Parallel Line Segments Research Articles

New evidence of visual space anisotropy with auto-stereograms.

Numerous research efforts have been directed toward determining the origin of anisotropies of visual space, in contrast to real space. Recent neurophysiological studies have placed the origin in the primary visual cortex (V1) or beyond. The present study sought to provide new psychophysical evidence of the origin of these anisotropies using auto-stereograms as visual stimuli in a relative depth judgment task. The observers were presented with a hidden three-dimensional shape that consisted of two pairs of parallel line segments that were located in different depth planes and oriented at 0° (horizontal line segments), 45°, and 90° (vertical line segments). The influence of orientation on the visual performance of five observers was evaluated. The encountered differences at 45° compared with cardinal orientations revealed a non-conclusive trend toward a negative impact of oblique orientation on the observers’ performance. Significant differences were found in accuracy between the horizontal and vertical orientations, and the best scores corresponded to vertical line segments. This finding may be interpreted as the expression of vertical-horizontal anisotropy in depth. The perception of hidden three-dimensional shapes in auto-stereograms occurs beyond the primary visual cortex in the dorsal stream, and the present findings provide psychophysical evidence of the location of vertical-horizontal anisotropy in non-retinotopic areas beyond V1. Keywords: auto-stereograms, depth perception, oblique effect, line orientation, vertical-horizontal anisotropy.

A unifying framework for duality and modeling in robust linear programs

In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robust linear program; one in which the primal is constructed to be “ultra-conservative” and one in which the primal is constructed to be “ultra-optimistic.” Furthermore, as one would expect, if the uncertainly in the primal is row-based, the corresponding uncertainty in the dual is column-based, and vice-versa. Several examples are provided that illustrate the properties of these primal and dual models.A second theme of the paper is about modeling in robust linear programming. We replace the ordinary activity vectors (points) and right-hand sides with well-known geometric objects such as hyper-rectangles, parallel line segments and hyper-spheres. In this manner, imprecision and uncertainty can be explicitly modeled as an inherent characteristic of the model. This is in contrast to the usual approach of using vectors to model activities and/or constraints and then, subsequently, imposing some further constraints in the model to accommodate imprecision and uncertainties. The unifying duality structure is then applied to these models to understand and interpret the marginal prices. The key observation is that the optimal solutions to these dual problems are comprised of two parts: a traditional “centrality” component along with a “robustness” component.

A decomposition approach for the car resequencing problem with selectivity banks

An important decision problem when mass-producing customized product to order is the sequencing problem, which decides on the succession of models launched down a mixed-model assembly line. To avoid work overload of workforce the car sequencing problem restricts the maximum occurrence of labor-intensive options, e.g., a sunroof, in a subsequence of a certain length by applying sequencing rules. In the real-world, frequently perturbations occur stirring up an initially planed sequence, so that a resequencing is required. This paper treats the car resequencing problem where a selectivity bank, which is a special form of buffer organization consisting of parallel line segments without assembly operations, is applied to reshuffle a given initial sequence and rule violations are to be minimized. The problem is formalized and suited heuristic solution procedures are presented and tested. Furthermore, the impact of differently sized mix-banks on resequencing flexibility is investigated.

Effects of Orientation and Contrast upon Targets in Straight and Curved Arrays

A regular array of black squares against a gray background increases the threshold for a light disk in an intersection of the alleys separating the squares, an illusion variously called the extinction illusion, "blanking" phenomenon, or "vanishing disk". Curving the alleys (making the squares into curved "tetragons") further increases the thresholds for both light and dark disks. This raises three questions: (1) Do the edges of the tetragons interact with similarly oriented components of a target? (2) Is blanking a different phenomenon from the obscuring (more moderate increase in threshold in the presence of an array) that affects dark disks, or is blanking simply weaker for dark disks? (3) Is blanking a function of light versus dark targets or dependent upon contrast relative to the polarity of the inducing array? We replaced the target disks with parallel line segments to explore the influence of orientation of the line segments relative to the nearby orientation of the alleys. We show that the blanking phenomenon is sensitive to the orientation of the line segments, while the weaker obscuring of dark targets is not. We also examine these effects with white tetragons. Reversing the polarity of the tetragons exchanged which line segments were orientation-sensitive, although the effectiveness of white tetragons for blanking was weaker than that of black tetragons. We consider possible reasons why white tetragons may be less effective than black tetragonsunder our conditions.

