scholarly journals The mean point of vergence is biased under projection

2019 ◽  
Vol 12 (4) ◽  
Author(s):  
Xi Wang ◽  
Kenneth Holmqvist ◽  
Marc Alexa
Keyword(s):  
Eye Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Calibration Method ◽  
Viewing Distance ◽  
Point Of Interest ◽  
Error Distributions ◽  
Centrally Symmetric ◽  
Vertical Error ◽  
The Mean

The point of interest in three-dimensional space in eye tracking is often computed based on intersecting the lines of sight with geometry, or finding the point closest to the two lines of sight. We first start by theoretical analysis with synthetic simulations. We show that the mean point of vergence is generally biased for centrally symmetric errors and that the bias depends on the horizontal vs. vertical error distribution of the tracked eye positions. Our analysis continues with an evaluation on real experimental data. The error distributions seem to be different among individuals but they generally leads to the same bias towards the observer. And it tends to be larger with an increased viewing distance. We also provided a recipe to minimize the bias, which applies to general computations of eye ray intersection. These findings not only have implications for choosing the calibration method in eye tracking experiments and interpreting the observed eye movements data; but also suggest to us that we shall consider the mathematical models of calibration as part of the experiment.

scholarly journals The Thinness of the Ocean in S–Θ–p Space and the Implications for Mean Diapycnal Advection

2007 ◽  
Vol 37 (6) ◽  
pp. 1714-1732 ◽  
Author(s):  
Trevor J. McDougall ◽  
David R. Jackett
Keyword(s):  
Dimensional Space ◽  
World Ocean ◽  
Three Dimensional ◽  
Small Scale ◽  
Lateral Motion ◽  
Hydrographic Data ◽  
Mixing Processes ◽  
The World ◽  
The Mean ◽  
Three Dimensional Space

Abstract It is shown that the ocean’s hydrography occupies little volume in the three-dimensional space defined by salinity–temperature–pressure (S–Θ–p), and the implications of this observation for the mean vertical transport across density surfaces are discussed. Although ocean data have frequently been analyzed in the two-dimensional temperature–salinity (S–Θ) diagram where casts of hydrographic data are often locally tight in S–Θ space, the relatively empty nature of the World Ocean in the three-dimensional S–Θ–p space seems not to have received attention. The World Ocean’s data lie close to a single surface in this three-dimensional space, and it is shown that this explains the known smallness of the ambiguity in defining neutral surfaces. The ill-defined nature of neutral surfaces means that lateral motion along neutral trajectories leads to mean vertical advection through density surfaces, even in the absence of small-scale mixing processes. The situation in which the ocean’s hydrography occupies a large volume in S–Θ–p space is also considered, and it is suggested that the consequent vertical diapycnal advection would be sufficiently large that the ocean would not be steady.

scholarly journals Viewing-patterns and perspectival painting: An eye-tracking study on the effect of the vanishing point

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Arthur Crucq
Keyword(s):  
Eye Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Picture Plane ◽  
Linear Perspective ◽  
Underlying Structure ◽  
Vanishing Point ◽  
Visual Feature ◽  
The Gaze

Linear perspective has long been used to create the illusion of three-dimensional space on the picture plane. One of its central axioms comes from Euclidean geometry and holds that all parallel lines converge in a single vanishing point. Although linear perspective provided the painter with a means to organize the painting, the question is whether the gaze of the beholder is also affected by the underlying structure of linear perspective: for instance, in such a way that the orthogonals leading to the vanishing point also automatically guides the beholder’s gaze. This was researched during a pilot study by means of an eye-tracking experiment at the Lab for Cognitive Research in Art History (CReA) of the University of Vienna. It appears that in some compositions the vanishing point attracts the view of the participant. This effect is more significant when the vanishing point coincides with the central vertical axis of the painting, but is even stronger when the vanishing point also coincides with a major visual feature such as an object or figure. The latter calls into question what exactly attracts the gaze of the viewer, i.e., what comes first: the geometrical construct of the vanishing point or the visual feature?

