scholarly journals Why does Necker Cube appear as the three-dimensional shape?

2020 ◽  
Author(s):  
Shohei Hidaka ◽  
Kohske Takahashi
Keyword(s):  
Visual Perception ◽  
Retinal Image ◽  
Dimensional Space ◽  
Necker Cube ◽  
3D Structure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Adjoint Functors ◽  
Novel Theory ◽  
Multiple Structures

Visual perception, receiving a two-dimensional (2D) visual input, often constructs the three-dimensional (3D) perceptual image. Although there are generally multiple structures in the external world that give an equivalent two-dimensional retinal image, the perceptual process naturally and easily infer only one 3D structure as the solution. However, the following problems are not obvious at all: what kind of structure can be obtained as a 3D perceptual image from certain 2D information, and why do we get a three-dimensional perceptual image instead of a two-dimensional one. In the present study, we investigate this problem by untangling the Necker cube phenomenon, and propose a novel theory of three-dimensional visual perception from the viewpoint of the efficiency of information coding. Among the possible structures that can yield the 2D retinal image of the Necker cube, the structure of the typical three-dimensional perceptual image of the Necker cube maximizes the symmetry (in group theory). This maximization of symmetry is characterized by the pairs of adjoint functors (in category theory). Therefore, according to this proposed theory, "the Necker cube" in the three-dimensional space is perceived as the most efficient encoding of the two-dimensional retinal image.

scholarly journals STRATEGIES TO EVALUATE THE VISIBILITY ALONG AN INDOOR PATH IN A POINT CLOUD REPRESENTATION

2017 ◽  
Vol IV-2/W4 ◽  
pp. 311-317 ◽  
Author(s):  
N. Grasso ◽  
E. Verbree ◽  
S. Zlatanova ◽  
M. Piras
Keyword(s):  
Visual Perception ◽  
Point Cloud ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Syntax ◽  
Point Of View ◽  
Indoor Environments ◽  
Two Dimensional ◽  
Visibility Graphs ◽  
Representations Of Space

Many research works have been oriented to the formulation of different algorithms for estimating the paths in indoor environments from three-dimensional representations of space. The architectural configuration, the actions that take place within it, and the location of some objects in the space influence the paths along which is it possible to move, as they may cause visibility problems. To overcome the visibility issue, different methods have been proposed which allow to identify the visible areas and from a certain point of view, but often they do not take into account the user’s visual perception of the environment and not allow estimating how much may be complicated to follow a certain path. In the field of space syntax and cognitive science, it has been attempted to describe the characteristics of a building or an urban environment by the isovists and visibility graphs methods; some numerical properties of these representations allow to describe the space as for how it is perceived by a user. However, most of these studies are directed to analyze the environment in a two-dimensional space. In this paper we propose a method to evaluate in a quantitative way the complexity of a certain path within an environment represented by a three-dimensional point cloud, by the combination of some of the previously mentioned techniques, considering the space visible from a certain point of view, depending on the moving agent (pedestrian , people in wheelchairs, UAV, UGV, robot).

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals The Formation of a Cavity in a 3D Flux Rope

2013 ◽  
Vol 8 (S300) ◽  
pp. 147-150 ◽  
Author(s):  
Donald Schmit ◽  
Sarah Gibson
Keyword(s):  
Ad Hoc ◽  
Numerical Models ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flux Rope ◽  
Multiple Structures ◽  
Field Lines ◽  
Hydrostatic Balance ◽  
Distinct Field ◽  
Three Dimensional Space

AbstractThere are currently no three dimensional numerical models which describe the magnetic and energetic formation of prominences self-consistently. Consequently, there has not been significant progress made in understanding the connection between the dense prominence plasma and the coronal cavity. We have taken an ad-hoc approach to understanding the energetic implications of the magnetic models of prominence structure. We extract one dimensional magnetic field lines from a 3D MHD model of a flux rope and solve for hydrostatic balance along these field lines incorporating field-aligned thermal conduction, uniform heating, and radiative losses. The 1D hydrostatic solutions for density and temperature are then mapped back into three dimensional space, which allows us to consider the projection of multiple structures. We find that the 3D flux rope is composed of several distinct field line types. A majority of the flux rope interior field lines are twisted but not dipped. These field lines are density-reduced relative to unsheared arcade field lines. We suggest the cavity may form along these short interior field lines which are surrounded by a sheath of dipped field lines. This geometric arrangement would create a cavity on top of a prominence, but the two structures would not share field lines or plasma.

