### Table of Contents

This short tutorial shows how to
compute **Fisher vector** and
**VLAD** encodings with VLFeat MATLAB
interface.

These encoding serve a similar purposes: summarizing in a vectorial statistic a number of local feature descriptors (e.g. SIFT). Similarly to bag of visual words, they assign local descriptor to elements in a visual dictionary, obtained with vector quantization (KMeans) in the case of VLAD or a Gaussian Mixture Models for Fisher Vectors. However, rather than storing visual word occurrences only, these representations store a statistics of the difference between dictionary elements and pooled local features.

# Fisher encoding

The Fisher encoding uses GMM to construct a visual word dictionary. To exemplify constructing a GMM, consider a number of 2 dimensional data points (see also the GMM tutorial). In practice, these points would be a collection of SIFT or other local image features. The following code fits a GMM to the points:

```
numFeatures = 5000 ;
dimension = 2 ;
data = rand(dimension,numFeatures) ;
numClusters = 30 ;
[means, covariances, priors] = vl_gmm(data, numClusters);
```

Next, we create another random set of vectors, which should be encoded using the Fisher Vector representation and the GMM just obtained:

```
numDataToBeEncoded = 1000;
dataToBeEncoded = rand(dimension,numDataToBeEncoded);
```

The Fisher vector encoding `enc`

of these vectors is
obtained by calling the `vl_fisher`

function using the
output of the `vl_gmm`

function:

```
encoding = vl_fisher(datatoBeEncoded, means, covariances, priors);
```

The `encoding`

vector is the Fisher vector
representation of the data `dataToBeEncoded`

.

Note that Fisher Vectors support several normalization options that can affect substantially the performance of the representation.

# VLAD encoding

The **V**ector
of **L**inearly **A**gregated **D**escriptors is similar to
Fisher vectors but (i) it does not store second-order information
about the features and (ii) it typically use KMeans instead of GMMs to
generate the feature vocabulary (although the latter is also an
option).

Consider the same 2D data matrix `data`

used in the
previous section to train the Fisher vector representation. To compute
VLAD, we first need to obtain a visual word dictionary. This time, we
use K-means:

```
numClusters = 30 ;
centers = vl_kmeans(dataLearn, numClusters);
```

Now consider the data `dataToBeEncoded`

and use
the `vl_vlad`

function to compute the encoding. Differently
from `vl_fisher`

, `vl_vlad`

requires the
data-to-cluster assignments to be passed in. This allows using a fast
vector quantization technique (e.g. kd-tree) as well as switching from
soft to hard assignment.

In this example, we use a kd-tree for quantization:

```
kdtree = vl_kdtreebuild(centers) ;
nn = vl_kdtreequery(kdtree, centers, dataEncode) ;
```

Now we have in the `nn`

the indexes of the nearest
center to each vector in the matrix `dataToBeEncoded`

. The
next step is to create an assignment matrix:

assignments = zeros(numClusters,numDataToBeEncoded); assignments(sub2ind(size(assignments), nn, 1:length(nn))) = 1;

It is now possible to encode the data using
the `vl_vlad`

function:

enc = vl_vlad(dataToBeEncoded,centers,assignments);

Note that, similarly to Fisher vectors, VLAD supports several normalization options that can affect substantially the performance of the representation.