Divergence Thresholds as Functions of Temporal Separation, Spatial Separation, and Retinal Locus

1983 ◽  
Vol 56 (2) ◽  
pp. 459-468 ◽  
Author(s):  
Marjorie J. Di Orio ◽  
Thomas L. Harrington
Keyword(s):  
Spatial Separation ◽  
Retinal Locus ◽  
Line Density ◽  
Information Analysis ◽  
Angular Divergence ◽  
Temporal Separation ◽  
Line Segments ◽  
Fast Motion ◽  
Straight Lines ◽  
Form Information

Human thresholds were measured for the detection of angular divergence between straight lines using pairs of line segments. The dependence of these thresholds on temporal separation between the two lines, spatial separation, and retinal locus was assessed. Results were comparable to prior divergence thresholds obtained by Harrington and Harrington in their study of “blur patterns.” In blur patterns motion parameters may be processed partly or wholly as form information rather than as motion information per se. Harrington and Harrington had used moderate blurring velocities, for which information on both motion and form were present. Observers may have been responding either to motion or to form. The study reported here used briefly presented two-line “blur patterns” with only form information. Analysis suggested that the form components of fast motion-produced blur patterns could be processed by the human visual system. Neither temporal nor spatial separation was a significant determiner of thresholds in accordance with Harrington and Harrington who found no effect of blur-line density in the range studied. Retinal locus was a factor as it was with blur patterns. Some possible mechanisms for the detection of divergence indicated by these results are discussed.

scholarly journals Comparison of the Spatial Limits on Direction Selectivity in Visual Areas MT and V1

2005 ◽  
Vol 93 (3) ◽  
pp. 1235-1245 ◽  
Author(s):  
Mark M. Churchland ◽  
Nicholas J. Priebe ◽  
Stephen G. Lisberger
Keyword(s):  
Apparent Motion ◽  
Great Majority ◽  
Spatial Separation ◽  
Direction Selectivity ◽  
Temporal Separation ◽  
Temporal Area ◽  
Mean Values ◽  
V1 Neurons ◽  
Preferred Direction ◽  
The Difference

We recorded responses to apparent motion from directionally selective neurons in primary visual cortex (V1) of anesthetized monkeys and middle temporal area (MT) of awake monkeys. Apparent motion consisted of multiple stationary stimulus flashes presented in sequence, characterized by their temporal separation (Δ t) and spatial separation (Δ x). Stimuli were 8° square patterns of 100% correlated random dots that moved at apparent speeds of 16 or 32°/s. For both V1 and MT, the difference between the response to the preferred and null directions declined with increasing flash separation. For each neuron, we estimated the maximum flash separation for which directionally selective responses were observed. For the range of speeds we used, Δ x provided a better description of the limitation on directional responses than did Δ t. When comparing MT and V1 neurons of similar preferred speed, there was no difference in the maximum Δ x between our samples from the two areas. In both V1 and MT, the great majority of neurons had maximal values of Δ x in the 0.25–1° range. Mean values were almost identical between the two areas. For most neurons, larger flash separations led to both weaker responses to the preferred direction and increased responses to the opposite direction. The former mechanism was slightly more dominant in MT and the latter slightly more dominant in V1. We conclude that V1 and MT neurons lose direction selectivity for similar values of Δ x, supporting the hypothesis that basic direction selectivity in MT is inherited from V1, at least over the range of stimulus speeds represented by both areas.

scholarly journals MÖBIUS TRANSFORMATIONS OF POLYGONS AND PARTITIONS OF 3-SPACE

2008 ◽  
Vol 17 (11) ◽  
pp. 1401-1413 ◽  
Author(s):  
RICHARD RANDELL ◽  
JONATHAN SIMON ◽  
JOSHUA TOKLE
Keyword(s):  
Simple Closed Curve ◽  
Exact Formula ◽  
Mirror Image ◽  
Line Segments ◽  
Large N ◽  
Möbius Group ◽  
Euclidean Metrics ◽  
Straight Lines ◽  
Figure Eight Knot ◽  
Polygonal Knots

