Pair Of Parallel Lines Research Articles

Using points at infinity for parameter decoupling in camera calibration

The majority of camera calibration methods, including the Gold Standard algorithm, use point-based information and simultaneously estimate all calibration parameters. In contrast, we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages. We formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points. Unlike previous vanishing point methods, parallel line pairs are not required. Additionally, the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters. We compare this method with vanishing point methods and the Gold Standard algorithm and demonstrate that it has comparable performance.

A simple centroid-based method to find the principal point of an image plane for a pincushion distortion

A method to find the principal point of an image plane is proposed in this paper for the case of a pincushion distortion. The analytical foundation of the method is that a pincushion distortion causes a pair of distortion-free parallel lines to become a pair of curves, which are termed conjugate curves in this paper, and the shortest line segment connecting the pair of conjugate curves passes through the principal point. Thus, the principal point can be obtained by computing the intersection point of the shortest line segments of different pairs of conjugate curves. However, the case for a digital image is a bit different from the above. For the same pair of conjugate curves, there is a group of shortest line segments, which is called a shortest segment set. The coincidence region of the shortest segment sets of different pairs of conjugate curves is a polygon, the centroid of which is considered as the principal point. Therefore, the proposed method firstly needs to capture the pincushion-distorted images of some pairs of parallel lines, secondly to find the corresponding polygon and lastly, to calculate the centroid point. A synthetic image and a real image are tested using this method, and the results are satisfying.

Left-hemisphere dominance in early nociceptive processing in the human parasylvian cortex

Pain perception comprises sensory and emotional dimensions. While the emotional experience is thought to be represented in the right hemisphere, we here report a left-hemisphere dominance for the early sensory component of pain perception using brain electrical source analysis of laser-evoked potentials. Ten right-handed subjects underwent several series of laser radiant heat stimuli to pairs of parallel lines on the dorsum of the left or right hand. Stimulus location and intensity were randomised independently. The sensory-discriminative aspects of pain were emphasised by asking the subjects to perform either a spatial or an intensity discrimination task and were contrasted with active distraction by mental arithmetics. Pain ratings obtained after each of the laser stimulus series revealed an analgesic effect of distraction (27%, P < 0.001). Four equivalent dipole sources were active in the latency range of 100–200 ms (bilateral operculoinsular cortex, midcingulate gyrus, postcentral gyrus). The sources in the operculoinsular cortex exhibited (a) the shortest peak latency (155 ± 6 ms), (b) the most pronounced enhancement during spatial and intensity discrimination tasks compared to active distraction (43%, P < 0.001), and (c) a significantly stronger source activity in the left hemisphere independent of stimulation side (23%, P < 0.05). The distribution of these sources extended into the dorsal insula. The postcentral source had the longest peak latency (180 ± 7 ms); its source strength was task-dependent (25%, P = 0.051) but exhibited no hemisphere dominance. The midcingulate source had an intermediate peak latency (169 ± 7 ms). Its source strength was modulated by tasks, but this modulation was significant only in the latency range >200 ms (46%, P < 0.001). These findings suggest a dominant role of the left frontal operculum and adjacent dorsal insula in the early sensory-discriminative dimensions of pain processing. This region has been proposed to be the cortical projection target of nociceptive pathways from the spinal cord to the ventroposteroinferior and ventromedial (its posterior part: VMpo) thalamic nuclei.

Evaluation of angular error between two lines

The error caused by the fitting of a set of data points to two lines having a specified angle is defined as the angular error. The evaluation of angular error needs to find two pairs of parallel lines that follow the angular constraint and bound the data points under the minimum zone criterion. The evaluation of angular error is difficult in mathematics, so it is usually simplified by treating one line as the datum and the form error of the other line calculated from the datum as the solution. The datum is assumed to be perfect that doesn’t tell the real properties of the actual line but gives incorrect solutions in general. To give an exact solution to the angular error problem based on the minimum zone criterion, a new mathematical model is proposed in this paper. The basic idea of this model is to rotate the data points of one line to the same direction as that of the other line so that the evaluation of angular error is simplified as solving a straightness problem. The angular error obtained from the proposed model is proved to be minimum. The proposed model offers a simple approach to solve the tough angular error problem, and it also provides a feasible tool to explore more complicated problems, like 3D angular error and polygon error.

