Boundary Completion in Illusory Contours: Interpolation or Extrapolation?

Perception ◽  
10.1068/p3420 ◽  
2003 ◽  
Vol 32 (8) ◽  
pp. 985-999 ◽  
Author(s):  
Thomas F Shipley ◽  
Philip J Kellman
Keyword(s):  
Illusory Contour ◽  
Network Models ◽  
Higher Order ◽  
Alternative Conception ◽  
Order Operator ◽  
Illusory Contours ◽  
Boundary Formation ◽  
Special Case ◽  
Boundary Completion ◽  
Contour Completion

Most computational and neural-style models of contour completion (ie illusory and occluded contours) are based on interpolation: the filling in of an edge between two visible edges. The results of three experiments suggest an alternative conception, that units are formed as a result of extrapolation from visible edges. In three experiments, subjects reported illusory contours between standard illusory-contour inducing elements and forms that do not, by themselves, induce illusory contours. We suggest that these forms are not a special case of inducing elements but that they represent a different class— receiving elements. Receiving elements are forms that can receive an illusory contour but cannot generate one, and they can alter contour formation. In experiment 1, receiving elements increased the judged clarity of illusory contours. In experiment 2, illusory edges were seen to connect to corners, line ends, and even the edges of circles. Boundary formation in motion displays also appears to be based on extrapolation. In experiment 3, subjects reported that small moving dots altered the formation of spatiotemporally defined boundaries. Implications for higher-order operator and network models of boundary formation are discussed.

Insect perception of illusory contours

1992 ◽  
Vol 337 (1279) ◽  
pp. 59-64 ◽  
Keyword(s):  
Human Visual System ◽  
Illusory Contour ◽  
Optic Lobe ◽  
Insect Vision ◽  
Local Contrast ◽  
Fault Line ◽  
Illusory Contours ◽  
Striped Pattern ◽  
Processing Power ◽  
As If

The human visual system sees an illusory contour where there is a fault line across a regular striped pattern. We demonstrate that bees respond as if they see the same illusory contour. There is also a type of neuron in the lobula of the dragonfly optic lobe which responds directionally to motion of the illusory contour as if to an edge or line. Apparently insects have a mechanism that sees illusory contours and therefore assists in the demarcation of edges and objects at places where local contrast falls to zero at an edge, or where one textured object partially obscures another. These results suggest that insect vision, although spatially crude and low in processing power, sees separate objects by similar mechanisms to our own.

An Illusory Contour Can Facilitate Visually Induced Self-Motion Perception

2018 ◽  
Vol 31 (8) ◽  
pp. 715-727
Author(s):  
Shinji Nakamura ◽  
Shin’ya Takahashi
Keyword(s):  
Motion Perception ◽  
Illusory Contour ◽  
Uniform Motion ◽  
Horizontal Line ◽  
Illusory Contours ◽  
End Points ◽  
Line Segments ◽  
Illusory Perception ◽  
Vertically Aligned ◽  
Self Motion

Abstract Uniform motion of a visual stimulus induces an illusory perception of the observer’s self-body moving in the opposite direction (vection). The present study investigated whether vertical illusory contours can affect horizontal translational vection using abutting-line stimulus. The stimulus consisted of a number of horizontal line segments that moved horizontally at a constant speed. A group of vertically aligned segments created a ‘striped column’, while line segments in adjoining columns were shifted vertically to make a slight gap between them. In the illusory contour condition, the end points of the segments within the column were horizontally aligned to generate vertical illusory contours. In the condition with no illusory contour, these end points were not aligned within the column so that the illusory contour was not perceived. In the current study, 11 participants performed this experiment, and it was shown that stronger vection was induced in the illusory contour condition than in the condition with no illusory contour. The results of the current experiment provide novel evidence suggesting that non-luminance-defined visual features have a facilitative effect on visual self-motion perception.

Artificial Polynomial and Trigonometric Higher Order Neural Network Group Models

2013 ◽  
pp. 78-102 ◽  
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Continuous Function ◽  
Trigonometric Polynomial ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Neural Network Models ◽  
Piecewise Continuous ◽  
Discontinuous Data

Real world financial data is often discontinuous and non-smooth. Accuracy will be a problem, if we attempt to use neural networks to simulate such functions. Neural network group models can perform this function with more accuracy. Both Polynomial Higher Order Neural Network Group (PHONNG) and Trigonometric polynomial Higher Order Neural Network Group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results obtained using Polynomial Higher Order Neural Network Group and Trigonometric polynomial Higher Order Neural Network Group financial simulators are presented, which confirm that PHONNG and THONNG group models converge without difficulty, and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using Polynomial Higher Order Neural Network (PHONN) and Trigonometric polynomial Higher Order Neural Network (THONN) models.