The image of a polygonal knot K under a spherical inversion of ℝ3 ∪ ∞ is a simple closed curve made of arcs of circles, perhaps some line segments, having the same knot type as the mirror image of K. But suppose we reconnect the vertices of the inverted polygon with straight lines, making a new polygon [Formula: see text]. This may be a different knot type. For example, a certain 7-segment figure-eight knot can be transformed to a figure-eight knot, a trefoil, or an unknot, by selecting different inverting spheres. Which knot types can be obtained from a given original polygon K under this process? We show that for large n, most n-segment knot types cannot be reached from one initial n-segment polygon, using a single inversion or even the whole Möbius group. The number of knot types is bounded by the number of complementary domains of a certain system of round 2-spheres in ℝ3. We show the number of domains is at most polynomial in the number of spheres, and the number of spheres is itself a polynomial function of the number of edges of the original polygon. In the analysis, we obtain an exact formula for the number of complementary domains of any collection of round 2-spheres in ℝ3. On the other hand, the number of knot types that can be represented by n-segment polygons is exponential in n. Our construction can be interpreted as a particular instance of building polygonal knots in non-Euclidean metrics. In particular, start with a list of n vertices in ℝ3 and connect them with arcs of circles instead of line segments: Which knots can be obtained? Our polygonal inversion construction is equivalent to picking one fixed point p ∈ ℝ3 and replacing each edge of K by an arc of the circle determined by p and the endpoints of the edge.

Size Distortions: Space-Time Interaction

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 114-114
Author(s):  
S Chukova ◽  
V E Gauzelman
Keyword(s):  
Random Order ◽  
Spatial Separation ◽  
Experimental Session ◽  
Reference Stimulus ◽  
Temporal Separation ◽  
Memory Processing ◽  
Modified Method ◽  
Time Interaction ◽  
Modular Model ◽  
Size Distortions

We used a modified method of constant stimuli to measure spatial interval discrimination thresholds. Horizontal intervals were indicated by a pair of dark vertical lines on a bright background. In each experimental session, thresholds were measured for seven reference stimuli, presented in random order. Reference stimulus separations varied from 9.52 to 16.66 min−1 in increments of 1.95 min−1. The interstimulus interval (ISI) was varied (50, 200, 500, and 1000 ms) between experimental sessions. Stimulus duration was constant at 500 ms. For all ISI durations, the point of subjective equality (PSE) for small spatial separation references was less than physical equality, the PSE for larger separations was greater, and the PSE was close to physical equality for reference stimuli in the centre of the range. This result is consistent with the modular model [V D Glezer, 1995 Vision and Mind (Mahwah, NJ: Lawrence Erlbaum)]. However, the magnitude of the PSE shifts was affected by the ISI duration: at 50 and 1000 ms, the small spatial intervals were more underestimated and the large ones were more overestimated than at 200 or 500 ms. The discriminability thresholds based on the slopes of the psychometric functions varied inversely with the ISI duration, but at the ISI of 1000 ms increased again. These findings demonstrate that in the sequential mode of presentation the temporal separation can be as important as the spatial separation distribution in determining the PSE. This suggests that these size distortions result more from memory processing than from spatial processing.