The Three-Dimensional Entity Creation Algorithm for Surface Reconstruction Based on Two-Dimensional Contour Lines

By the use of "cut and suture" algorithm and the introduction of control points, a three-dimensional entity creation algorithm was proposed, with the characteristics of the local flat taken into account. This method cut the adjacent contour lines into two parallel line segments through the automatic search of feature contour's control points (or human interaction selection). After the construction of unconstrained Delaunay triangulation network on the basis of lines' planar points, line sections were sutured from the incisions, followed by the completion the three-dimensional entity surface reconstruction of contours. The multi-layers ore profile data based on drilling geological interpretation were tested. The results show that this algorithm is fast and reliable. The reconstructed three-dimensional surface is smooth and natural, similar to the actual surface morphology.The method bears a practical merit for assisting the interpretation of three-dimensional geological forms in geological survey.

Viviani's Theorem and Its Extension

SummaryViviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant.Let us say that a polygon has the CVS property if the sum of distances from any inner point to its sides is constant. An amazing converse of Viviani's theorem is deduced: if just three noncollinear points inside a convex polygon have equal sums of distances then the polygon has the CVS property. For concave polygons the situation is quite different. For polyhedra analogous results are deduced.

A detection method for streak artifacts and radiological noise in a non-uniform region in a CT image

By using the CT images obtained by subtracting two CT images acquired under the same conditions and slice locations, we have devised a method for detecting streak artifacts in non-uniform regions and only radiological noise components in CT images. A chest phantom was scanned using 16- and 64-multidetector row helical CT scanners with various mAs values at 120 kVp. The upper lung slice image was employed as a target image for evaluating the streak artifacts and radiological noise. One hundred parallel line segments with a length of 80 pixels were placed on the subtracted CT image, and the largest CT value in each CT value profile was employed as a feature variable of the streak artifacts; these feature variables were analyzed with the extreme value theory (Gumbel distribution). To detect only the radiological noise, all CT values contained in the 100 line profile were plotted on normal probability paper and the standard deviation was estimated from the inclination of its fitted line for the CT value plots. The two detection methods devised in this study were able to evaluate the streak artifacts and radiological noise in the CT images with high accuracy.

Statistical characteristics of streak artifacts on CT images: Relationship between streak artifacts and mA s values

The purpose of this study is to investigate how streak artifacts on computed tomography (CT) images vary with reduction in radiation doses by assessing the quantitative relationship between the streak artifacts and milliampere-time product (mA s) values. A commercially available chest phantom was used to measure the streak artifacts on the CT images obtained using a 4- and 16-multidetector-row helical CT scanners with various mA s values at a constant tube voltage of 120 kVp. The cardiac slice image was employed as a target image for evaluating the streak artifacts on the CT image. Eighty parallel line segments with a length of 20 pixels were placed perpendicular to numerous streak artifacts on the cardiac slice image, and the largest difference between adjacent CT values in each of the 80 CT-value profiles of these line segments was employed as a feature variable of streak artifacts; these feature variables have been analyzed by the extreme value theory. The largest difference between adjacent CT values in each CT-value profile can be statistically modeled by a Gumbel distribution. Further, the maximum level of streak artifacts on CT images that will be tolerated for clinical use and low-dose CT screening examination was expected to be estimated using the location parameter in the Gumbel distribution.

Design of sharp-rejection, compact, wideband bandstop filters

A general procedure is described to design a sharp-rejection wideband bandstop filter by using interference of the signals propagating through two parallel transmission line segments having different electrical lengths and characteristic impedances. Bandwidth and rejection level of the filters can be controlled by changing the impedances of the lines. A simple transmission line model is used for filter analysis. Design graphs are presented. Theoretical prediction is verified by fabricating two filters in microstrip technology. Good agreements is obtained among theoretical prediction, full-wave simulation and measurements.

Analysis of streak artefacts on CT images using statistics of extremes

We have analysed the statistical characteristics of streak artefacts on CT images using the statistics of extremes, and have devised a new method of evaluating streak artefacts on CT images. The CT images of four polymer tubes placed on the chest wall of a commercially available chest phantom were used as the target objects for our analysis. 40 parallel line segments with a length of 20 pixels were placed perpendicular to numerous streak artefacts on the polymer tube image, and the largest difference between adjacent CT values in each of the 40 CT value profiles of these line-segments was employed as a feature variable of a streak artefact; these feature variables have been analysed by extreme value theory. Using the mean rank method, a Gumbel distribution was shown to be the most suitable extreme value distribution for the largest difference between adjacent CT values in each CT value profile. This enabled us to demonstrate that the streak artefacts on CT images can be statistically modelled by a Gumbel distribution. Both the location parameter and the scale parameter of the estimated Gumbel probability density distribution were large on the CT slices in which the shoulder bone or liver was included.

