# A database of 3D neighborhood motion maps

** Published:**

2D neighborhood motion maps have allowed us to study local alterations of discrete spaces under digitized rigid motions. Nevertheless, computation of 3D neighborhood motions maps is a challenging problem. In Quadric Arrangement in Classifying Rigid Motions of a 3D Digital Image, we have introduced the first algorithm to compute neighborhood motion maps for digitized rigid motions on \(\mathbb{Z}^3\). Our implementation evolved since (see RigidMotionsMapleTools ) and has been improved.

## Table of content

# Up to date, we have managed to compute

Neighborhood motions maps of \(\mathcal{N}_1\) (6-neighborhood). (The last update on 2017-04-30. Click the DOI badge to download.)

Neighborhood motions maps of \(\mathcal{N}_2\) (18-neighborhood). (The last update on 2017-05-08. Click the DOI badge to download.)

Neighborhood motions maps of \(\mathcal{N}_3\) (26-neighborhood). (The last update on 2017-06-06. Click the DOI badge to download.)

The files are SQLite3 databases. You can use our 3DNMMVierwerDB to visualize neighborhood maps and see the parameters for which they were obtained.

# Our second-degree polynomials

Some people might be more interested in our quadrics than in the whole problem. These can be downloaded by clicking on the following DOI badge:

In particular, the files contain:

The set of 81 quadrics obtained for \(\mathcal{N}_1\) (6-neighborhood).

The set of 513 quadrics obtained for \(\mathcal{N}_2\) (18-neighborhood).

The set of 741 quadrics obtained for \(\mathcal{N}_3\) (26-neighborhood).

The files are Maple source code files and can be loaded to Maple in the following way:

```
read("<path/to/file.mpl>");
```

The above code will create a list Q such that each element of Q contains a polynomial.

It is worth to mention that each set of quadrics can be partitioned into three subsets. Moreover, by permuting variables in one of such subsets, we can obtain the other two subsets. We plan to exploit this property to improve our algorithm for computing arrangement of quadrics.

# How to cite

Any results obtained with the database should cite *Quadric Arrangement in Classifying Rigid Motions of a 3D Digital Image* and should refer to the DOI of a given database file.

# Acknowledgments

Special thanks for Hugues Talbot of ESIEE Paris, LIGM for allowing us to use his blade class machine. Also, we would like to thank David Cœurjolly, CNRS, University of Lyon, LIRIS for running some computations on the CC-IN2P3 cluster in Lyon.