Poggendorff Illusion as a Function of Orientation of Transversal and Parallel Lines

Adult human subjects (8 male, 8 female undergraduates) with normal vision were required to judge various orientations of the Poggendorff illusion. The transversal and parallel line-segments of the illusion were manipulated to produce the orientations to be judged. Minimum illusion occurred when the transversal line-segment was oriented 90° with respect to true vertical or true horizontal. Magnitude of illusion increased as the transversal line-segment deviated from these positions. The findings suggested that there is a stability of horizontal and vertical orientations. In addition, the hypothesis that visual acuity plays a role in the perception of the Poggendorff illusion was proposed.

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THE MINIMUM GUARDING TREE PROBLEM

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830914500116 ◽

2014 ◽

Vol 06 (01) ◽

pp. 1450011 ◽

Cited By ~ 3

Author(s):

ADRIAN DUMITRESCU ◽

JOSEPH S. B. MITCHELL ◽

PAWEL ŻYLIŃSKI

Keyword(s):

Approximation Algorithms ◽

Nonempty Subset ◽

Parallel Line ◽

Minimum Length ◽

Np Hard ◽

Orthogonal Axis ◽

Line Segments ◽

Parallel Lines ◽

Simple Alternative ◽

Axis Parallel

Given a set ℒ of non-parallel lines in the plane and a nonempty subset ℒ′ ⊆ ℒ, a guarding tree for ℒ′ is a tree contained in the union of the lines in ℒ such that if a mobile guard (agent) runs on the edges of the tree, all lines in ℒ′ are visited by the guard. Similarly, given a connected arrangement 𝒮 of line segments in the plane and a nonempty subset 𝒮′ ⊆ 𝒮, we define a guarding tree for 𝒮′. The minimum guarding tree problem for a given set of lines or line segments is to find a minimum-length guarding tree for the input set. We provide a simple alternative (to [N. Xu, Complexity of minimum corridor guarding problems, Inf. Process. Lett.112(17–18) (2012) 691–696.]) proof of the problem of finding a guarding tree of minimum length for a set of orthogonal (axis-parallel) line segments in the plane. Then, we present two approximation algorithms with factors 2 and 3.98, respectively, for computing a minimum guarding tree for a subset of a set of n arbitrary non-parallel lines in the plane; their running times are O(n8) and O(n6 log n), respectively. Finally, we show that this problem is NP-hard for lines in 3-space.

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POINT AND LINE SEGMENT RECONSTRUCTION FROM VISIBILITY INFORMATION

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195900000115 ◽

2000 ◽

Vol 10 (02) ◽

pp. 189-200 ◽

Cited By ~ 7

Author(s):

S. K. WISMATH

Keyword(s):

Polynomial Time ◽

Line Segment ◽

Collinearity Judgment as a Function of Induction Angle

Perceptual and Motor Skills ◽

10.2466/pms.1994.78.2.655 ◽

1994 ◽

Vol 78 (2) ◽

pp. 655-674 ◽

Cited By ~ 12

Author(s):

Ernest Greene

Keyword(s):

Line Segment ◽

Poggendorff Illusion ◽

Orientation Selectivity ◽

Induction Effect ◽

Neural Models ◽

Line Segments ◽

Tilt Illusion ◽

Test Segment ◽

Segment Orientation ◽

Basic Induction

The misalignment which is seen in the Poggendorff illusion can be studied with better control by using a configuration which has only two line segments. Two experiments were conducted in which subjects judged collinearity of a test segment, this judgment being subjected to a biasing influence from a second (induction) segment. Exp. 1 held the test segment at one of three orientations relative to the observer (30°, 45°, and 60°) and systematically varied the orientation of the induction segment in 15° increments through the range of possible positions. The orientation of the page relative to the observer was varied as well. Exp. 2 varied the test segment through a greater range of angles and sampled more levels of induction segment orientation. Analysis indicated that projection errors follow orderly rules similar in kind to but different in magnitude from those observed for the Tilt Illusion, most notably, (a) misprojection is greatest when the orientation of the interfering line is similar to that of the line segment being projected and (b) the strength of this influence decreases as the relative angle becomes orthogonal. Also, the orientation of the segment being projected relative to the observer serves to modulate the strength of the basic induction effect. These perceptual interactions are discussed in relation to neural models for orientation selectivity.

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Less is more: Simple stimuli provoke more variable search strategies.

10.31234/osf.io/8kshm ◽

2020 ◽

Author(s):

Anna Nowakowska ◽

Alasdair D F Clarke ◽

Jessica Christie ◽

Josephine Reuther ◽

Amelia R. Hunt

Keyword(s):

Line Segment ◽

Search Strategies ◽

Complex Objects ◽

Search Behaviour ◽

Line Segments ◽

Surface Level ◽

Efficient Search ◽

Less Is More ◽

Dramatic Shift

We measured the efficiency of 30 participants as they searched through simple line segment stimuli and through a set of complex icons. We observed a dramatic shift from highly variable, and mostly inefficient, strategies with the line segments, to uniformly efficient search behaviour with the icons. These results demonstrate that changing what may initially appear to be irrelevant, surface-level details of the task can lead to large changes in measured behaviour, and that visual primitives are not always representative of more complex objects.

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Explanation for Neon Color Effect in Achromatic Line Segments on Chromatic Inducers Based on the Multiple Interpretation Hypothesis

Perceptual and Motor Skills ◽

10.2466/pms.101.1.267-282 ◽

2005 ◽

Vol 101 (1) ◽

pp. 267-282

Author(s):

Seiyu Sohmiya

Keyword(s):

Visual System ◽

Line Segment ◽

Color Contrast ◽

Achromatic Color ◽

Line Segments ◽

Color Effect ◽

Complementary Color ◽

Multiple Interpretation ◽

Color Induction ◽

Simultaneous Color Contrast

In van Tuijl's neon configurations, an achromatic line segment on a blue inducer produces yellowish illusory color in the illusory area. This illusion has been explained based on the idea of the complementary color induced by the blue inducer. However, it is proposed here that this illusion can be also explained by introducing the assumption that the visual system unconsciously interprets an achromatic color as information that is constituted by transparent and nontransparent colors. If this explanation is correct, not only this illusion, but also the simultaneous color contrast illusion can be explained without using the idea of the complementary color induction.

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ALPHA-REGULAR STICK UNKNOTS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216512500599 ◽

2012 ◽

Vol 21 (06) ◽

pp. 1250059 ◽

Cited By ~ 1

Author(s):

CHRISTOPHER FRAYER ◽

CHRISTOPHER SCHAFHAUSER

Keyword(s):

Line Segment ◽

Line Segments

Suppose Pn is a regular n-gon in ℝ2. An embedding f : Pn ↪ ℝ3 is called an α-regular stick knot provided the image of each side of Pn under f is a line segment of length 1 and any two consecutive line segments meet at an angle of α. The main result of this paper proves the existence of α-regular stick unknots for odd n ≥ 7 with α in the range [Formula: see text]. All knots constructed will have trivial knot type, and we will show that any non-trivial α-regular stick knot must have [Formula: see text].

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