Financial Data Prediction by Artificial Sine and Cosine Trigonometric Higher Order Neural Networks

2021 ◽  
pp. 262-301
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Data Simulation ◽  
Neural Network Models ◽  
Data Prediction ◽  
Higher Order Neural Networks

This chapter develops two new nonlinear artificial higher order neural network models. They are sine and sine higher order neural networks (SIN-HONN) and cosine and cosine higher order neural networks (COS-HONN). Financial data prediction using SIN-HONN and COS-HONN models are tested. Results show that SIN-HONN and COS-HONN models are good models for some sine feature only or cosine feature only financial data simulation and prediction compared with polynomial higher order neural network (PHONN) and trigonometric higher order neural network (THONN) models.

Modeling higher order adaptivity of a network by multilevel network reification

2020 ◽  
Vol 8 (S1) ◽  
pp. S110-S144 ◽  
Author(s):  
Jan Treur
Keyword(s):  
Network Architecture ◽  
Network Models ◽  
Higher Order ◽  
Second Order ◽  
Adaptation Level ◽  
Network Adaptation ◽  
Base Level ◽  
Generic Architecture ◽  
Adaptation Processes ◽  
Base Network

AbstractIn network models for real-world domains, often network adaptation has to be addressed by incorporating certain network adaptation principles. In some cases, also higher order adaptation occurs: the adaptation principles themselves also change over time. To model such multilevel adaptation processes, it is useful to have some generic architecture. Such an architecture should describe and distinguish the dynamics within the network (base level), but also the dynamics of the network itself by certain adaptation principles (first-order adaptation level), and also the adaptation of these adaptation principles (second-order adaptation level), and may be still more levels of higher order adaptation. This paper introduces a multilevel network architecture for this, based on the notion network reification. Reification of a network occurs when a base network is extended by adding explicit states representing the characteristics of the structure of the base network. It will be shown how this construction can be used to explicitly represent network adaptation principles within a network. When the reified network is itself also reified, also second-order adaptation principles can be explicitly represented. The multilevel network reification construction introduced here is illustrated for an adaptive adaptation principle from social science for bonding based on homophily and one for metaplasticity in Cognitive Neuroscience.

Parallelism and the Perception of Illusory Contours

Perception ◽  
1993 ◽  
Vol 22 (5) ◽  
pp. 589-595 ◽  
Author(s):  
Marc K Albert
Keyword(s):  
Illusory Contour ◽  
Illusory Contours ◽  
Gestalt Principles ◽  
Contour Strength

The role of symmetry in the perception of illusory contours has been a subject of controversy ever since Kanizsa proposed his theory of illusory contours based on Gestalt principles. Today it is widely agreed that illusory contours do not necessarily occur more readily with inducers that can be ‘amodally’ completed to symmetrical objects than with inducers that cannot. But the question of whether symmetrical inducers produce weaker illusory contours than do unsymmetrical ones is still controversial. A novel determinant of illusory contour strength, parallelism, is proposed. Experiments are reported which indicate that illusory contours induced by ‘blobs’ which have boundaries that are nearby and parallel to the illusory contour are weaker than illusory contours induced by blobs that do not have this property. It is suggested that the display that has been most widely used by researchers to support their claims for a weakening of illusory contours with symmetrical inducers is weak primarily because of parallelism.

scholarly journals Causality and passivity in elastodynamics

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150256 ◽  
Author(s):  
Ankit Srivastava
Keyword(s):  
Fourier Transforms ◽  
Constitutive Relations ◽  
Higher Order ◽  
Causal Effects ◽  
Passive System ◽  
One Dimensional ◽  
The Real ◽  
Analogous Question ◽  
Derivatives Of ◽  
Special Case

What are the constraints placed on the constitutive tensors of elastodynamics by the requirements that the linear elastodynamic system under consideration be both causal (effects succeed causes) and passive (system does not produce energy)? The analogous question has been tackled in other areas but in the case of elastodynamics its treatment is complicated by the higher order tensorial nature of its constitutive relations. In this paper, we clarify the effect of these constraints on highly general forms of the elastodynamic constitutive relations. We show that the satisfaction of passivity (and causality) directly requires that the hermitian parts of the transforms (Fourier and Laplace) of the time derivatives of the constitutive tensors be positive semi-definite. Additionally, the conditions require that the non-hermitian parts of the Fourier transforms of the constitutive tensors be positive semi-definite for positive values of frequency. When major symmetries are assumed these definiteness relations apply simply to the real and imaginary parts of the relevant tensors. For diagonal and one-dimensional problems, these positive semi-definiteness relationships reduce to simple inequality relations over the real and imaginary parts, as they should. Finally, we extend the results to highly general constitutive relations which include the Willis inhomogeneous relations as a special case.

