1 research outputs found
Extending the Morphological Hit-or-Miss Transform to Deep Neural Networks
While most deep learning architectures are built on convolution, alternative
foundations like morphology are being explored for purposes like
interpretability and its connection to the analysis and processing of geometric
structures. The morphological hit-or-miss operation has the advantage that it
takes into account both foreground and background information when evaluating
target shape in an image. Herein, we identify limitations in existing
hit-or-miss neural definitions and we formulate an optimization problem to
learn the transform relative to deeper architectures. To this end, we model the
semantically important condition that the intersection of the hit and miss
structuring elements (SEs) should be empty and we present a way to express
Don't Care (DNC), which is important for denoting regions of an SE that are not
relevant to detecting a target pattern. Our analysis shows that convolution, in
fact, acts like a hit-miss transform through semantic interpretation of its
filter differences. On these premises, we introduce an extension that
outperforms conventional convolution on benchmark data. Quantitative
experiments are provided on synthetic and benchmark data, showing that the
direct encoding hit-or-miss transform provides better interpretability on
learned shapes consistent with objects whereas our morphologically inspired
generalized convolution yields higher classification accuracy. Last,
qualitative hit and miss filter visualizations are provided relative to single
morphological layer