scholarly journals On Riemannian Geometries of Visual Space

2021 ◽  
Author(s):  
Jacek Turski
Keyword(s):  
Riemannian Geometry ◽  
Physical Space ◽  
Visual Space ◽  
Gaze Direction ◽  
Relative Depth ◽  
Metric Tensor ◽  
The Gaze ◽  
Zero Curvature ◽  
Riemannian Geometries ◽  
Straight Lines

This is a study of the phenomenal geometries constructed in the Riemannian geometry framework from simulated iso-disparity conics in the horizontal visual plane of the binocular system with the asymmetric eyes (AEs). The iso-disparity conic's arcs in the Cyclopean direction are the frontal visual geodesics. For the eyes' resting vergence posture, which depends on parameters of the AE, the iso-disparity conics are frontal straight lines in physical space. For all other fixations, the iso-disparity conics consist of families of the ellipses or hyperbolas depending on both the AE's parameters and the bifoveal fixation. An assumption underlying the relevant architecture of the human visual system is combined with results from simulated iso-disparity straight lines, giving the relative depth as a function of the distance. This establishes the metric tensor in binocular space of fixations for the eyes' resting vergence posture. The resulting geodesics in the gaze direction, give the distance to the horizon and zero curvature. For all other fixations, only the sign of the curvature can be inferred from the global behavior of the simulated iso-disparity conics.

Riemannian Geometries of Variable Curvature in Visual Space: Visual Alleys, Horopters, and Triangles in Big Open Fields

Perception ◽  
1976 ◽  
Vol 5 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Antonio M Battro ◽  
Scipione di Pierro Netto ◽  
Reinier J A Rozestraten
Keyword(s):  
Riemannian Geometry ◽  
Dimensional Space ◽  
Visual Space ◽  
Open Spaces ◽  
Variable Curvature ◽  
Individual Function ◽  
Negative Constant ◽  
The Subject ◽  
The Individual ◽  
Riemannian Geometries

Luneburg's model for computation of the curvature K of visual two-dimensional space (horizontal visual surface) was tested with equidistant and parallel alleys in large open spaces. Forty-six subjects used stakes to produce 406 experimental alleys of variable sizes (from 5 × 1 to 240 m × 48 m). The results show that, contrary to results obtained under laboratory conditions with small alleys and light spots, the individual curvature of visual space does not have a negative constant value. K varies in the interval −1 to +1 in ninety computed settings: K ≥ 0 ( N = 38); K < 0 ( N = 52). Therefore the Lobachevskian geometry currently attributed to visual space ought to be replaced by a Riemannian geometry of variable curvature. Moreover K is an individual function dependant on the size of the alley (distance from the subject), and visual perception would be better understood as scale-dependent. Independently of Luneburg's model we have tested the constancy of the curvature hypothesis in experiments with horopters and visual triangles. The results obtained invalidate Luneburg's hypothesis also.

scholarly journals Geometric Constraints of Visual Space

i-Perception ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 204166952110552
Author(s):  
Casper J. Erkelens
Keyword(s):  
Free Parameter ◽  
Physical Space ◽  
Visual Space ◽  
Geometric Constraints ◽  
Vanishing Point ◽  
Geometric Features ◽  
Space Model ◽  
3D Space ◽  
Parallel Lines ◽  
Straight Lines

Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to straight lines in visual space. A second requirement is that parallel lines oriented in depth in physical space, converge to a finite vanishing point in visual space. A rational function for perceived distance, compatible with the perspective-space model of visual space, satisfies the requirements. The function is unique. Analysis of alternative functions shows there is little tolerance for deviations. Conservation of the straightness of lines constrains visual space to having a single geometry. Visual space is described by an analytical function having one free parameter, that is, the distance of the vanishing point.

scholarly journals Fear-specific leftward bias in gaze direction judgment

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yue Zhang ◽  
Qiqi Hu ◽  
Xinwei Lai ◽  
Zhonghua Hu ◽  
Shan Gao
Keyword(s):  
Judgment Task ◽  
Gaze Direction ◽  
Emotional Information ◽  
Cerebral Lateralization ◽  
Low Level ◽  
The Gaze ◽  
Fearful Faces ◽  
Perception Bias ◽  
Behavioural Experiments ◽  
Direction Judgment