The incidence of killer activity and extracellular proteases in tropical yeast communities

1997 ◽  
Vol 43 (4) ◽  
pp. 328-336 ◽  
Author(s):  
Jacqueline Abranches ◽  
Leda C. Mendonça-Hagler ◽  
Allen N. Hagler ◽  
Paula B. Morais ◽  
Carlos A. Rosa
Keyword(s):  
Killer Toxin ◽  
Spatial Separation ◽  
Extracellular Proteases ◽  
Temporal Separation ◽  
Killer Activity ◽  
Killer Yeasts ◽  
Sporobolomyces Roseus ◽  
Nitrogen Nutrients ◽  
Pichia Kluyveri ◽  
Ascomycetous Yeasts

The presence of killer and proteolytic yeasts was studied among 944 isolates representing 105 species from tropical yeast communities. We found 13 killer toxin producing species, with Pichia kluyveri being the most frequent. Other killer yeast isolates were Candida apis, Candida bombicola, Candida fructus, Candida krusei, Candida sorbosa, Hanseniaspora uvarum, Issatchenkia occidentalis, Kloeckera apis, Kluyveromyces marxianus, Pichia membranaefaciens, Pichia ohmeri-like, and Sporobolomyces roseus. The communities from which killer yeasts were isolated had strains sensitive to them, and there were interspecific and intraspecific differences in the spectra of their killer activities. Pichia kluyveri had the broadest spectra of activity against sensitive isolates, and it apparently produced different toxins. The coexistence of sensitive and killer yeasts using the same substrate suggests that there is spatial separation in microhabitats or temporal separation in different stages of successions. Basidiomycetous yeasts were more frequently proteolytic than ascomycetous yeasts. Extracellular proteases could be important for the yeasts to have access to more nitrogen nutrients and obtain a better balance with available carbon sources.Key words: killer yeasts, extracellular proteases, tropical yeast communities.

Resource partitioning between two species of Ceutorhynchus (Coleoptera: Curculionidae) on Echium plantagineum in a Mediterranean habitat

1993 ◽  
Vol 83 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Guy J. Forrester
Keyword(s):  
Biological Control ◽  
Resource Partitioning ◽  
Spatial Separation ◽  
Temporal Separation ◽  
Southern France ◽  
Early Larval Stage ◽  
Tap Root ◽  
Mediterranean Habitat ◽  
Different Parts ◽  
Original Index

AbstractTwo weevil species, Ceutorhynchus geographicus (Goeze) and C. larvatus Schultze, feed on Echium plantagineum (Boraginaceae) in southern France. This paper shows that they do not compete for resources in the host's native environment. Niche overlaps of the two weevils were measured using the proportional overlap measure and Morisita's original index. The two species showed significant overlap in niche requirements during the egg and early larval stage. During the final two larval instars, larvae feed on different parts of the plant, C. geographicus in the tap root and C. larvatus in the root crown. Spatial separation in niche requirements is augmented by a temporal separation, C. larvatus emerging in the field about one month earlier than C. geographicus. In Europe and in Australia, to which E. plantagineum has been introduced and has become a serious weed, the host-plant has an extended germination period during the autumn. The differences in emergence times of the two species mean that their niches are separated both in time and in space. Should the two species be released into Australia they would not compete for resources. They may, however, be able to displace other species of the stemfeeding guild that are also proposed as candidates for the biological control of E. plantagineum.

A Method of Multi-View Images 3D Restructuring of Discrete Line Segments

2014 ◽  
Vol 644-650 ◽  
pp. 2359-2365
Author(s):  
Xiao Bo Lin
Keyword(s):  
Renewal Process ◽  
Analytical Method ◽  
High Efficiency ◽  
Target Function ◽  
Optimal Result ◽  
Simulation Data ◽  
Linear Restriction ◽  
Line Segments ◽  
Straight Line ◽  
Straight Lines

In this paper, the average reprojection geometrical errors on all images of a spatial straight line is taken as the restructuring and optimization target function to ensure the optimal result to be acquired; a spatial straight line is expressed by use of the Plücker coordinates for the proposal of the analytical method of correcting the double linear restriction on the Plücker coordinates of noise-included spatial straight lines; during the optimization process, to ensure parameters that meet double linear restriction, the iteration renewal process is expressed by at least 4 parameters, to increase the precision of restructuring results. Experiments results derived from simulation data and real images have all demonstrated the high efficiency and precision of the algorithm proposed in this paper.