Polygon Graph Recognition

For any fixed integerk≥2, define the class ofk-polygon graphs as the intersection graphs of chords inside a convexk-polygon, where the endpoints of each chord lie on two different sides. The case wherek=2 is degenerate; for our purpose, we view any pair of parallel lines as a 2-polygon. Hence, polygon graphs are all circle graphs. Interest in such graphs arises since a number of intractable problems on circle graphs can be solved in polynomial time onk-polygon graphs, for any fixedk, given a polygon representation of the input graph. In this paper we show that determining whether a given circle graph is ak-polygon graph, for any fixedk, can be solved inO(4kn2) time. The algorithm exploits the structure of a decomposition tree of the input graph and produces ak-polygon representation, if one exists. In contrast, we show that determining the minimum value ofkis NP-complete.

A high-speed algorithm for line detection

A high-speed method for line detection is proposed in this paper. By shifting the black points in a black/white image I, a parallel line for each straight line on I will be generated. Through the use of the geometric property on a pair of parallel lines, the parameter sets of those lines possibly on I can be obtained immediately. Since the transform from image space to parameter space is one to few points, the proposed method can significantly reduce the number of transforms for evaluating possible parameter sets. Experimental results are also given to show the correctness and effectiveness of the proposed method.

Teaching Conceptual Knowledge with Multiple-Related Exemplars: Enhancement of Concept Formation, Transfer, and Absence of Stimulus Overselection

In Exp. I ( N = 32), 4 1/2-yr.-old children discriminated between two stimulus compounds, multiple and related stimulus components displayed together (3 pairs of parallel lines vs 3 pairs of nonparallel lines) or multiple but unrelated displayed components (3 unrelated objects vs 3 other unrelated objects). Although between-group acquisition was the same, significantly more children trained with multiple-related stimulus components responded appropriately to each of the relevant components of the compound when they were presented separately during test trials, i.e., less stimulus overselection. In Exp. II ( N = 15), multiple-related training of parallelness led to faster concept attainment, and proportionally more children got almost perfect transfer scores than when training consisted of presenting pairs of single examples of parallel and nonparallel lines during each trial.

Modulation of event-related potentials by the repetition of drawings of novel objects

In experiment 1, event-related potentials (ERPs) were recorded from 13 scalp sites while subjects viewed a series of line drawings of novel objects. Most of the drawings were of objects that were structurally possible, while the remainder were of structurally impossible objects; the task was to respond to each presentation of an impossible object. Approximately one third of the possible objects were repetitions of the immediately preceding drawing. Compared to the ERPs elicited by first presentations, the ERPs elicited by repetitions were more negative-going. This negative repetition effect comprised two temporally and topographically distinct components. In experiment 2, subjects monitored drawings of unstructured patterns, so as to detect occasional ‘targets’ containing a pair of parallel lines. Repetitions of ‘non-target’ patterns elicited ERPs which were largely indistinguishable from those elicited by first presentations. Thus, the negative repetition effects found in experiment 1 are not merely a consequence of repeating visual patterns in a demanding discrimination task. Possible reasons why novel objects should elicit ERP repetition effects opposite in polarity to those observed in tasks employing verbal or meaningful pictorial stimuli are discussed.

Determination of finite strain in bedding surfaces using sedimentary structures and trace fossils: A comparison of techniques

Determination of the two-dimensional finite strain in turbidite bedding surfaces is important in both structural and sedimentological investigations of deformed sediments. The Meguma Group of Nova Scotia is one such sequence, in which the directional distribution of paleocurrent markers has been modified by strain. Previous strain determinations have used sand volcanoes as strain markers, which do not deform homogeneously with their matrix and, hence, may underestimate the true strain ratio. Intraclasts and concretions also suffer inhomogeneous deformation and are of limited use as strain markers. Hexagonal trace fossil networks can provide more reliable strain estimates but are rare. Widths of burrows exposed on bedding surfaces provide a new, straightforward means of measuring strain. Each burrow is represented by a pair of parallel lines. The separation of the lines is proportional to the burrow width, and their direction represents burrow orientation. The lines are tangential to the strain ellipse, which can be discerned despite initial scatter in burrow widths.

