| Summary: | 碩士 === 國立中正大學 === 資訊工程研究所 === 81 === Stack filters are nonlinear filters which are based on the
positive Boolean functions (PBF) as their window operators and
nonlinear operators. Thus, a good data structure of these
functions will make us easy to investigate their properties and
behaviors. Matrix representation of a PBF is such a good data
structure that leads us into a new approach of the study of
stack filters and stack neural networks. The powerful ability
of matrix computation would make it easu to study stack filters
and stack neural networks and also the broad fields that use
the PBFs. In this thesis, we propose a subclass of positive
Boolean functions called associative positive Boolean functions
(APBFs) which can be represented by the matrix form. A matrix
of size (n+1)*(n+1) is used to represent an n-variable APBF. It
is better than the Boolean expression whose storage is of
exponential order. Moreover, it satisfies the requirement of
associative memory of neural networks and is more efficient to
store in memory. The algorithms to transfer between this data
structure and the Boolean expression are prosed. Furthermore,
we also prosed the retrieval method and some basic Boolean
operations upon this new data structure. So, all the operations
upon this data structure can be established and we can use the
matrix representation of this sbclass of the positive Boolean
functions to study stack filters and stack neural networks.
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