Quantitative Model for Dynamic Spatial Distortion in Virtual Environments

Zixiong Peng; Zhenping Xia; Yueyuan Zhang; Chaochao Li; Yuanshen Zhang

doi:10.3788/LOP232351

Laser & Optoelectronics Progress, Volume. 61, Issue 10, 1011007(2024)

Quantitative Model for Dynamic Spatial Distortion in Virtual Environments

Zixiong Peng¹, Zhenping Xia^1,2、*, Yueyuan Zhang¹, Chaochao Li², and Yuanshen Zhang¹

¹College of Electronics and Information Engineering, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

²College of Physical Science and Technology, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

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Figures & Tables(8)

Fig. 1. 3D content acquisition, display and perception. (a) Image acquisition by parallel camera system; (b) the observer perceives the virtual scene

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Fig. 2. Geometric distortions in different virtual spaces. (a) Distortion free point cloud for accurate perception by viewers ; (b) the distance between the eye pupil and the baseline of the parallel camera does not match; (c) the distance between the viewing distance of the viewer and the convergence distance of the camera does not match; (d) pincushion distortion

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Fig. 3. Flowchart of the distortion quantification algorithm

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Fig. 4. The dynamic distortion value in the set scene. (a) Similarity curve; (b) distorted velocity curve; (c) distorted acceleration curve

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Fig. 5. Six reference point clouds selected for the experiment. (a) LongDress; (b) Hhi; (c) Shark; (d) Horse; (e) Dolphin; (f) Cat

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Fig. 6. Visual perception experiment settings

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Table 1. Symbols used in the space coordinate transformations

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Table 1. Symbols used in the space coordinate transformations

Variable	Geometric meaning
P	Points in the object space
（X_o，Y_o，Z_o）	Object spatial coordinates
（X_i，Y_i，Z_i）	Image spatial coordinates
（X_c，Y_c）	Camera sensor plane coordinates，X_cl for the left camera and X_cr for the right camera
（X_s，Y_s）	Display screen plane coordinates，X_sl for the left view and X_sr for the right view
α	Single camera view field
β	Single eye view field
t	Baseline length between the cameras
e	Inter-Pupillary Distance，IPD
W_c	Width of the camera sensor
W_s	Width of the display screen
C	Convergence distance of the 3D camera system
V	Viewing distance of the 3D display system
f	Focal length of the camera
h	Camera sensor offset for convergence

Table 2. Performance indicators of different objective methods
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Table 2. Performance indicators of different objective methods
Method Indicator
PLCC SROCC RMSE
p2point ^［11］ 0.83 0.75 0.34
p2plane ^［12］ 0.70 0.54 0.45
3D-2D^［16］ 0.75 0.49 0.41
PSNR-geom ^［14］ 0.86 0.71 0.34
Proposed method 0.93 0.86 0.24

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Zixiong Peng, Zhenping Xia, Yueyuan Zhang, Chaochao Li, Yuanshen Zhang. Quantitative Model for Dynamic Spatial Distortion in Virtual Environments[J]. Laser & Optoelectronics Progress, 2024, 61(10): 1011007

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