Symbol recognition system based on 3D stereo vision

2020 ◽  
pp. 1-10
Author(s):  
Linlin Wang
Keyword(s):  
Camera Calibration ◽  
Stereo Vision ◽  
Stereo Matching ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Recognition System ◽  
Symbol Recognition ◽  
Two Dimensional ◽  
Measuring Machine ◽  
Left And Right

With the continuous development of computer science and technology, symbol recognition systems may be converted from two-dimensional space to three-dimensional space. Therefore, this article mainly introduces the symbol recognition system based on 3D stereo vision. The three-dimensional image is taken by the visual coordinate measuring machine in two places on the left and right. Perform binocular stereo matching on the edge of the feature points of the two images. A corner detection algorithm combining SUSAN and Harris is used to detect the left and right camera calibration templates. The two-dimensional coordinate points of the object are determined by the image stereo matching module, and the three-dimensional discrete coordinate points of the object space can be obtained according to the transformation relationship between the image coordinates and the actual object coordinates. Then draw the three-dimensional model of the object through the three-dimensional drawing software. Experimental data shows that the logic resources and memory resources occupied by image preprocessing account for 30.4% and 27.4% of the entire system, respectively. The results show that the system can calibrate the internal and external parameters of the camera. In this way, the camera calibration result will be more accurate and the range will be wider. At the same time, it can effectively make up for the shortcomings of traditional modeling techniques to ensure the measurement accuracy of the detection system.

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

Vision

2018 ◽  
Author(s):  
Nico Orlandi
Keyword(s):  
Visual Perception ◽  
Cognitive Science ◽  
Three Dimensional ◽  
Psychological State ◽  
Psychological Process ◽  
Two Dimensional ◽  
Vision Science ◽  
Psychological Theories ◽  
Black Surface ◽  
Obvious Manner

Why do things look to us as they do? This question, formulated by psychologist Kurt Koffka, identifies the main problematic of vision science. Consider looking at a black cat. We tend to see both the cat and its colour as the same at different times. Despite the ease with which this perception occurs, the process by which we perceive is fairly complex. The initial stimulation that gives rise to seeing, consists in a pattern of light that projects on the retina – a light-sensitive layer of the eye. The so-called ‘retinal image’ is a two-dimensional projection that does not correspond in any obvious manner to the way things look. It is not three-dimensional, coloured and shaped in a similar fashion to the objects of our experience. Indeed the light projected from objects is not just different from what we see, it is also both continuously changing and ambiguous. Because the cat moves around, the light it reflects changes from moment to moment. The cat’s projection on the retina correspondingly changes in size. We do not, however, see the cat as changing in size. We tend to see it as size-constant and uniformly coloured through time. How do we explain this constancy? Along similar lines, the cat’s white paws cause on the retina a patch of light that differs in intensity from the rest. This patch could also be caused by a change in illumination. A black surface illuminated very brightly can look like a white surface illuminated very dimly. This means that the light hitting the retina from the paws is underdetermined – it does not uniquely specify what is present. But, again, we tend to see the paws as consistently white. We do not see them as shifting from being white to being black, but illuminated brightly. How do we explain this stability? A central aim of theories of vision is to answer these questions. The science that attempts to address these queries is interdisciplinary. Traditionally, philosophical theories of vision have influenced psychological theories and vice versa. The collaboration between these disciplines eventually developed into what is now known as cognitive science. Cognitive science includes – in addition to philosophy and psychology – computer science, linguistics and neuroscience. Cognitive scientists aim primarily to understand the process by which we see. Philosophers are interested in this topic particularly as it connects to understanding the nature of our acquaintance with reality. Theories of vision differ along many dimensions. Giving a full survey is not possible in this entry. One useful difference is whether a theory presumes that visual perception involves a psychological process. Psychological theories of vision hold that in achieving perception – which is itself a psychological state – the organism uses other psychological material. Opponents of psychological theories prefer to make reference to physiological, mechanical and neurophysiological explanations.

