Mathematical model for wide range gaze tracking system based on corneal reflections and pupil using stereo cameras

2012 ◽  
Author(s):  
Takashi Nagamatsu ◽  
Michiya Yamamoto ◽  
Ryuichi Sugano ◽  
Junzo Kamahara
Keyword(s):  
Mathematical Model ◽  
Tracking System ◽  
Gaze Tracking ◽  
Wide Range ◽  
Stereo Cameras

scholarly journals A Method of Free-Space Point-of-Regard Estimation Based on 3D Eye Model and Stereo Vision

2018 ◽  
Vol 8 (10) ◽  
pp. 1769
Author(s):  
Zijing Wan ◽  
Xiangjun Wang ◽  
Lei Yin ◽  
Kai Zhou
Keyword(s):  
Tracking System ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
Model Parameters ◽  
Gaze Tracking ◽  
Calibration Process ◽  
Eye Model ◽  
Stereo Cameras ◽  
Spatial Coordinates ◽  
Tracking Device

This paper proposes a 3D point-of-regard estimation method based on 3D eye model and a corresponding head-mounted gaze tracking device. Firstly, a head-mounted gaze tracking system is given. The gaze tracking device uses two pairs of stereo cameras to capture the left and right eye images, respectively, and then sets a pair of scene cameras to capture the scene images. Secondly, a 3D eye model and the calibration process are established. Common eye features are used to estimate the eye model parameters. Thirdly, a 3D point-of-regard estimation algorithm is proposed. Three main parts of this method are summarized as follows: (1) the spatial coordinates of the eye features are directly calculated by using stereo cameras; (2) the pupil center normal is used to the initial value for the estimation of optical axis; (3) a pair of scene cameras are used to solve the actual position of the objects being watched in the calibration process, and the calibration for the proposed eye model does not need the assistance of the light source. Experimental results show that the proposed method can output the coordinates of 3D point-of-regard more accurately.

Calibration for Gaze Tracking System Based on Stereo Cameras and Plane Mirror

2011 ◽  
Vol 31 (4) ◽  
pp. 0415002
Author(s):  
张琼 Zhang Qiong ◽  
王志良 Wang Zhiliang ◽  
迟健男 Chi Jiannan ◽  
史雪飞 Shi Xuefei
Keyword(s):  
Tracking System ◽  
Plane Mirror ◽  
Gaze Tracking ◽  
Stereo Cameras

The Research on Eye Tracking for Gaze Tracking System

2010 ◽  
Vol 36 (8) ◽  
pp. 1051-1061 ◽  
Author(s):  
Chuang ZHANG ◽  
Jian-Nan CHI ◽  
Zhao-Hui ZHANG ◽  
Zhi-Liang WANG
Keyword(s):  
Eye Tracking ◽  
Tracking System ◽  
Gaze Tracking

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

scholarly journals Deep-Learning-Based Pupil Center Detection and Tracking Technology for Visible-Light Wearable Gaze Tracking Devices

2021 ◽  
Vol 11 (2) ◽  
pp. 851
Author(s):  
Wei-Liang Ou ◽  
Tzu-Ling Kuo ◽  
Chin-Chieh Chang ◽  
Chih-Peng Fan
Keyword(s):  
Deep Learning ◽  
Visible Light ◽  
Tracking System ◽  
Recall Rate ◽  
Detection Accuracy ◽  
Learning Technology ◽  
Tracking Errors ◽  
Gaze Tracking ◽  
Detection Technology ◽  
Pupil Tracking

In this study, for the application of visible-light wearable eye trackers, a pupil tracking methodology based on deep-learning technology is developed. By applying deep-learning object detection technology based on the You Only Look Once (YOLO) model, the proposed pupil tracking method can effectively estimate and predict the center of the pupil in the visible-light mode. By using the developed YOLOv3-tiny-based model to test the pupil tracking performance, the detection accuracy is as high as 80%, and the recall rate is close to 83%. In addition, the average visible-light pupil tracking errors of the proposed YOLO-based deep-learning design are smaller than 2 pixels for the training mode and 5 pixels for the cross-person test, which are much smaller than those of the previous ellipse fitting design without using deep-learning technology under the same visible-light conditions. After the combination of calibration process, the average gaze tracking errors by the proposed YOLOv3-tiny-based pupil tracking models are smaller than 2.9 and 3.5 degrees at the training and testing modes, respectively, and the proposed visible-light wearable gaze tracking system performs up to 20 frames per second (FPS) on the GPU-based software embedded platform.

