The quality of the separation algorithms in Figure 17.16 (RGB clustering) and in Figure 17.11 (neural network) is roughly similar. The RGB cluster-based result contains more high-frequency noise since the algorithm is based on the point-to-point look-up table approach and it doesn't perform any neighborhood analysis. This noise could easily be cleaned up by a simple postprocessor, eliminating isolated pixels, but we didn't perform it so far. In our approach, image smoothness analysis is represented by another class of algorithms, discussed in Section 17.3.5.

The most important point to stress is that the RGB cluster-based method is much faster than the backpropagation method. Indeed, in the RGB clustering algorithm, the pixellabel assignment is performed by a simple local look-up table computation which involves five numerical operations per pixel. The JPL backpropagation algorithm, employed in computing the result in Figure 17.11, contains 27 input neurons, 10 hidden neurons, and 7 output neurons, requiring about 700 numerical operations per pixel. The neural network chip speeds up the backpropagation-based separation algorithm by a factor of 10. In consequence, our algorithm is faster by a factor of 100 than the JPL software algorithm and it is still faster by a factor of 10 when compared with the JPL hardware implementation.

Our interpretation of these results and understanding of the backpropagation approach in view of our experience based on numerical/graphical experiments described above is as follows. Both algorithms contain similar components. In both cases, we enter some color mapping information into the system during the ``training'' stage and we construct some internal look-up table. In our case, this look-up table is constructed as a set of labelled polyhedral regions, realizing a partition of the RGB cube, whereas in the backpropagation case it is implemented in terms of the hidden units. Our look-up table is optimal for the problem at hand, whereas backpropagation uses the ``general-purpose'' look-up table offered by its general-purpose inputoutput mapping capabilities. It is therefore understandable that our algorithm is much faster.

Still, both algorithms are probably functionally equivalent, that is, the backpropagation algorithm effectively constructs a very similar look-up table, performing RGB clustering in terms of hidden units and synaptic weights. But it does this in a very inefficient way. One says that neural network is always the ``second best'' solution of the problem. In complex perceptual or pattern matching problems, this truly best solution is often unknown and the neural network approach is useful, whereas in the early/medium vision problems such as map separates, the machine vision techniques are competitive in quality and more efficient. However, we stress that backpropagation, even if less efficient, is a convenient way to get reasonable results quickly as far as user development time is concerned. It maximizes initial user productivity-not algorithmic performance.

The backpropagation algorithm produces a cleaner separated image as seen in Figures 17.11 and 17.16. This is due to the fact that the backpropagation operates on a input window and the RGB clustering uses window-that is, just a single pixel. Some smearing is therefore built into the neural network during the training period. The corresponding vision algorithms, involving the neighborhood analysis based on image smoothness, are discussed in the next Section.

Wed Mar 1 10:19:35 EST 1995