AbstractPrevious studies have shown that humans have a left spatial attention bias in cognition and behaviour. However, whether there exists a leftward perception bias of gaze direction has not been investigated. To address this gap, we conducted three behavioural experiments using a forced-choice gaze direction judgment task. The point of subjective equality (PSE) was employed to measure whether there was a leftward perception bias of gaze direction, and if there was, whether this bias was modulated by face emotion. The results of experiment 1 showed that the PSE of fearful faces was significantly positive as compared to zero and this effect was not found in angry, happy, and neutral faces, indicating that participants were more likely to judge the gaze direction of fearful faces as directed to their left-side space, namely a leftward perception bias. With the response keys counterbalanced between participants, experiment 2a replicated the findings in experiment 1. To further investigate whether the gaze direction perception variation was contributed by emotional or low-level features of faces, experiment 2b and 3 used inverted faces and inverted eyes, respectively. The results revealed similar leftward perception biases of gaze direction in all types of faces, indicating that gaze direction perception was biased by emotional information in faces rather than low-level facial features. Overall, our study demonstrates that there a fear-specific leftward perception bias in processing gaze direction. These findings shed new light on the cerebral lateralization in humans.

scholarly journals What is unique about the human eye? Comparative image analysis on the external eye morphology of human and nonhuman great apes

2021 ◽  
Author(s):  
Fumihiro Kano ◽  
Takeshi Furuichi ◽  
Chie Hashimoto ◽  
Christopher Krupenye ◽  
Jesse G Leinwand ◽  
...  
Keyword(s):  
Image Analysis ◽  
Eye Gaze ◽  
Great Apes ◽  
Gaze Direction ◽  
Human Eye ◽  
The Gaze ◽  
Eye Morphology ◽  
New Findings ◽  
Heated Debate ◽  
Signaling Hypothesis

The gaze-signaling hypothesis and the related cooperative-eye hypothesis posit that humans have evolved special external eye morphology, including exposed white sclera (the white of the eye), to enhance the visibility of eye-gaze direction and thereby facilitate conspecific communication through joint-attentional interaction and ostensive communication. However, recent quantitative studies questioned these hypotheses based on new findings that humans are not necessarily unique in certain eye features compared to other great ape species. Therefore, there is currently a heated debate on whether external eye features of humans are distinguished from those of other apes and how such distinguished features contribute to the visibility of eye-gaze direction. This study leveraged updated image analysis techniques to test the uniqueness of human eye features in facial images of great apes. Although many eye features were similar between humans and other species, a key difference was that humans have uniformly white sclera which creates clear visibility of both eye outline and iris; the two essential features contributing to the visibility of eye-gaze direction. We then tested the robustness of the visibility of these features against visual noises such as darkening and distancing and found that both eye features remain detectable in the human eye, while eye outline becomes barely detectable in other species under these visually challenging conditions. Overall, we identified that humans have distinguished external eye morphology among other great apes, which ensures robustness of eye-gaze signal against various visual conditions. Our results support and also critically update the central premises of the gaze-signaling hypothesis.

scholarly journals Landmark-Centered Coding in Frontal Cortex Visual Responses

2020 ◽  
Author(s):  
Adrian Schütz ◽  
Vishal Bharmauria ◽  
Xiaogang Yan ◽  
Hongying Wang ◽  
Frank Bremmer ◽  
...  
Keyword(s):  
Frontal Cortex ◽  
Visual Space ◽  
List Type ◽  
Visual Response ◽  
Visual Responses ◽  
Visual Landmarks ◽  
Specific Target ◽  
Visual Coding ◽  
The Gaze ◽  
Landmark Configuration

