  We revisit the exact Seiberg-Witten (SW) map on Dirac-Born-Infeld actions,
making a connection with the deformation quantization scheme. The picture on
field dependent induced gravity from noncommutativity becomes more transparent
in the context of deformation quantization. We also find an exact SW map for an
adjoint scalar field, consistent with that deduced from RR couplings of
unstable non-BPS D-branes. The dual description via the exact SW map can again
be interpreted as the ordinary field theory coupling to gravity induced by
gauge fields. Using the exact SW maps, we further discuss several aspects of
topological invariants in noncommutative (NC) gauge theory. Especially, it is
shown that the K-theory class on NC instantons is mapped to the usual second
Chern class via exact SW map and it leads to an exact SW map between
commutative and NC Chern-Simons terms.