The systematics of the tube-dwelling diatom Nitzschia martiana and Nitzschia section Spathulatae

Nitzschia martiana (C. A. Ag.) Van Heurck is a tube-forming diatom of warmer waters. The tubes are rugose externally and contain bundles of long thin cells. The valves bear plain flaps of silica (conopea) externally, which arise near the central raphe system and extend over much of the valve surface; in the light microscope they can be detected as a pair of parallel lines alongside the raphe system. Beneath the conopea the valve arches inwards, so that tube-like canals are formed on the outside of the cell wall. There are no central raphe endings and the fibulae are rib-like. These characters, shown here to be shared by Nz. angularis Wm. Smith, indicate that Nz. martiana should be transferred into the section Spathulatae within the subgenus Nitzschia.

Depth dependent damage profile in stainless steel irradiated with He-ions

Type 316 stainless steel was irradiated with 24 MeV He-ions up to 3.2 × 10 20 ions/m 2 at ambient temperature. A peak in microhardness occurred at a distance of 105 μm from the irradiated surface. Small dislocation loops were seen at depths ranging from 105 to 114 μm with the peak in number density at 110 μm. A pair of parallel lines with a space of 8 μm centered at a distance of 107 μm from the irradiated surface were revealed on the top surface of the specimen by chemical etching after post-irradiation annealing for l h at 1023 K. The parallel lines correspond to arrays of fairly large Frank loops aligned in narrow bands on each side of a region containing helium bubbles. The observed damage profiles agree with those predicted by Littmark and Ziegler.

Plasma polymerized methyl-methacrylate as an electron-beam resist

Plasma polymerized methyl-methacrylate thin film was formed on a glass substrate coated with chromium as a resist for electron-beam lithography. The polymerizations were conducted at two discharge frequencies of 13.56 MHz and 5 KHz using a capacitively coupled discharge electrode system in a bell-jar-type reactor. Delineations were carried out using an electron beam whose diameter and acceleration voltage were 0.5 μm and 20 kV, respectively. As a test pattern, 25 pairs of parallel lines and spaces each having a 10-μm width were delineated in a rectangular area of 0.5×0.5 mm2. Each line of 10-μm width was depicted by sweeping over using the electron beam with 20 repetitions. The patterns were developed on the chromium by CCl4 plasma etching.

Spatial resolution and nonlinearities of simple cells in the cat visual cortex measured with parallel line pairs.

The spatial resolution of simple cells in cat visual cortex was measured by stimulation with pairs of 6? wide parallel light bars of various spacings. These double lines were moved across the receptive field and were taken as resolved if there was a 10% deflection between the double peak responses of cells. As a control, recordings were also made from several geniculate fibers. The smallest bar separations resolved by simple cells were larger than those which have been found for cells of the lateral geniculate nucleus (LGN), although the smallest cortical receptive field centers were as small as those of LGN-cells. The correlation between optimal resolving power of a cell and the width of its excitatory receptive field was much weaker in cortical simple cells than in LGN cells. In contrast to the LGN, the double line responses of most simple cells differ markedly from an additive superposition of two single line responses spaced according to the actual interline distance. As possible mechanisms underlying these nonlinearities three different connectivity schemes were investigated. Two of these models were based on receptive field concepts; the third one used intracortical circuits. Only the latter model could explain all the nonlinear effects seen in the neurophysiological experiments.

Attraction of parallels as a function of intercontour distance.

