Geometric Registration for Deformable Shapes 4.1 Dynamic - - PowerPoint PPT Presentation

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Sep 16, 2022 150 likes •512 views

Geometric Registration for Deformable Shapes 4.1 Dynamic Registration Scan Registration Eurographics 2010 Course Geometric Registration for Deformable Shapes Scan Registration Solve for inter-frame motion: Eurographics 2010 Course

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Geometric Registration for Deformable Shapes

4.1 Dynamic Registration

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Scan Registration

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Scan Registration

Solve for inter-frame motion:

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Scan Registration

Solve for inter-frame motion:

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

The Setup

Given: A set of frames {P0, P1, ... Pn} Goal: Recover rigid motion {α1, α2, ... αn} between adjacent frames

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

The Setup

Smoothly varying object motion Unknown correspondence between scans Fast acquisition → motion happens between frames

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Insights

Rigid registration → kinematic property of space- time surface (locally exact) Registration → surface normal estimation Extension to deformable/articulated bodies

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Time Ordered Scans

tj tj+1 tj+2

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Space-time Surface

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Space-time Surface

→

t ∆

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Space-time Surface

→

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Spacetime Velocity Vectors

Tangential point movement → velocity vectors orthogonal to surface normals

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Spacetime Velocity Vectors

Tangential point movement → velocity vectors orthogonal to surface normals

) ( ). (

~ ~

j i j i

p n p v

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Final Steps

(rigid) velocity vectors →

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Final Steps

(rigid) velocity vectors !

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Registration Algorithm

1. Compute time coordinate spacing (σ), and form

space-time surface.

2. Compute space time neighborhood using ANN,

and locally estimate space-time surface normals.

3. Solve linear system to estimate (cj,cj).
4. Convert velocity vectors to rotation matrix +

translation vector using Plücker coordinates and quarternions.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Normal Estimation: PCA Based

Plane fitting using PCA using chosen neighborhood points.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Normal Estimation: Iterative Refinement

Update neighborhood with current velocity estimate.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Normal Refinement: Effect of Noise

Stable, but more expensive.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Normal Estimation: Local Triangulation

Perform local surface triangulation (tetrahedralization).

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Normal Estimation

Stable, but more expensive.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Comparison with ICP

ICP point-plane Dynamic registration

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Rigid: Bee Sequence (2,200 frames)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Rigid: Coati Sequence (2,200 frames)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Handling Large Number of Frames

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Rigid/Deformable: Teapot Sequence

(2,200 frames)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformable Bodies

Cluster points, and solve smaller systems. Propagate solutions with regularization.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformable: Hand (100 frames)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformable: Hand (100 frames)

scan #1 : scan #50 scan #1 : scan #100

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformation + scanner motion: Skeleton (100 frames)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformation + scanner motion: Skeleton (100 frames)

scan #1 : scan #50 scan #1 : scan #100

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Deformation + scanner motion: Skeleton (100 frames)

rigid components

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Performance (on 2.4GHz Athlon Dual Core, 2GB RAM)

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Conclusion

Simple algorithm using kinematic properties of space-time surface. Easy modification for deformable bodies. Suitable for use with fast scanners.

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

Limitations

Need more scans, dense scans, … Sampling condition → time and space

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Eurographics 2010 Course – Geometric Registration for Deformable Shapes

thank you