scholarly journals FPT-ALGORITHMS FOR MINIMUM-BENDS TOURS

2011 ◽  
Vol 21 (02) ◽  
pp. 189-213 ◽  
Author(s):  
VLADIMIR ESTIVILL-CASTRO ◽  
APICHAT HEEDNACRAM ◽  
FRANCIS SURAWEERA
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Fixed Parameter Tractable ◽  
Line Segments ◽  
Fpt Algorithms ◽  
Fixed Parameter ◽  
Axis Parallel ◽  
Np Complete ◽  
Number Of Bends ◽  
Straight Lines

This paper discusses the κ-BENDS TRAVELING SALESMAN PROBLEM. In this NP-complete problem, the inputs are n points in the plane and a positive integer κ, and we are asked whether we can travel in straight lines through these n points with at most κ bends. There are a number of applications where minimizing the number of bends in the tour is desirable because bends are considered very costly. We prove that this problem is fixed-parameter tractable (FPT). The proof is based on the kernelization approach. We also consider the RECTILINEAR κ-BENDS TRAVELING SALESMAN PROBLEM, which requires that the line-segments be axis-parallel. 1 Note that a rectilinear tour with κ bends is a cover with κ-line segments, and therefore a cover by lines. We introduce two types of constraints derived from the distinction between line-segments and lines. We derive FPT-algorithms with different techniques and improved time complexity for these cases.

Un théorème d'unicité pour les hyperplans poissoniens

1974 ◽  
Vol 11 (01) ◽  
pp. 184-189 ◽  
Author(s):  
G. Matheron
Keyword(s):  
Poisson Point Process ◽  
Convex Set ◽  
Compact Convex ◽  
Minkowski Sum ◽  
Line Segments ◽  
Supporting Function ◽  
Compact Convex Set ◽  
Finite Sums ◽  
Tangential Cone ◽  
Straight Lines

A stationary Poisson process of hyperplanes in Rn is characterized (up to an equivalence) by the function θ such that θ(s) is the density of the Poisson point process induced on the straight lines with direction s. The set of these functions θ is a convex cone ℛ1, a basis of which is a simplex Θ, and a given function θ belongs to ℛ1 if and only if it is the supporting function of a symmetrical compact convex set which is a finite Minkowski sum of line segments or the limit of such finite sums. Another application is given concerning the tangential cone at h = 0 of a coveriance function.

scholarly journals The Perceptual Organisation of Visual Elements: Lines

2021 ◽  
Vol 11 (12) ◽  
pp. 1585
Author(s):  
Liliana Albertazzi ◽  
Luisa Canal ◽  
Rocco Micciolo ◽  
Iacopo Hachen
Keyword(s):  
Subjective Evaluation ◽  
Visual Stimuli ◽  
Semantic Differential ◽  
The Other ◽  
Sharp Bound ◽  
Line Segments ◽  
Variable Type ◽  
Visual Elements ◽  
Perceptual Characteristics ◽  
Straight Lines

The aim of this study is to verify the conditions under which a series of visual stimuli (line segments) will be subjectively perceived as visual lines or surfaces employing four experiments. Two experiments were conducted with the method of subjective evaluation of the line segments, and the other two with the Osgood semantic differential. We analysed five variables (thickness, type, orientation, and colour) potentially responsible for the lines’ categorisation. The four experiments gave similar results: higher importance of the variables thickness and type; general lower significance of the variable colour; and general insignificance of the variable orientation. Interestingly, for the variable type, straight lines are evaluated as surfaces more frequently than curved lines and perceived as geometrical, flat, hard, static, rough, sharp, bound, sour, frigid, masculine, cold and passive. Curved lines are prevalently evaluated as lines, and categorised as organic, rounded, soft, dynamic, fluffy, blunt, free, sweet, sensual, feminine, warm and active. These results highlight the specificity of perceptual characteristics for the considered variables and confirm the relevance of the characteristics of variables such as thickness and type.

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