The effect of the coordination orientation of N atoms on polymeric structures: synthesis and characterization of one- and two-dimensional CuII coordination polymers based on 4-amino-3-(pyridin-2-yl)-5-[(pyridin-3-ylmethyl)sulfanyl]-1,2,4-triazole

2019 ◽  
Vol 75 (4) ◽  
pp. 443-450
Author(s):  
Guiying Zhu ◽  
Yang Lu ◽  
Guoxia Jin ◽  
Xuan Ji ◽  
Jianping Ma
Keyword(s):  
Hydrogen Bonding ◽  
Coordination Polymers ◽  
3D Structure ◽  
Three Dimensional ◽  
Great Influence ◽  
Two Dimensional ◽  
3D Network ◽  
Solvent Molecules ◽  
Bonding Systems ◽  
Polymeric Structures

Three new one- (1D) and two-dimensional (2D) CuII coordination polymers, namely poly[[bis{μ2-4-amino-3-(pyridin-2-yl)-5-[(pyridin-3-ylmethyl)sulfanyl]-1,2,4-triazole}copper(II)] bis(methanesulfonate) tetrahydrate], {[Cu(C13H12N5S)2](CH3SO3)2·4H2O} n (1), catena-poly[[copper(II)-bis{μ2-4-amino-3-(pyridin-2-yl)-5-[(pyridin-4-ylmethyl)sulfanyl]-1,2,4-triazole}] dinitrate methanol disolvate], {[Cu(C13H12N5S)2](NO3)2·2CH3OH} n (2), and catena-poly[[copper(II)-bis{μ2-4-amino-3-(pyridin-2-yl)-5-[(pyridin-4-ylmethyl)sulfanyl]-1,2,4-triazole}] bis(perchlorate) monohydrate], {[Cu(C13H12N5S)2](ClO4)2·H2O} n (3), were obtained from 4-amino-3-(pyridin-2-yl)-5-[(pyridin-3-ylmethyl)sulfanyl]-1,2,4-triazole with pyridin-3-yl terminal groups and from 4-amino-3-(pyridin-2-yl)-5-[(pyridin-4-ylmethyl)sulfanyl]-1,2,4-triazole with pyridin-4-yl terminal groups. Compound 1 displays a 2D net-like structure. The 2D layers are further linked through hydrogen bonds between methanesulfonate anions and amino groups on the framework and guest H2O molecules in the lattice to form a three-dimensional (3D) structure. Compound 2 and 3 exhibit 1D chain structures, in which the complicated hydrogen-bonding interactions play an important role in the formation of the 3D network. These experimental results indicate that the coordination orientation of the heteroatoms on the ligands has a great influence on the polymeric structures. Moreover, the selection of different counter-anions, together with the inclusion of different guest solvent molecules, would also have a great effect on the hydrogen-bonding systems in the crystal structures.

scholarly journals Capacity of Inhomogeneous Hybrid Wireless Networks in Three-Dimensional Space

2015 ◽  
Vol 11 (9) ◽  
pp. 47
Author(s):  
Feng Wu ◽  
Jiang Zhu ◽  
Yilong Tian ◽  
Zhipeng Xi
Keyword(s):  
Sensor Node ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Capacity ◽  
Throughput Capacity ◽  
Two Dimensional ◽  
Hybrid Wireless Networks ◽  
Node Distribution ◽  
Analytical Expressions ◽  
Three Dimensional Space

Network capacity has been widely studied in recent years. However, most of the literatures focus on the networks where nodes are distributed in a two-dimensional space. In this paper, we propose a 3D hybrid sensor network model. By setting different sensor node distribution probabilities for cells, we divide all the cells in the network into dense cells and sparse cells. Analytical expressions of the aggregate throughput capacity are obtained. We also find that suitable inhomogeneity can increase the network throughput capacity.

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