  We find a closed form for Seiberg-Witten (SW) map between ordinary and
noncommutative (NC) Dirac-Born-Infeld actions. We show that NC Maxwell action
after the exact SW map can be regarded as ordinary Maxwell action coupling to a
metric deformed by gauge fields. We also show that reversed procedure by
inverse SW map leads to a similar interpretation in terms of induced NC
geometry. This implies that noncommutativity in field theory can be interpreted
as field dependent fluctuations of spacetime geometry, which genuinely realizes
an interesting idea recently observed by Rivelles.