An adaptive blink detector to initialize and update a view-basedremote eye gaze tracking system in a natural scenario

2009 ◽  
Vol 30 (12) ◽  
pp. 1144-1150 ◽  
Author(s):  
Diego Torricelli ◽  
Michela Goffredo ◽  
Silvia Conforto ◽  
Maurizio Schmid
Keyword(s):  
Tracking System ◽  
Eye Gaze ◽  
Gaze Tracking

Robust sideslip angle observer of commercial vehicles based on cornering stiffness estimation using neural network

2022 ◽  
pp. 095440702110724
Author(s):  
Chenyu Zhou ◽  
Liangyao Yu ◽  
Yong Li ◽  
Jian Song
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Stability Control ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Commercial Vehicles ◽  
Sideslip Angle ◽  
The Neural Network ◽  
Wide Range ◽  
The Mathematical Model

Accurate estimation of sideslip angle is essential for vehicle stability control. For commercial vehicles, the estimation of sideslip angle is challenging due to severe load transfer and tire nonlinearity. This paper presents a robust sideslip angle observer of commercial vehicles based on identification of tire cornering stiffness. Since tire cornering stiffness of commercial vehicles is greatly affected by tire force and road adhesion coefficient, it cannot be treated as a constant. To estimate the cornering stiffness in real time, the neural network model constructed by Levenberg-Marquardt backpropagation (LMBP) algorithm is employed. LMBP is a fast convergent supervised learning algorithm, which combines the steepest descent method and gauss-newton method, and is widely used in system parameter estimation. LMBP does not rely on the mathematical model of the actual system when building the neural network. Therefore, when the mathematical model is difficult to establish, LMBP can play a very good role. Considering the complexity of tire modeling, this study adopted LMBP algorithm to estimate tire cornering stiffness, which have simplified the tire model and improved the estimation accuracy. Combined with neural network, A time-varying Kalman filter (TVKF) is designed to observe the sideslip angle of commercial vehicles. To validate the feasibility of the proposed estimation algorithm, multiple driving maneuvers under different road surface friction have been carried out. The test results show that the proposed method has better accuracy than the existing algorithm, and it’s robust over a wide range of driving conditions.

Probabilistic Model of the Reflectivity of Construction Materials of the Agroindustrial Complex

2021 ◽  
Vol 3 (44) ◽  
pp. 111-115
Author(s):  
Tat’yana R. Gallyamova ◽  
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Reflection Coefficient ◽  
Probabilistic Method ◽  
Construction Materials ◽  
Research Purpose ◽  
Visible Range ◽  
Industrial Complex ◽  
Large Area ◽  
Wide Range

When developing modern lighting technologies for objects of the agro-industrial complex, the problem arises of assessing the contribution of reflected light to the normalized illumination. The reflective properties of the surfaces of materials are characterized by a reflection coefficient ρ, which reaches a value of 0.7. This allows us to consider the reflective surfaces as an additional light source and the possibility of reducing energy consumption costs. (Research purpose) The research purpose is in developing a mathematical model that allows us to estimate the spectral reflection coefficient ρ(λ) of materials of construction technologies of the agro-industrial complex in the ultraviolet and visible spectral regions. (Materials and methods) That the disadvantage of various models is the lack of an analytical method for calculating the reflection coefficient in a wide range of wavelengths. We used a probabilistic method to overcome this disadvantage. (Results and discussion) The developed mathematical model makes it possible to estimate the reflection coefficient of the rough surface of materials in a wide range of the spectrum. For concrete, the area of agreement between theory and experiment is in the wavelength range from 250 to 1000 nm. The saturation mode predicted by the theory (the independence of the reflection coefficient from the wavelength) at a reflection coefficient of 0.4 is consistent with the experimental values in the visible range of the spectrum for construction materials of the agro-industrial complex, in particular, gray textured concrete, gray facade paint, light wood, gray silicate brick, new plaster without whitewash. (Conclusions) In the case of normal light incidence, the developed mathematical model allows us to theoretically estimate the reflection coefficient of the rough surfaces of construction technologies of the agro-industrial complex. The proposed model can be used in the development and design of a system of technological lighting of large-area premises (for example, when keeping birds on the floor), as well as for developing recommendations for reducing the energy consumption of existing lighting systems.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

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