On intersecting a set of parallel line segments with a convex polygon of minimum area

Let S = {l1, l2, l3, . . . , ln} be a set of n vertical line segments in the plane. Though not essential, to simplify proofs we assume that no two li ’s are on the same vertical line. A convex polygon weakly intersects S if it contains a point of each line segment on its boundary or interior. In this paper, we propose an O(n logn) algorithm for the problem of finding a minimum area convex polygon that weakly intersects S. The principal motivation behind this paper is the open problem proposed by Tamir [5] at the fourth Computational Geometry day at NYU to decide if there exists a convex polygon whose boundary intersects a set of arbitrarily oriented line segments.

Output-sensitive algorithms for optimally constructing the upper envelope of straight line segments in parallel

The importance of the sensitivity of an algorithm to the output size of a problem is well-known especially if the upper bound on the output size is known to be not too large. In this paper we focus on the problem of designing very fast parallel algorithms for constructing the upper envelope of straight-line segments that achieve the O ( n log H ) work-bound for input size n and output size H. When the output size is small, our algorithms run faster than the algorithms whose running times are sensitive only to the input size. Since the upper bound on the output size of the upper envelop problem is known to be small ( n α ( n ) ), where α ( n ) is a slowly growing inverse-Ackerman's function, the algorithms are no worse in cost than the previous algorithms in the worst case of the output size. Our algorithms are designed for the arbitrary CRCW PRAM model. We first describe an O ( log n · ( log H + log log n ) ) time deterministic algorithm for the problem, that achieves O ( n log H ) work bound for H = Ω ( log n ) . We then present a fast randomized algorithm that runs in expected time O ( log H · log log n ) with high probability and does O ( n log H ) work. For log H = Ω ( log log n ) , we can achieve the running time of O ( log H ) while simultaneously keeping the work optimal. We also present a fast randomized algorithm that runs in O ˜ ( log n / log k ) time with nk processors, k > log Ω ( 1 ) n . The algorithms do not assume any prior input distribution and the running times hold with high probability.

Immune evolutionary algorithms with domain knowledge for simultaneous localization and mapping

Immune evolutionary algorithms with domain knowledge were presented to solve the problem of simultaneous localization and mapping for a mobile robot in unknown environments. Two operators with domain knowledge were designed in algorithms, where the feature of parallel line segments without the problem of data association was used to construct a vaccination operator, and the characters of convex vertices in polygonal obstacle were extended to develop a pulling operator of key point grid. The experimental results of a real mobile robot show that the computational expensiveness of algorithms designed is less than other evolutionary algorithms for simultaneous localization and mapping and the maps obtained are very accurate. Because immune evolutionary algorithms with domain knowledge have some advantages, the convergence rate of designed algorithms is about 44% higher than those of other algorithms.

Protein structure comparison using bipartite graph matching and its application to protein structure classification.

A measure of protein structure similarity is calculated from the matching of pairs of secondary structure elements between two proteins. The interaction of each pair was estimated from their axial line segments and combined with other geometric features to produce an optimal discrimination between intrafamily and interfamily relationships. The matching used a fast bipartite graph-matching algorithm that avoids the computational complexity of searching for the full subgraph isomorphism between the two sets of interactions. The main algorithm used was the "stable marriage" algorithm, which works on the ranked "preferences" of one interaction for another. The method takes 1/10 of a second for a typical comparison making it suitable as a fast pre-filter for slower, more exhaustive approaches. An application to protein structure classification is described.

