Related Work - Hierarchical Neural Networks for Image Interpretation - page 41

The success of Gabor filters [79] also shows that the intermediate representations
are interesting. These filters are localized in space at u and in frequency at ξ with
Gaussian envelopes g :

g u,ξ ( x ) = g ( x − u ) e iξx ;

g u,ξ ( ω ) = g ( ω − ξ ) e −iu ( ω−ξ ) .

Gabor filters resemble properties of V1 simple neurons in the human visual system
and are very useful for texture discrimination [231], for example.

3.1.2 Neural Networks

The hierarchical image representations discussed so far had very few, if any, param-
eters to adapt to a specific set of images. Neural networks with more free parameters
have been developed that produce representations which can be tuned to a dataset
by learning procedures. These representations need not to be invertible since they
are used, for instance, for classification of an object present in the image.
Neocognitron. One classical example of such adaptable hierarchical image repre-
sentations is the Neocognitron, proposed by Fukushima [77] for digit recognition.
The architecture of this network is illustrated in Figure 3.6. It consists of several
levels, each containing multiple cell planes. The resolution of the planes decreases
from the input towards the upper levels of the hierarchy. The cell planes consist of
identical feature detectors that analyze a receptive field located in the input.
The size of the receptive fields increases with height, as do the invariance to
small translations and the complexity of the features. The cells in the first level
of the network analyze only a small input region and extract edge features. Cells
located at the second level receive input from the edge features and extract lines and
corners. Increasingly complex features, such as digit parts, are extracted at the third
level. Feature detectors at the topmost level react to the entire image and represent
digit classes.

Fig. 3.6. The Neocognitron proposed by Fukushima [77]. Digit features of increasing com-
plexity are extracted in a hierarchical feed-forward neural network.