.. _two-level:

Two-level operators
===================

Training WOperators with large windows requires big training sets to avoid overfitting.
Two-level operators mitigate this problem by combining the output of many individual WOperators
into a *second level pattern*, which is then classified again to obtain the final pixel value. 
The resulting operator uses, indirectly, information from the union the windows of 
all operators combined. More information about two level operators can be found at 
*Nina S. T. Hirata, "Multilevel Training of Binary Morphological Operators" at IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009*.


In *TRIOSlib* two-level operators can be implemented using the *CombinationPattern* *Feature Extractors*.
This class receives as input a set of WOperators and assembles the second level pattern with their
outputs. In the example below we combine windows generated randomly, but more interesting and powerful
combination methods are available in the literature.


.. literalinclude:: ../test/two_level_test.py