Neural Abstraction Pyramid Architecture - Hierarchical Neural Networks for Image Interpretation - page 82

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Fig. 4.10. Local contrast normalization. The high-resolution output R 0 is shown over time.

• Q l - squared contrast [0 , 1]
- contains local energy
- two lateral projections from C ±
l

with square transfer function f sqr

• S l - smoothed contrast [0 , 2]
- lateral projection computes smoothed version of Q l using 5 × 5 binomial kernel
- forward projection from S l− 1 that averages 2 × 2 windows with total weight 0 . 5
- backward projection from S l +1 that expands to 2 × 2 cells of S l with weight 0 . 5
- bias weight of output unit 0 . 1
• D ±

l - normalized contrast [0 , 0 . 5]
- lateral projection from C ±

l and logarithmic transfer function f log
- lateral projection from S l and logarithmic transfer function f log
- weight from smoothed contrast projection to output sum is − 1
- output unit has exponential transfer function and computes C ±

l /S l

• R l - result [ − 0 . 5 , 0 . 5]
- lateral projection subtracts D

l from D l
- backward projection from R l +1 that expands to 2 × 2 cells of R l with weight 0 . 5
The central operation of the network is the division C ±

−

l /S l . It is implemented

with two features, D l and D −

l , since the arguments of the logarithmic transfer
function f log must be nonnegative. Another property of the implementation is that
the smoothed contrast level S l is not only computed within a scale, but that contrast
present at adjacent scales increases S l . This extends the lateral competition to a com-
petition between scales and produces masking effects in scale. Small high-contrast
details can mask larger-scale contrasts and vice versa.
Figure 4.10 displays the development of the high-resolution output R 0 over time.
After the first iteration, only small-scale contrast is present in the output since the
backward projection is not effective yet. During the following iterations, larger-scale
contributions arrive. The change of the network's activity decreases monotonically
after the initial iterations. The network dynamics converges quickly towards the
attractor shown in Figure 4.8(b).