (ISI=400, 800, or 1200 ms). Reaction time to discriminate location of the target was measured for three subjects who fixated on a fixation point. In our results, IOR took place in conditions (ii) and (iii). This suggests that localisation of the cue occurs without visual awareness, which then leads to IOR.

Connected component and simple polygon intersection searching

Efficient data structures are given for the following two query problems: (i) preprocess a setP of simple polygons with a total ofn edges, so that all polygons ofP intersected by a query segment can be reported efficiently, and (ii) preprocess a setS ofn segments, so that the connected components of the arrangement ofS intersected by a query segment can be reported quickly. In these problems we do not want to return the polygons or connected components explicitly (i.e., we do not wish to report the segments defining the polygon, or the segments lying in the connected components). Instead, we assume that the polygons (or connected components) are labeled and we just want to report their labels. We present data structures of sizeO(n 1+e) that can answer a query in timeO(n 1+e+k), wherek is the output size. If the edges ofP (or the segments inS) are orthogonal, the query time can be improved toO(logn+k) usingO(n logn) space. We also present data structures that can maintain the connected components as we insert new segments. For arbitrary segments the amortized update and query time areO(n 1/2+e) andO(n 1/2+e+k), respectively, and the space used by the data structure isO(n 1+e. If we allowO(n 4/3+e space, the amortized update and query time can be improved toO(n 1/3+e andO(n 1/3+e+k, respectively. For orthogonal segments the amortized update and query time areO(log2 n) andO(log2 n+klogn), and the space used by the data structure isO (n logn). Some other related results are also mentioned.

The omni wedge: A method to produce wedged fields at arbitrary orientations

A method to produce wedged fields at any orientation relative to the collimator is described. The wedged field is generated by combining two appropriately weighted orthogonal wedged field segments at fixed collimator and gantry positions. The method requires only that wedged fields can be produced in orthogonal directions without rotating the collimator, such as is commonly provided on most radiation therapy accelerators by sets of standard and rotated wedges. Expressions are derived relating the effective wedge angle and orientation to the weighting and wedge angles of the orthogonal wedged field segments. This technique will be important when using multileaf collimator field shaping for which collimator rotation is dictated by target or critical structure shape and orientation. The term omni wedge is introduced to describe this technique.

Further Results on Generalized Intersection Searching Problems: Counting, Reporting, and Dynamization

In a generalized intersection searching problem, a set, S, of colored geometric objects is to be preprocessed so that given some query object, q, the distinct colors of the objects intersected by q can be reported efficiently or the number of such colors can be counted efficiently. In the dynamic setting, colored objects can be inserted into or deleted from S. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunately, the techniques known for the standard problems do not yield efficient solutions for the generalized problems. Moreover, previous work (R. Janardan and M. Lopez, Generalized intersection searching problems, Internat. J. Comput. Geom. Appl. 3 (1993), 39-69) on generalized problems applies only to the static reporting problems. In this paper, a uniform framework is presented to solve efficiently the counting/reporting versions of a variety of generalized intersection searching problems in static/dynamic settings. These problems include 1-, 2-, and 3-dimensional range searching, quadrant searching, interval intersection searching, 1- and 2-dimensional point enclosure searching, and orthogonal segment intersection searching.

External-Storage Data Structures for Plane-Sweep Algorithms

In this paper we develop a technique for transforming an internal memory datastructure into an external storage data structure suitable for plane-sweep algorithms. We use this technique to develop external storage versions of the range tree and the segment tree. We also obtain an external priority queue. Using the first two structures, we solve the orthogonal segment intersection, the isothetic rectangle intersection, and the batched range searching problem in the optimal number of I/O-operations. Unlike previously known I/O-algorithms the developed algorithms are straightforward generalizations of the ordinary internal memory plane-sweep algorithms. Previously almost no dynamic data structures were known for the model we are working in.

Projective Pose Estimation of Linear and Quadratic Primitives in Monocular Computer Vision

In this paper the relevance of perspective geometry for 3D scene analysis from a single view is asserted. Analytic procedures for perspective inversion of special primitive configurations are presented. Four configurations are treated: (1) four coplanar segments; (2) three orthogonal segments; (3) a circle arc; (4) a quadric of revolution. A complete and thorough illustration of the developed methodologies is given. The importance of the selected primitives is illustrated in different application contexts. Experimental results on real images are provided for configurations (3) and (4).

