Guided by Time-varying Tensor Fields Kai Xu, Lintao Zheng , Zihao - - PowerPoint PPT Presentation

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Guided by Time-varying Tensor Fields Kai Xu, Lintao Zheng , Zihao - - PowerPoint PPT Presentation

Apr 01, 2024 49 likes โ€ข534 views

Autonomous Reconstruction of Unknown Indoor Scenes Guided by Time-varying Tensor Fields Kai Xu, Lintao Zheng , Zihao Yan, Guohang Yan, Eugene Zhang, Matthias Niessner, Oliver Deussen, Daniel Cohen-Or, Hui Huang Shenzhen University National

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Autonomous Reconstruction of Unknown Indoor Scenes Guided by Time-varying Tensor Fields

Kai Xu, Lintao Zheng, Zihao Yan, Guohang Yan, Eugene Zhang, Matthias Niessner, Oliver Deussen, Daniel Cohen-Or, Hui Huang

Shenzhen University Oregon State University Stanford University National University of Defense Technology University of Konstanz Tel-Aviv University

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SLIDE 2

Video

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SLIDE 3

Background

Commodity RGBD sensors & real-time reconstruction

KinectFusion

[Izadi et al. 2011]

Registration & fusion Reconstruction (Localization) (Mapping) (Localization) (Mapping)

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SLIDE 4

Background

Human scanning is a laborious task Huge human effort Inaccurate scanning

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Motivation

Never feel tired Automatic Stable and accurate movement

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Difficulty of auto-scanning in unknown scenes

Slow and smooth scanning Fast exploration

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Our solution

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SLIDE 8

Pipeline

Scanning and online reconstruction Field updating and field-guided path finding Estimating camera trajectory

Local path advection Global path routing

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SLIDE 9

Key techniques

Tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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SLIDE 10

Key techniques

Tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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2D Tensor Field

In a 2D domain, assign every point a direction, but NOT orientation

Vector field Tensor field

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2D Tensor Field

Assign every point a tensor:

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Why Tensor field?

Fewer singularities Potential field Gradient field Tensor field

[Khatib et al. 1986] [Shade and Newman 2011]

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SLIDE 14

Why Tensor field?

Sink-free Vector field

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Why Tensor field?

Sink-free Potential field Gradient field Tensor field

[Khatib et al. 1986] [Shade and Newman]

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Why Tensor field? Tensor fields do have degenerate points

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Tensor field update

The currently scanned scene is projected onto the floor plane

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Tensor field update

Based on the tangential constraint of the 2D projection, a 2D tensor field is computed

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Tensor field update

A smooth transition from ๐‘ˆ๐‘ขโˆ’1 to ๐‘ˆ๐‘ข ?

๐‘ˆ๐‘ข ๐‘ˆ๐‘ขโˆ’1 Time-varying tensor fields

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SLIDE 20

Tensor field update

Time-varying tensor fields update

Key frame ๐‘ˆ๐‘ข Key frame ๐‘ˆ๐‘ขโˆ’1

Solve a spatial-temporal Laplacian system spatial-temporal constraint

๐‘ˆ

๐‘˜โˆ’1

๐‘ˆ

๐‘˜

๐‘ˆ

๐‘˜+1

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SLIDE 21

Key techniques

Tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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SLIDE 22

Key techniques

Tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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SLIDE 23

Local Path Generation

Particle advection over tensor field

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Key Points

Geometry-aware tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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Global path planning

Degenerate points

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Global path planning

Topological graph of tensor field

Node: Degenerate points Edge: Separatrix lines connecting degen. points

For a partial scene For the full scene Medial axis

Robot path finding ๏ƒ  Finding paths over the field topo. graph !

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Global path planning

Degenerate points

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Global path planning

How to select brunch at a trisector? High uncertainty Low uncertainty Trisector point

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Global path planning

Path routing with field topology

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Global path planning

Path routing with field topology

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Global path planning

Path routing with field topology

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Key Points

Geometry-aware tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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Field topology control

Movement of a degenerate point

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Field topology control

Movement of degenerate points

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Field topology control

Cancellation of degenerate pairs

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Key Points

Geometry-aware tensor field update

2D tensor field Time-varying tensor fields update

Field guided path planning

Local path generation by particle advection Global path finding by field topology Field topology control

Path-constrained camera trajectory estimation

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SLIDE 37

Camera Trajectory Optimization

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Camera Trajectory Optimization

  • Visibility to unknown
  • Linear speed
  • Angular speed

๐‘ž๐‘ก ๐‘ž๐‘กโˆ’1 ๐‘ž๐‘ก+1 ๐‘ž๐‘ก+2

0-1 integer programming

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Camera Trajectory Optimization

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๐‘ž๐‘ก ๐‘ž๐‘กโˆ’1 ๐‘ž๐‘ก+1 ๐‘ž๐‘ก+2

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SLIDE 40

Results

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SLIDE 41

Results

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Results

Scanning quality Scanned along potential field path Scanned along tensor field path

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Results

Scanning quality Non-smooth camera trajectory Optimized camera trajectory

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Evaluation

Effect of global path planning

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Comparison

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Future work Field guidance over non-planar ground surfaces, such as terrains ?

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Future work Use 3D tensor fields to guide robot grasping in complicated 3D environment ?

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Thank you for attention!