The Projector Calibration Based on ZHANG’s Self-Calibration Method

2014 ◽  
Vol 981 ◽  
pp. 364-367
Author(s):  
Guang Yu ◽  
Bo Yang Yu ◽  
Shu Cai Yang ◽  
Li Wen ◽  
Wen Fei Dong ◽  
...  
Keyword(s):  
Camera Calibration ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Calibration Method ◽  
Linear Calibration ◽  
Self Calibration ◽  
Operation Process ◽  
Projector Calibration ◽  
Calibration Algorithm ◽  
Relationship Of

Projector calibration can be seen as a special case of the camera calibration. It can establish the relationship of the three dimensional space coordinates for points and projector image coordinates for points DMD by using a projector to project coding pattern. In camera calibration, ZHANG’s self-calibration was conducted in the maximum likelihood linear refinement. Operation process takes the lens distortion factors into account finding out the camera internal and external parameters finally. Using this algorithm to the projector calibration can solve the traditional linear calibration algorithm which is complex and poor robustness. Otherwise, it can improve the practicability of calibration method. This method can both calibrate the internal and external parameters of projector, which can solve the problem of independently inside or outside calibration.

Convolutional Neural Networks for Real-Time Eye Tracking in Interactive Applications

2021 ◽  
pp. 455-473
Author(s):  
Michael Burch ◽  
Andrei Jalba ◽  
Carl van Dueren den Hollander
Keyword(s):  
Eye Tracking ◽  
Real Time ◽  
Network Architecture ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Face Alignment ◽  
Interactive Applications ◽  
Processing Power ◽  
Real Time Applications ◽  
Pose Alignment

Face alignment and eye tracking for interactive applications should be performed with very low latency or users will notice the delay. In this chapter, a face alignment method for real-time applications is introduced featuring a convolutional neural network architecture for face and pose alignment. The performance of the novel method is compared to a face alignment algorithm included in the freely available OpenFace toolkit, which also focuses on real-time applications. The approach exceeds OpenFace's performance on both our own and the 300W test sets in terms of accuracy and robustness but requires significant parallel processing power, currently provided by the GPU. For the eye tracking application, stereo cameras are used as input to determine the position of a user's eyes in three-dimensional space. It does not require synchronized recordings, which may contain redundant information, and instead prefers staggered recordings, which maximize the number of possible model updates.

About approximation of 3-D random fields and statistical simulation

2003 ◽  
Vol 11 (3) ◽  
Author(s):  
Zoya O. Vyzhva
Keyword(s):  
Random Fields ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Statistical Simulation ◽  
Gaussian Random Fields ◽  
Statistical Characteristics ◽  
Mean Square ◽  
The Mean ◽  
Isotropic Random ◽  
Three Dimensional Space

The estimator of the mean-square approximation of 3-D homogeneous and isotropic random field is investigated. The problem of statistical simulation of realizations of random fields in threedimensional space is considered. The algorithm for the receiving of this realization has been formulated, which has been constructed on the base the mean-square approximation of random fields estimator. It has been constructed the statistical model for the Gaussian random fields in three-dimensional space, which has been given by its statistical characteristics.

scholarly journals Calibration Method for Central Catadioptric Camera Using Multiple Groups of Parallel Lines and Their Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yue Zhao ◽  
Xin Yang
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Image Plane ◽  
Calibration Method ◽  
Great Circle ◽  
Parallel Lines ◽  
Projection Properties ◽  
Multiple Groups ◽  
Catadioptric Camera ◽  
High Degree

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.

scholarly journals Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Mushtaq Abdal Rahem ◽  
Marjorie Darrah
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Computational Method ◽  
Behavior Patterns ◽  
Group Consensus ◽  
Mean And Variance ◽  
Consensus Measure ◽  
The Mean ◽  
Common Problems ◽  
Better Than

There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs.