Constraint-based channel routing for analog and mixed analog/digital circuits

A well-defined methodology for mapping the constraints on a set of critical coupling capacitances into constraints in the vertical-constraint (VC) graph of a channel is presented. The approach involves directing undirected edges, adding directed edges, and increasing the weights of edges in the VC graph in order to meet crossover constraints between orthogonal segments and adjacency constraints between parallel segments while attempting to cause minimum increase in the channel height due to the constraints. Use is made of shield nets when necessary. A formal description of the conditions under which the crossover and the adjacency constraints are satisfied is provided and used to construct the appropriate mapping algorithms. The problem of imposing matching constraints on the routing parasitics in a channel with lateral symmetry is addressed. It is observed that perfect matching is not possible for a matched pair of nets with intersecting horizontal spans. A technique to achieve almost perfect mirror symmetry is presented for such pairs of nets. >

GENERALIZED INTERSECTION SEARCHING PROBLEMS

A new class of geometric intersection searching problems is introduced, which generalizes previously-considered intersection searching problems and is rich in applications. In a standard intersection searching problem, a set S of n geometric objects is to be preprocessed so that the objects that are intersected by a query object q can be reported efficiently. In a generalized problem, the objects in S come aggregated in disjoint groups and what is of interest are the groups, not the objects, that are intersected by q. Although this problem can be solved easily by using an algorithm for the standard problem, the query time can be Ω(n) even though the output size is just O(1). In this paper, algorithms with efficient, output-size-sensitive query times are presented for the generalized versions of a number of intersection searching problems, including: interval intersection searching, orthogonal segment intersection searching, orthogonal range searching, point enclosure searching, rectangle intersection searching, and segment intersection searching. In addition, the algorithms are also space-efficient.

Efficient dynamic algorithms for some geometric intersection problems

Efficient dynamic algorithms are presented for four geometric intersection problems. These include: (1) reporting the subset of a set S of nonintersecting segments in the plane that are intersected by a query segment of fixed slope; (2) reporting the segments of S that are intersected by a query segment whose supporting line passes through a fixed point; (3) the orthogonal segment intersection search problem; and (4) the point enclosure problem for isothetic hyper-rectangles in d-dimensional space, d ⩾ 2. These algorithms are the first linear-space solutions to Problems 1–3 and for Problem 4 in the plane. For Problem 3, the update time improves upon the previous best algorithm by a logarithmic factor without affecting the query time. For Problem 4, the update time either matches or improves upon the previous best algorithms, but the query time is larger by a logarithmic factor. No dynamic algorithms were known previously for Problems 1 and 2.

A bucketing algorithm for the orthogonal segment intersection search problem and its practical efficiency

The orthogonal segment intersection search problem is stated as follows: given a setS ofn orthogonal segments in the plane, report all the segments ofS that intersect a given orthogonal query segment. For this problem, we propose a simple and practical algorithm based on bucketing techniques. It constructs, inO(n) time preprocessing, a search structure of sizeO(n) so that all the segments ofS intersecting a query segment can be reported inO(k) time in the average case, wherek is the number of the reported segments. The proposed algorithm as well as existing algorithms is implemented in FORTRAN, and their practical efficiencies are investigated through computational experiments. It is shown that ourO(k) search time,O(n) space, andO(n) preprocessing time algorithm is in practice the most efficient among the algorithms tested.

Dynamic orthogonal segment intersection search

We consider two restricted types of dynamic orthogonal segment intersection search problems. One is the problem in which the underlying set is updated only by insertions. In the other, the set is updated only by deletions. We show that an intermixed sequence of O( n) queries and updates in both problems can be executed on-line in O( n log n + K) time and O( n log n) space, where K is the total number of reported intersections. Our algorithms utilize set-union and set-splitting algorithms. Especially, we present a linear-time algorithm for the incremental set-splitting problem, and use it for the problem in which only insertions are allowed. The data structures developed here give new better solutions for various geometric problems on orthogonal segments. Several applications of the data structures are also discussed.