Pollack (1964) found attraction of simultaneously presented parallel lines under fixation. Using the Delboeuf figure, Ogasawara ( 1952) found that attraction of concentric circles increased, then decreased as separation between the contours increased. Widening the space between the parallels of the Poggendorf figure results in an increased illusory effect (e.g., Hill, 1971), suggesting that attraction increases as separation increases. The distance between a pair of parallel lines was varied from 3 to 15 rnm. in 2-mm. steps. Lines were located to one side of a central fixation dot, with comparison dots, whose spacing varied about that of the corresponding test lines, equidistant on the opposite side. Control stimuli merely substituted dots for tesc lines. No stimulus exceeded a total visual angle of 3. Stimuli were presented tachistoscopically for 250 msec. to two trained adult Ss, who judged the spacing of the dots relative to that of the lines. A modified method of constant stimuli was used, converting attraction magnitudes into percentages by subtracting control PSEs from tesc PSEs over 16 trials. For both Ss, attraction was small (0 to 4%) for 3- to 9-mm. separations, but a sharp increase occurred at 11 mrn. ( 13% co 14% ). For S1, attraction with wider separations increased and leveled off, while the effect declined and leveled off for S2. Results are considered consistent with Ogasawara's findings. (With wider separations, the effect would be expected to decrease for S1.) The occurrence of attraction under the present restricted viewing conditions suggests that it is a basic contour interaction process. Implications for explanation of the Poggendorf illusion are currently under investigation.

Transverse field effects in nematic liquid crystals

A novel electro-optic effect has been observed in thin homeotropic nematic layers. Electrodes, such as a pair of parallel lines, are located on a planar surface in contact with the liquid. Deformation of the homeotropic ordering occurs when the applied field exceeds a threshold strength. Induced optical birefringence and diffraction have been observed, and electrically controlled optical transmission and reflection have been attained. Experimental data are given for a cyano-aniline mixture with ε∥ − ε⊥ &amp;gt; 0 and for negative-anisotropy materials.

Solids of Constant Breadth

The Reuleaux triangle of Figure 1(a) is obtained by drawing three circular arcs of radius d with centres at the vertices of an equilateral triangle of side d. It can be rolled between a pair of parallel lines at distance d apart and is said to be of constant breadth d.Applying an analogous construction in three dimensions to a regular tetrahedron of side d, we obtain a solid figure bounded by four spherical triangles intersecting in six circular arcs, the centre of each spherical portion being at the opposite vertex of the tetrahedron and its radius of curvature being d. This figure has two modes of rolling between parallel planes. In the first mode a vertex touches one of the planes and the opposite spherical surface rolls on the other; in the second mode, opposite circular edges touch the planes. The distance separating the planes in the first mode is d; in the second mode, the separation is d when the points of contact with the tetrahedron are at the opposite ends of the circular arcs, but this distance increases to d(√3 − ½√2), or l·025d, when the centres of the circular edges touch the planes. By slightly rounding one edge in each of the three opposed pairs, a solid of constant breadth may be produced. The geometry of this process is illustrated at Figure 1(b).

A class of exact, time-dependent, free-surface flows

Attention is drawn to a class of inviscid irrotational flows which satisfy the conditions at a time-dependent free surface exactly. The flows are related to the ellipsoids of Dirichlet (1860).Depending on a parameter P, the cross-section may take the form of a variable ellipse (P 0) or a pair of parallel lines (P = 0). The elliptical case was investigated both theoretically and experimentally by Taylor (1960). The hyperbolic case (P > 0) is remarkable in that the flow develops a singularity when the angle between the asymptotes approaches a right-angle. It is suggested that this solution represents a possible instability near the crest of a standing gravity wave of large amplitude.In the intermediate case (P = 0) the solution describes an open-channel flow in which the fluid filaments are stretched uniformly in a horizontal direction. The latter flow is demonstrated experimentally.

Impact of instruction on development of deaf children's originality of thinking.

