## What is good meshification algorithm?

• Processes unorganized point cloud
• Real-time processing
• Provides compression
• Incremental update
• Ideal for robotics applications including
• Visualization for effective human-robot interaction
• SLAM
• Grasping
• Traversability assessment
Voxel Planes, Ryde et al., IROS 2013.

## Existing work

Marching Cubes
• Requires scalar field
• Generates pair of surfaces
Greedy Projection (Marton et al. 2009)
- No compression
Poisson (Kazhdan et al. 2006)
- Closed water tight surfaces
Voxel Planes, Ryde et al., IROS 2013.

## Voxel planes

### Rapid meshification and compression of point clouds

Voxel Planes, Ryde et al., IROS 2013.

## Occupancy grids

Voxel Planes, Ryde et al., IROS 2013.

## Occupancy grids

• Processes unorganized point cloud
• Real-time processing
• Provides compression
• Incremental update
• Ideal for robotics applications including
• Visualization for effective human-robot interaction
• SLAM
• ?? Grasping
• ?? Traversability assessment

Voxel Planes, Ryde et al., IROS 2013.

## Voxel planes algorithm (simplified)

Voxel Planes, Ryde et al., IROS 2013.

## Result

Voxel Planes, Ryde et al., IROS 2013.

## Sliding window approach

Without sliding window
With sliding window

Voxel Planes, Ryde et al., IROS 2013.

## Voxel planes with sliding windows

Voxel Planes, Ryde et al., IROS 2013.

## Gaussians incremental update

$\renewcommand{\v}[1]{\mathbf{#1}} % format for vectors \DeclareMathOperator{\cov}{cov}$ $p_i = \frac{N_i}{\sum_i N_i}$

$$\bar{X} = \sum_i p_i \bar{X_i} \label{eq:mog_mean}$$ $$\cov X = \sum_i p_i \left( \cov X_i + \bar{X_i} \bar{X_i}^\top - \bar{X} \bar{X}^\top \right) \label{eq:mog_cov}$$

Voxel Planes, Ryde et al., IROS 2013.

## Blockwise data structure

Voxel Planes, Ryde et al., IROS 2013.

## Experiments

### Comparison with Greedy Projection and Marching cubes

Voxel Planes, Ryde et al., IROS 2013.

## Qualitative comparison

Voxel Planes, Ryde et al., IROS 2013.

## Runtime comparison

Voxel Planes, Ryde et al., IROS 2013.

## Compression efficiency

Voxel Planes, Ryde et al., IROS 2013.

## Thermogauss dataset (Borrmann et al. 2009)

Voxel Planes, Ryde et al., IROS 2013.

## Thermogauss results

Voxel Planes, Ryde et al., IROS 2013.

## Conclusion

• Meshification for robotics
• Processes unorganized point cloud
• Supports incremental update
• Faster than marching cubes
• Provides better compression than marching cubes and greedy projection
Voxel Planes, Ryde et al., IROS 2013.

## Coloring surfaces by normals

• Requirements

• Same colors for opposing normals
• Continous colorspace
• Flipping normals

• Creates discontinuity around the flipping plane
• Stretch the hemisphere to enclose the sphere
\begin{align*} [R, G, B] &= \frac{1}{2} \left[ \sin2\theta\cos\phi + 1, \sin2\theta\sin\phi + 1, \cos2\theta + 1 \right] \end{align*}
Voxel Planes, Ryde et al., IROS 2013.

## Questions?

### Acknowledgements

This material is based upon work partially supported by the Federal Highway Administration under Cooperative Agreement No. DTFH61-07-H-00023. Any opinions, findings, conclusions or recommendations are those of the authors and do not necessarily reflect the views of the FHWA.