We show how to apply Generalized Q-Sampling Imaging [Yeh2010] to diffusion MRI datasets. You can think of GQI as an analytical version of DSI orientation distribution function (ODF) (Garyfallidis, PhD thesis, 2012).

First import the necessary modules:

```
import numpy as np
from dipy.data import fetch_taiwan_ntu_dsi, read_taiwan_ntu_dsi, get_sphere
from dipy.reconst.gqi import GeneralizedQSamplingModel
from dipy.direction import peaks_from_model
```

Download and read the data for this tutorial.

```
fetch_taiwan_ntu_dsi()
img, gtab = read_taiwan_ntu_dsi()
```

img contains a nibabel Nifti1Image object (data) and gtab contains a
`GradientTable`

object (gradient information e.g. b-values). For example to
read the b-values it is possible to write:

```
print(gtab.bvals)
```

Load the raw diffusion data and the affine.

```
data = img.get_data()
print('data.shape (%d, %d, %d, %d)' % data.shape)
```

data.shape `(96, 96, 60, 203)`

This dataset has anisotropic voxel sizes, therefore reslicing is necessary.

```
affine = img.affine
```

Read the voxel size from the image header.

```
voxel_size = img.header.get_zooms()[:3]
```

Instantiate the model and apply it to the data.

```
gqmodel = GeneralizedQSamplingModel(gtab, sampling_length=3)
```

The parameter `sampling_length`

is used here to

Lets just use one slice only from the data.

```
dataslice = data[:, :, data.shape[2] // 2]
mask = dataslice[..., 0] > 50
gqfit = gqmodel.fit(dataslice, mask=mask)
```

Load an ODF reconstruction sphere

```
sphere = get_sphere('repulsion724')
```

Calculate the ODFs with this specific sphere

```
ODF = gqfit.odf(sphere)
print('ODF.shape (%d, %d, %d)' % ODF.shape)
```

ODF.shape `(96, 96, 724)`

Using `peaks_from_model`

we can find the main peaks of the ODFs and other
properties.

```
gqpeaks = peaks_from_model(model=gqmodel,
data=dataslice,
sphere=sphere,
relative_peak_threshold=.5,
min_separation_angle=25,
mask=mask,
return_odf=False,
normalize_peaks=True)
gqpeak_values = gqpeaks.peak_values
```

`gqpeak_indices`

show which sphere points have the maximum values.

```
gqpeak_indices = gqpeaks.peak_indices
```

It is also possible to calculate GFA.

```
GFA = gqpeaks.gfa
print('GFA.shape (%d, %d)' % GFA.shape)
```

With parameter `return_odf=True`

we can obtain the ODF using `gqpeaks.ODF`

```
gqpeaks = peaks_from_model(model=gqmodel,
data=dataslice,
sphere=sphere,
relative_peak_threshold=.5,
min_separation_angle=25,
mask=mask,
return_odf=True,
normalize_peaks=True)
```

This ODF will be of course identical to the ODF calculated above as long as the same data and mask are used.

```
np.sum(gqpeaks.odf != ODF) == 0
```

True

The advantage of using `peaks_from_model`

is that it calculates the ODF only
once and saves it or deletes if it is not necessary to keep.

- Yeh2010
Yeh, F-C et al., Generalized Q-sampling imaging, IEEE Transactions on Medical Imaging, vol 29, no 9, 2010.

Example source code

You can download `the full source code of this example`

. This same script is also included in the dipy source distribution under the `doc/examples/`

directory.