Presently there are four different methods (Kohl, 1966) employed in the instruction of deaf children: (a) the pure oral method, (b) the oral method, (c) the natural language method, and (d) the Rochester or combined system method Conflicting views exist about the relative usefulness of these methods or their combinations. However, the originality scores obtained on Torrance's Thinking Creatively With Picrures Test might favor deaf children taught under the natural language method as opposed to those taught under the combined system method. The 35 second grade deaf boys and girls came from a School for the Deaf located in the Southeastern United States and were of different ages, mental, and hearing abilities. These Ss were divided at the beginning of the year into four classes, each one being taught by a different teacher. Three classes (N = 27) were taught by teachers who employed the combined-system method while the fourth class (N = 8) was taught by a teacher who used the natural language method. In the first task of the creativity tesr, Thinking Creatively With Pictures, Form A (Torrance, 1966), Ss are asked to draw a picture in which a piece of colored paper shaped like a pear with adhesive backing is an integral part. In the second task, Ss draw pictures by adding lines to 10 incomplete figures. In the third task, pictures using 30 pairs of parallel lines are drawn. In each task, Ss are instructed to produce pictures which are both unusually original and extremely elaborate. These tasks involve acquisition of information from relationships among stimuli which are seen repeatedly and perceiving stimuli in different ways. After the imposed time on each task was over, a teacher for the deaf helped Ss record their titles individually. Each task was scored for originality by the writer according to the standard scoring directions. This score is determined for each response separately and is based on the weight given each response. Responses showing statistical infrequency were assigned scoring weights of two points; obvious, irrelevant, and incomprehensible responses were assigned weights of zero. The means (and standard deviations) for groups with the natural language method and the combined-system method were 26 (4.3) and 22.7 (6.8) respectively (t = 1.66; F = 2.45, df = 1, 0 > .Or). These Ss constitute two independent groups and the measure of originality constitutes an ordinal scale. The results obtained by applying the MannWhitney U test indicate that the quality and quantity of creative originality scores of these two groups of deaf children is not a sufficient basis for concluding that either method of instruction is superior.

Effects of Direction upon Speed of Mirror-Drawing

Method: Subjects. Forty-eight right-handed girls served as the Ss. They were randomly selected from a group of 303 right-handed girls in a third semester course in English, required of all Liberal Arts students. Apparatus and materials. Whipple's mirror-drawing apparatus,2 two stop-watches, an accumulative timer, and a stimulus-sheet (Fig. 1) were used in this study. The stimulus-sheet shows eight pairs of parallel lines (radii ), each beginning 3/8 in. from their common center. The parallel lines of each radius were 31/8 in. long and 1/16 in. apart and were divided at 1/g-in. intervals into 25 cells or parts. The radii proceeded in the eight cardinal directions. Fig. 1 shows the directions as found on the stimulus-sheet; not as reflected in the mirror. Procedure. S was seated at a table facing the apparatus with the stimulus-sheet flat upon the table before her (with the result that the vertical direction required movements in toward and out from the body and the horizontal direction required movements to the left and right of the center of the body). E was seated to the left beside her with the timing devices out of S's sight. After being shown the stimulus-sheet in the mirror, S was instructed to draw a line with a pencil between a specific set of parallel lines as rapidly and as accurately as possible. Beginnltng with the division or cell closest to the center, the pencil mark was required to pass through every one of them. If the pencil left the confines of the parallel lines, S had to reenter at the point of departure. S was told which radius she was to trace and how it appeared in the mirror. S closed her eyes and E placed the point of the pencil at the beginning point the division nearest the center of the sheet and at 'Go,' she opened her eyes and began tracing the path. Each S traced the eight radii once, and the sequence of radii was counterbalanced among the 48 Ss. Five measures were obtained from every S for every position: the time required to trace (1) the first half of every radius; (2) the second half; (3) the entire radius; (4) the time outside the boundary lines; and (5 the time within them. Time was measured in units of 1/5 sec.

Hering's illusion.

A series of optical experiments was designed to investigate several factors that may help to explain the Hering Illusion. In this illusion subjects are shown two vertical lines crossed by angular lines which stem from the point midway between them; subjects then report the straight pair of parallel lines as appearing curved in a bow‐shaped manner.Findings indicate increased perceived curvature of the lines when the angles presented are greater in number or size. The illusion is further increased if the angles and lines are shown sequentially rather than simultaneously. Similar results occur on presentation of a circle cutting through the rays of a quadrangular star; the circle looks ‘squarish’. When lines or circles are presented to one eye only while the other eye receives the angles or star, this illusion still holds.All perceived curvature shows anti‐apical distortion, which appears due to neuro‐cortical after‐effects underlying visual perception.