A new variant of the barberpole effect: Psychophysical data and computer simulations

The classic barberpole effect shows that perceived direction of motion of parallel line segments depends on the orientation of the frame defined by segment end points. A stimulus configuration was created by crossing two oblique barberpoles. Perceived motion in the crossed portion of the configuration is bi-stable, alternating between two oblique directions defined by the two component barberpoles. Ratings of dominance of perceived motion direction in the crossed portion of two barberpoles of different width and orientation revealed a strong preference for the wider component barberpole and a weak preference for the nearer-to-vertical component barberpole. A network model is presented in which each unit inhibits units with different direction sensitivity and co-extensive receptive fields, and excites units with equal direction sensitivity and neighboring receptive fields. Simulations of the temporal evolution of the spatial activity profile exhibit the effect of barberpole width and the bi-stability of percepts. Fatigue of highly adapted units enables the gradual emergence of non-adapted units. Small initial variations can lead to profound differences in the final state of the system, explaining the quasi-random fluctuation between the two perceptual variants.

Minimizing the total projection of a set of vectors, with applications to layered manufacturing

In layered manufacturing (LM), a three-dimensional polyhedral solid is built as a stack of two-dimensional slices. Each slice (a polygon) is built by filling its interior with a sequence of parallel line segments (of some small non-zero width), in a process called hatching. A critical step in hatching is choosing a direction which minimizes the number of segments. In this paper, this problem is approximated as the problem of finding a direction which minimizes the total projected length of a certain set of vectors. Efficient algorithms are proposed for the latter problem, using techniques from computational geometry. Experimental and theoretical analyses show that this approach yields results that approximate closely the optimal solution to the hatching problem. Extensions of these results to several related problems are also discussed.

POINT AND LINE SEGMENT RECONSTRUCTION FROM VISIBILITY INFORMATION

In general, visibility reconstruction problems involve determining a set of objects in the plane that exhibit a specified set of visibility constraints. In this paper, an algorithm is presented for reconstructing a set of parallel line segments from specified visibility information contained in an extended endpoint visibility graph. The algorithm runs in polynomial time and relies on simple vector arithmetic to generate a system of linear inequalities. A related problem, solvable with the same technique, is the point reconstruction problem, in which the cyclic ordering and the x-coordinates of a set of points is specified. A second contribution is the definition of an extension of the visibility graph called the Stab Graph, which contains extra visibility information.

On the Geometry of Locally Nonconical Convex Sets

A convex subset Q of a Hausdorff topological vector space is called locally nonconical (LNC) if for every two points x,y∈Q there is a relative neighborhood U of x in Q such that U+\(\tfrac{1}{2}\)(y-x) ⊂Q. A geometric characterization (Theorem 2.2) of closed LNC sets with nonempty interior in a Hilbert space is supplied. It states that any proper line segment ]x,y[ contained in bd(Q), the topological boundary of Q, lies inside a relative neighborhood in bd(Q) composed of parallel line segments. It is shown that one half of this characterization, at least, generalizes to the setting of a locally convex Hausdorff topological vector space (LCHTVS). This leads to the observation that the set ext(Q) of extreme points of any LNC set Q in an LCHTVS is closed. Finally, it is proven that, in the same setting, all LNC sets are uniformly stable and, hence, stable.

An O( n3) time algorithm for recognizing threshold dimension 2 graphs

Threshold dimension 2 graphs are the (edge-)intersection of two threshold graphs T 1 and T 2. Moreover they are the intersection graphs of points, axially parallel line segments and rectangles in the first quadrant of the Euclidean plane subject to the following constraints: 1. (1) line segments have one endpoint on one of the axes, 2. (2) the lower left corner of each rectangle is the origin and 3. (3) except for the above, every point, endpoint of a line segment and corner of a rectangle has unique x and y coordinates. Ma (1993) showed that the above geometrical representation called rectangle model can be constructed in O( n 3) time providing the vertices that correspond to the rectangles are known. In this paper, we prove that there always exists a rectangle model in which the rectangles correspond to the vertices common to all maximum cliques. As the maximum cliques of a threshold dimension 2 graph can be found in O( n 3), the overall running time of our recognition algorithm is O( n 3), which compares favorably to the previous approaches with time complexity O( n 5) and O( n 4), respectively.

A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains

We introduce a new method for computing the geodesic Voronoi diagram of point sites in a simple polygon and other restricted polygonal domains. Our method combines a sweep of the polygonal domain with the merging step of a usual divide-and-conquer algorithm. The time complexity is O..nC k/ log.nC k// where n is the number of vertices and k is the number of points, improving upon previously known bounds. Space is O.nC k/. Other polygonal domains where our method is applicable include (among others) a polygonal domain of parallel disjoint line segments and a polygonal domain of rectangles in the L1 metric.