Neural Abstraction Pyramid Architecture - Hierarchical Neural Networks for Image Interpretation - page 67

2I × 2J ×K/2 I ×J ×K I/2 ×J/2 × 2K
layer (l− 1) layer l layer (l + 1)
Fig. 4.2. As the spatial resolution decreases, when going up the hierarchy, the number of
feature arrays increases. Different grayscales represent different features. In the lower layers
few grayscales are available at many locations while in the higher layers many variations of
shading can be accessed at few positions.
to all feature arrays of a layer is required to compute a feature cell, the total number
of connections rises by a factor of four when increasing the number of features to
4K, instead of 2K, in layer ( l + 1) . The choice of 2K features leads to a constant
number of total connections within each layer and to the reduction by a factor of two
in representation size when going up one layer. Hence, in this case the size of the
entire pyramid is less than double the size of its lowest layer and the total number of
connections is linear in the number of layers and in the number of bottom-layer cells.
Since the size of the representation decreases with height, not all details of an image
can be represented in the higher layers. Thus, there is some incentive in discovering
image structure that can be used to efficiently encode the abstract representations.
4.1.2 Distributed Representations
The feature cells in the Neural Abstraction Pyramid contain simple processing el-
ements that make a single value, the activity, available to other cells. The activ-
ity of a cell represents the strength of the associated feature at a certain position.
This resembles the computation by neurons in the brain. Such a massively parallel
approach to image processing requires millions of processing elements for high-
resolution images. Thus, it is necessary to make the individual processors simple
to keep the costs of simulating these on a serial machine or implementing them
in VLSI hardware within reasonable bounds. No complex data structures are used
in the architecture. The communication between processing elements only requires
access to cell activities via weighted links.
Figure 4.3 magnifies one layer l of the pyramid. All feature cells that share the
same location ( i,j ) within a layer form a hypercolumn. A hypercolumn describes all
aspects of the corresponding image window in a distributed sparse representation.
Neighboring hypercolumns define a hyper-neighborhood.
This definition is motivated by the interwoven feature maps present in cortical
areas, like in the primary visual cortex (compare to Section 2.2). All feature cells
that describe the same image location at the same level of abstraction are accessible
within close proximity. This facilitates interaction between these cells. Such inter-