Related Work - Hierarchical Neural Networks for Image Interpretation - page 50

(a) (b)
Fig. 3.11. Hierarchical Kalman filter proposed by Rao and Ballard [187]: (a) predictive esti-
mator (PE) module that integrates top-down predictions r td and a feed-forward error signal
( I − U r ) to an estimate r of the causes of an image I ; matrix U mediates between the image and
the causes; (b) general architecture of the system: local PEs are combined by a higher-level
PE (images adapted from [187]).
(a) (b)
Fig. 3.12. Hierarchical Kalman filter receptive fields: (a) Level 1 receptive fields resemble
Gabor-like responses of simple cells; (b) Level 2 receptive fields cover a larger area and are
more complex (images from [187]).
have been passed through a center-surround filter and have been weighted with a
Gaussian window. They are extracted from adjacent image windows that have an
offset of 5 pixels horizontally. Level 1 contains three identical PEs that maintain r
with 32 neurons. On Level 2, a single PE receives input from all three local PEs and
represents r h with 128 neurons. Its receptive field has a size of 26 × 16 pixels.
Some of the receptive fields that emerge when the network is trained on natural
image patches are shown in Figure 3.12. The Level 1 neurons have Gabor-like recep-
tive fields that detect local orientation. These responses resemble V1 simple cells.
Level 2 neurons have more complex receptive fields that are obtained by combining
Level 1 features.
Rao and Ballard demonstrated that Level 1 neurons display end-stopping be-
havior that is explained by predictive coding. Since longer oriented lines are more
probable in natural images than short lines, an orientation-selective cell responds
stronger to a short line inside its classical receptive field than to a longer line, which
can be predicted by a higher-level module. Since the cell signals only the difference
between this prediction and the input, it is less active.
Such a predictive coding scheme could be an efficient way to communicate be-
tween the levels of the visual system. It removes redundancy because only those
parts of the signal that are not already known to the receiver are sent. Several mech-
anisms in the visual system can be viewed from this perspective. Center-surround
receptive fields in the retina and the LGN compute the difference between the cen-