Smooth Assembled Mappings for Large-Scale Real Walking Zhi-Chao Dong - - PowerPoint PPT Presentation

▶

May 10, 2023 403 likes •822 views

Smooth Assembled Mappings for Large-Scale Real Walking Zhi-Chao Dong , Xiao-Ming Fu, Chi Zhang, Kang Wu, Ligang Liu University of Science and Technology of China Immersive virtual reality A perception of being physically present in a

SLIDE 1

Smooth Assembled Mappings for Large-Scale Real Walking

Zhi-Chao Dong, Xiao-Ming Fu, Chi Zhang, Kang Wu, Ligang Liu University of Science and Technology of China

SLIDE 2

HTC Vive Oculus Rift Sony Play Station

Immersive virtual reality

A perception of being physically present in a non-physical world
VR systems provide an engrossing total environment

SLIDE 3

Locomotion in immersive VR

Joystick
Walking-in-place
Real walking

stationary, unnatural

SLIDE 4

Joystick
Walking-in-place
Real walking

simulated walking, less natural

Locomotion in immersive VR

SLIDE 5

Joystick
Walking-in-place
Real walking

Locomotion in immersive VR

walk freely, natural

SLIDE 6

Goal: mapping for real walking

Build a mapping between the virtual scene and the real workspace
Optimal: bijective and isometric mapping

Real workspace Virtual scene

SLIDE 7

Challenge

Virtual scene and real workspace often differ significantly in sizes, shapes.
How to explore large virtual scene in smaller real workspace?

Virtual scene Real workspace

SLIDE 8

Existing methods in real walking

Space manipulation
[Suma et al. 2011, 2012], [Vasylevska and Kaufmann 2017], [Vasylevska et al. 2013]

[Vasylevska et al. 2013]

SLIDE 9

Redirected walking
[Razzaque et al. 2001, 2002], [Williams et al. 2007], [Steinicke et al. 2010],[Hodgson

and Bachmann 2013], [Azmandian et al. 2014], [Nescher et al. 2014] ···

[Nescher et al. 2014] [Steinicke et al. 2010]

Existing methods in real walking

SLIDE 10

[Sun et al. 2016]

Space mapping method
[Sun et al. 2016] : computing a global mapping between virtual and real scenes

Existing methods in real walking

SLIDE 11

Problem: severe distortion

Mapping the large-scale virtual scene globally may result in severe distortions

and artifacts. The greater size ratio, the larger distortions

extremely large distortion

SLIDE 12

Our idea

Smooth Assembled Mappings (SAM):
A divide-and-conquer strategy
Benefits:

map substantially large virtual scenes into smaller real workspaces with low isometric distortion achieve better walking experience

SLIDE 13

Our Method

1. Decomposition
Decompose the virtual scene into small super-patches
2. Mapping assembly
Each super-patch is mapped into real workspace
3. Global refinement
Reduce the distortion globally
Key challenges:
How to achieve low distortion mappings for large-scale virtual

scene?

How to keep smoothness between local mappings?

SLIDE 14

Decomposition

Input

Partition patches

SLIDE 15

Decomposition

Input

Super-patches

SLIDE 16

Mapping assembly

Compute mappings for all super-patches one by one in a width-first order.

The first super-patch Mapping result

SLIDE 17

The second super-patch Mapping and assembly

Mapping assembly

Compute mappings for all super-patches one by one in a width-first order.

SLIDE 18

The other super-patches Mapping and assembly

Mapping assembly

Compute mappings for all super-patches one by one in a width-first order.

SLIDE 19

Mapping a local quad patch

Bézier patch as a map:

𝑔 𝑣, 𝑤 =

𝑗=0 𝑜 𝑘=0 𝑛

𝑑𝑗,𝑘𝐶𝑗

𝑜 𝑣 𝐶 𝑘 𝑛(𝑤)

 𝑑𝑗,𝑘: control points  𝐶𝑗

𝑜 𝑣 : Bernstein polynomial basis function

𝑔 One patch Real workspace

𝑄𝑙 𝑇𝑆

SLIDE 20

Distortion cost: conforming low-distortion mapping

Distance-preserving cost:

𝐹𝑗𝑡𝑝(𝑞) =

𝑘=1 2

𝜏

𝑘 2 + 𝜏 𝑘 −2

 𝜏

𝑘: singular value of 𝐾(𝑞)

 When 𝜏1 = 𝜏2 = 1, the mapping is isometric, i.e., distance-preserving

𝜏2

𝜏1

SLIDE 21

Boundary cost: avoiding colliding

Exterior boundary cost

𝐹𝑓𝑦𝑢 𝑞 =

𝑘=1 4

2 𝑒𝑘 + 𝑒𝑘

2 + 𝜗

Interior obstacle cost [Sun et al. 2016]

𝐹𝑗𝑜𝑢 𝑞 = exp − 1 2𝜏2 𝑣′2 𝑥2 + 𝑤′2 ℎ2

𝑣′ 𝑤′ = 𝑣 𝑤 cos 𝜄𝑑 sin 𝜄𝑑 − sin 𝜄𝑑 cos 𝜄𝑑 − 𝑣𝑑 𝑤𝑑

interior 𝑞 𝑒𝑘 > 0

SLIDE 22

Constraints

1 2 𝑜 − 2 𝑜 − 1

𝑄𝑙 𝑄𝑚

Smoothness constraints:

𝒅𝑜,𝑘

𝑙

= 𝒅0,𝑘

𝑚

𝒅𝑜,𝑘

𝑙

− 𝒅𝑜−1,𝑘

𝑙

= 𝒅1,𝑘

𝑚

− 𝒅0,𝑘

𝑚

𝒅𝑜,𝑘

𝑙

− 2𝒅𝑜−1,𝑘

𝑙

+ 𝒅𝑜−2,𝑘

𝑙

= 𝒅2,𝑘

𝑚

− 2𝒅1,𝑘

𝑚

+ 𝒅0,𝑘

𝑚

Local bijection constraints:

det 𝐾(𝑞) > 0

𝐾(𝑞) is the Jacobian of the mapping at 𝑞

SLIDE 23

Formulation and optimization

min distoriton cost + boundary cost

s. t. smoothness constraint

local bijection constraint

Optimization process

Super-patch based assembly
Newton’s method

SLIDE 24

Global optimization

Perform a global optimization after all assemblies

SLIDE 25

Recap: our SAM method

SLIDE 26

Experiments

SLIDE 27

3.6𝑛 × 3.6𝑛 sketch map real workspace

Setup

SLIDE 28

User studies: various virtual scenes

SLIDE 29

Interior obstacles

SLIDE 30

Comparison to [Sun et al. 2016]: simulation

SLIDE 31

Comparison to [Sun et al. 2016]: user study

SLIDE 32

Comparisons with redirected walking

SLIDE 33

Comparisons with redirected walking

SLIDE 34

Comparisons with redirected walking

Square: user Circle: wolf

SLIDE 35

Comparisons with redirected walking

Red: user Green: wolf

SLIDE 36

Applications

SLIDE 37

Conclusion

A novel divide-and-conquer method for mapping large-scale virtual

scene into small real workspace

Much less distortion
Better walking experience
Can work for any large virtual scenes

SLIDE 38

Limitations

Pathways with large widths
Only pathway-type scene

Future work

Open scenes
Mapping scenes in AR

Conclusion

SLIDE 39

Acknowledgements

All participants of user studies
Qi Sun ([Sun et al. 2016]), Stony Brook University
Mahdi Azmandian ([Azmandian et al. 2016]), University of

Southern California

Peng Song, Xuejin Chen, University of Science and Technology
f China

SLIDE 40