Binarization of Matrix Codes - Hierarchical Neural Networks for Image Interpretation - page 162

forward, lateral, and backward projections with linear transfer functions. Forward
projections come from 4 × 4 windows of all feature arrays in the layer below. Lateral
projections originate from the 5 × 5 hyper-neighborhood in the same layer and back-
ward projections access a single cell of all feature arrays in the layer above. The
weights can have positive or negative values and are allowed to change their sign
during training. The network has a total of 11,910 different weights. Most of them
are located in the top layer since the few weights in the lower layers are shared far
more often than the ones in the higher layers.
The version of the Neural Abstraction Pyramid network that is used for binariza-
tion has relatively few feature arrays. The reason for this restriction was the need to
limit the computational effort of simulating the pyramid on a PC. Due to the rel-
atively high resolution of the input images, the iterative binarization of one Data
Matrix code required about two seconds on a Pentium 4 1.7GHz PC.
The undegraded Data Matrix images as well as their degraded versions are pre-
sented to the network without any preprocessing. One of the feature arrays in the
bottom layer is used as network output.
The target values that are used as the desired output for the supervised training
are computed using the adaptive thresholding method for the undegraded images.
The network is trained to iteratively produce them not only for the original images,
but for the degraded versions of these images as well. This approach has the ad-
vantage that the effort for producing a desired output for low-quality images is not
necessary. If one wanted to produce a desired output for the degraded images with-
out relying on the original versions, one would need to use time-consuming manual
labeling which is avoided by using the adaptive thresholding for the undegraded
originals.
The 515 high-contrast images were partitioned randomly into 334 training im-
ages (TRN) and 181 test examples (TST). For each example, one degraded version is
added to the sets. The network is trained for ten iterations with a linearly increasing
error-weight using backpropagation through time (BPTT) and RPROP, as described
in Section 6.
8.6 Experimental Results
After training, the network is able to iteratively solve the binarization task. Fig-
ure 8.11 displays how the activities of all features evolve over time for one of the
degraded test examples. It can be seen that the lower layers represent the cell struc-
ture of the code, while the higher layers are dominated by representations of the
background level and the local black-and-white ratio. One can furthermore observe
that the network performs an iterative refinement of an initial solution with most
changes occurring in the first few iterations and fewer changes towards the end of
the computation. In fact, the activities of iteration 7 and 11 are hardly distinguish-
able.
In Figure 8.12, the activities of the two Layer 0 feature arrays are displayed
in more detail. The upper row shows the development of the output. In the first