SummaryVisual landmarks influence spatial cognition [1–3], navigation [4,5] and goal-directed behavior [6–8], but their influence on visual coding in sensorimotor systems is poorly understood [6,9–11]. We hypothesized that visual responses in frontal cortex control gaze areas encode potential targets in an intermediate gaze-centered / landmark-centered reference frame that might depend on specific target-landmark configurations rather than a global mechanism. We tested this hypothesis by recording neural activity in the frontal eye fields (FEF) and supplementary eye fields (SEF) while head-unrestrained macaques engaged in a memory-delay gaze task. Visual response fields (the area of visual space where targets modulate activity) were tested for each neuron in the presence of a background landmark placed at one of four oblique configurations relative to the target stimulus. 102 of 312 FEF and 43 of 256 SEF neurons showed spatially tuned response fields in this task. We then fit these data against a mathematical continuum between a gaze-centered model and a landmark-centered model. When we pooled data across the entire dataset for each neuron, our response field fits did not deviate significantly from the gaze-centered model. However, when we fit response fields separately for each target-landmark configuration, the best fits shifted (mean 37% / 40%) toward landmark-centered coding in FEF / SEF respectively. This confirmed an intermediate gaze / landmark-centered mechanism dependent on local (configuration-dependent) interactions. Overall, these data show that external landmarks influence prefrontal visual responses, likely helping to stabilize gaze goals in the presence of variable eye and head orientations.HighlightsPrefrontal visual responses recorded in the presence of visual landmarksResponse fields showed intermediate gaze / landmark-centered organizationThis influence depended on specific target-landmark configurations

scholarly journals Conscious awareness of visual space: A tripartite encoding model.

2020 ◽  
Author(s):  
Dhanraj Vishwanath
Keyword(s):  
Visual Space ◽  
Spatial Separation ◽  
Ideal Observer ◽  
Conscious Awareness ◽  
Relative Depth ◽  
Visual Stream ◽  
3D Vision ◽  
Fine Grained ◽  
Near Space ◽  
Dorsal Visual Stream

The prevailing model of 3D vision proposes that the visual system recovers a single objective and internally consistent representation of physical 3D space based on a process of ideal-observer probabilistic inference. A significant challenge for this model has been in explaining the contents of our subjective awareness of visual space. Here I argue that integrating phenomenological observations, empirical data, evolutionary logic and neurophysiological evidence leads to the conjecture that the human conscious awareness of visual space is underwritten by multiple, sometimes mutually inconsistent, spatial encodings. By assessing four primary competencies in the conscious awareness of space, three major types of spatial encodings are conjectured. Among the most primitive of these is proposed to support the competency of the conscious awareness of distance at an ambulatory scale (operationally defined as egocentric distance) and is hypothesised to involve temporal archicortex regions. The second is proposed to support the competency of awareness of object layout and 3D shape without scale (operationally, relative depth), likely instantiated in the ventral visual stream of the neocortex. This encoding is hypothesised to have evolved from more primitive encodings that provide a depth-ordered segmentation of the visual field. The third encoding is proposed to support the competency of fine-grained awareness of intra- and inter-object spatial separation in near space (operationally, scaled or absolute depth) and instantiated in the dorsal visual stream. This encoding is conjectured to underlie the phenomenology of object solidity, spatial separation, tangibility and object realness that is often referred to as stereopsis. The combined effect of the first and third competencies (ambulatory distance and near-space scaled spatial separation) is conjectured to contribute to the feeling of spatial immersion and presence.

Geometry and Visual Space from Antiquity to the Early Moderns

Space ◽  
2020 ◽  
pp. 184-222
Author(s):  
Gary Hatfield
Keyword(s):  
Visual Perception ◽  
Distance Perception ◽  
Visual Space ◽  
Field Of View ◽  
Size Perception ◽  
Mental Calculation ◽  
Straight Lines ◽  
Comparative Examination

This chapter examines the development of a geometrical framework for understanding and explaining spatial aspects of visual perception, including perception of the sizes, shapes, and positions of things in the field of view. The structure of this framework is built on the fact that vision typically occurs in straight lines (rectilinearly). Within this framework, the chapter selectively focuses on size perception. This focus allows for a comparative examination of how a single problem was treated geometrically by various theorists, ancient, medieval, and modern. The theorists examined are Euclid and Ptolemy, who were extramissionists, and Ibn al-Haytham, Kepler, Descartes, and Berkeley, each of whom adopted, in one way or another, an intromissionist scheme. In comparing Descartes and Berkeley, notice is taken of Berkeley’s interpretive bent in treating Descartes’s account of distance perception in a way that requires mental calculation, where Descartes sometimes offered psychophysiological mechanisms (avoiding mental calculation).

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