Non-periodic Space Structures

1987 ◽  
Vol 2 (2) ◽  
pp. 93-108 ◽  
Author(s):  
Haresh Lalvani
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Structures ◽  
Infinite Class ◽  
Space Filling ◽  
Higher Dimensional ◽  
Centrally Symmetric ◽  
Interesting Class ◽  
Periodic Space ◽  
Three Dimensional Space

An interesting class of two- and three-dimensional space structures can be derived from projections of higher-dimensional structures. Regular polygons and regular-faced polyhedra provide the geometry of families of n-stars from which two- and three-dimensional projections of n-dimensional grids can be derived. These projections are rhombic space grids composed of all-space filling rhombi and rhombohedra with edges parallel to n directions. An infinite class of single-, double- and multi-layered grids can be derived from n-sided polygons and prisms, and a finite class of multi-directional grids from the polyhedral symmetry groups. The grids can be periodic, centrally symmetric or non-periodic, and act as skeletons to generate corresponding classes of space-filling, packings and labyrinths.

ON ANOMALOUS DIFFUSION OF GROWING CLUSTERS

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 875-880 ◽  
Author(s):  
ADAM GADOMSKI ◽  
JERZY LUCZKA
Keyword(s):  
Anomalous Diffusion ◽  
Materials Science ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mean Square Displacement ◽  
Polymer Science ◽  
The Mean ◽  
Continuous Random Walk ◽  
Mass Dependent ◽  
Three Dimensional Space

A continuous random walk of a growing cluster of dimension df is studied. It is assumed that its behavior is represented by a standard diffusion equation. A diffusion coefficient is assumed to be a cluster mass dependent power function which in the dilute solution regime takes a form first suggested by Kirkwood. The mass of the cluster increases in time according to another power law. It results in anomalous diffusion of the cluster in a three dimensional space which, in a linear case, is manifested by either power or logarithmic law of the mean square displacement. Some interesting examples and realizations of that process in polymer science, colloid physicochemistry or materials science are pointed out.

scholarly journals THE DEVELOPMENT OF ASSESSMENT INSTRUMENT USING TESLET MODELS IN STEREOCHEMISTRY MATERIALS

2019 ◽  
Vol 3 (1) ◽  
pp. 29 ◽  
Author(s):  
Annisaul Khasanah Wulandari
Keyword(s):  
Quantitative Data ◽  
Chemistry Education ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Field Testing ◽  
Assessment Instrument ◽  
Study Program ◽  
Analysis Technique ◽  
Education Study ◽  
The Mean

Stereochemistry is the study of molecules in three-dimensional space regarding how atoms in a molecule are arranged in one room relative to the other. Stereochemistry is a difficult course. Therefore, it is necessary to diagnose the difficulty of learning using the testlet model. This study is aimed at developing an appropriate testlet model for the assessment instrument. This research uses the development model of Borg and Gall's assessment instrument with ten stages, but this research is limited to the fifth stage only, namely 1) Research and Information Collection, 2) Planning 3) Develop Preliminary Form of Product 4) Preliminary Field Testing, and 5) Preliminary Product Revision. The data collection techniques were in the form of validation questionnaires from expert teams and students' response questionnaires. The data analysis technique used qualitative and quantitative data. The qualitative data were from the results of a review of validation by a team of experts who are Postgraduate Lecturers of Chemistry Education at Universitas Riau and lecturers of the Chemistry Education Study Program at the Faculty of Tarbiyah and Teaching at UIN Suska Riau. The quantitative data were obtained from the calculation of the mean scores of the validation questionnaire by two lecturers of the Postgraduate of Chemistry Education at Universitas Riau and one lecturer in the Chemistry Education Study Program at the Tarbiyah Faculty and Teacher Training at UIN Suska Riau as the experts. The results of the study show that the mean score of validation from the expert team is 3.97 on the aspect of material with valid category, 3.97 on the aspect of construction with valid category, 3.88 on the aspect of language with valid category; and the results of the students' response questionnaires are 51.58 on the time readability questionnaire and 8.08 on the aspect of time adequacy.

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