Cue-dependent deficits in grating orientation discrimination after V4 lesions in macaques

1996 ◽  
Vol 13 (3) ◽  
pp. 529-538 ◽  
Author(s):  
Peter De Weerd ◽  
Robert Desimone ◽  
Leslie G. Ungerleider
Keyword(s):  
Visual Field ◽  
Normal Control ◽  
Illusory Contour ◽  
Visual Area ◽  
Orientation Discrimination ◽  
Fixation Target ◽  
Illusory Contours ◽  
Pattern Vision ◽  
Area V4

AbstractTo examine the role of visual area V4 in pattern vision, we tested two monkeys with lesions of V4 on tasks that required them to discriminate the orientation of contours defined by several different cues. The cues used to separate the contours from their background included luminance, color, motion, and texture, as well as phase-shifted abutting gratings that created an “illusory” contour. The monkeys were trained to maintain fixation on a fixation target while discriminating extrafoveal stimuli, which were located in either a normal control quadrant of the visual field or in a quadrant affected by a lesion of area V4 in one hemisphere. Comparing performance in the two quadrants, we found significant deficits for contours defined by texture and for the illusory contour, but smaller or no deficits for motion-, color-, and luminance-defined contours. The data suggest a specific role of V4 in the perception of illusory contours and contours defined by texture.

scholarly journals A note on Weingarten hypersurfaces in the warped product manifold

2014 ◽  
Vol 25 (14) ◽  
pp. 1450121 ◽  
Author(s):  
Haizhong Li ◽  
Yong Wei ◽  
Changwei Xiong
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Higher Order ◽  
Product Manifold ◽  
Weingarten Surfaces ◽  
Warped Product Manifold ◽  
Higher Order Mean Curvature ◽  
Special Case ◽  
Differential Geom

In this paper, we consider the closed embedded hypersurface Σ in the warped product manifold [Formula: see text] equipped with the metric g = dr2 + λ(r)2 gN. We give some characterizations of slice {r} × N by the condition that Σ has constant weighted higher-order mean curvatures (λ′)αpk, or constant weighted higher-order mean curvature ratio (λ′)αpk/p1, which generalize Brendle's [Constant mean curvature surfaces in warped product manifolds, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 247–269] and Brendle–Eichmair's [Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94(3) (2013) 387–407] results. In particular, we show that the assumption convex of Brendle–Eichmair's result [Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94(3) (2013) 387–407] is unnecessary. Here pk is the kth normalized mean curvature of the hypersurface Σ. As a special case, we also give some characterizations of geodesic spheres in ℝn, ℍn and [Formula: see text], which generalize the classical Alexandrov-type results.

The Multiple Determination of Illusory Contours: 2. An Empirical Investigation

Perception ◽  
1983 ◽  
Vol 12 (3) ◽  
pp. 293-303 ◽  
Author(s):  
Diane F Halpern ◽  
Billie Salzman ◽  
Wayne Harrison ◽  
Keith Widaman
Keyword(s):  
Illusory Contour ◽  
Factor Model ◽  
Illusory Contours ◽  
Contour Perception ◽  
Confirmatory Factor ◽  
Linear Effects ◽  
Explained Variance ◽  
Taxonomic Approach ◽  
Contour Strength

Judgments of contour strength or saliency for twenty-four illusory-contour configurations were subjected to a confirmatory factor analysis. A four-factor model that posited the involvement of simultaneous contrast, linear effects (assimilation and dissimilation), depth/completion cues, and feature analyzers accounted for a substantial proportion of the variance in judgments of illusory-contour strength. The hierarchical addition of a fifth factor, diffuse illusory contours, significantly improved the overall fit of the model, but added little to the proportion of explained variance. The taxonomic approach adopted provides support for a multiprocess model of illusory-contour perception.

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