# Computing Centerlines

## Medial Curve skeletons with AOF based Anchor
Anchor based medial curve computation uses some measure to define an end point. AOF(Average Outward Flux) uses the average outward flux of the
gradient field of signed distance function of an object. A negative value of flux, of the gradient field of signed (positive inside) distance function of
and object is a good indicator of end (medial) points. To run medial thinning in order of the distance to the object surface with end points 'anchored' 
using negative AOF values, run the following command:

```bash
$ skeltool -priority distance -curve -input <path/to/input/image> -anchor aof -outputFolder <output/folder/name>
```
Medial curve of a simple dinosaur sample image can be computed as follows.

```bash
$ skeltool -priority distance -curve -input data/dinosaur.tif -smooth 0.2  -fillholes -anchor aof -outputFolder results
```

<figure style="display:block; margin: 0 auto; text-align: center; width:600px">
<img alt="dinosaur-aof-anchor" src="images/dino-medialcurve-aof-anchor.png"/>
<figcaption>Sample dinosaur object in translucent blue with reddish colored medial curve inside</figcaption>
</figure>

If everything runs without errors you should see `dinosaur_distance_curve.tif` inside `results` folder. In the above command, options `-smooth` and `-fillholes`
are additional preprocessing steps that you may also want to run to get 'cleaner' skeletons.

For a more complex object, you may want to control the number of branches. Setting the threshold for AOF defined end point is a good way of doing this.
The default threshold value for aof is `-30`. Below are some example of medial curves computed using `aof` achnored end point for a few threshold values

AOF anchored medial curves using the default threshold value of `-30`

```bash
$ skeltool -priority distance -curve -input data/astropiece.tif -anchor aof -threshold -30  -outputFolder results
```

<figure style="display:block; margin: 0 auto; text-align: center; width:600px">
<img alt="astropiece-aofanchor-T-30" src="images/astropiece-medialcurve-aof-anchor-30.png"/>
<figcaption>A complex object in translucent blue with reddish-blue medial curve inside</figcaption>
</figure>

A larger threshold of `-20` (closer to `zero`) leads to many more branches.


```bash
$ skeltool -priority distance -curve -input data/astropiece.tif -anchor aof -threshold -20 -outputFolder results
```

<figure style="display:block; margin: 0 auto; text-align: center; width:600px">
<img alt="astropiece-aofanchor-T-20" src="images/astropiece-medialcurve-aof-anchor-20.png"/>
<figcaption>A complex object in translucent blue with reddish-blue medial curve inside</figcaption>
</figure>


A smaller  threshold on aof value (`-35`) can lead to a sparse skeleton as shown below.

```bash
$ skeltool -priority distance -curve -input data/astropiece.tif -anchor aof -threshold -35 -outputFolder results
```

<figure style="display:block; margin: 0 auto; text-align: center; width:600px">
<img alt="astropiece-aofanchor-T-35" src="images/astropiece-medialcurve-aof-anchor-35.png"/>
<figcaption>A complex object in translucent blue with reddish-blue medial curve inside</figcaption>
</figure>