  Matrix configurations define noncommutative spaces endowed with extra
structure including a generalized Laplace operator, and hence a metric
structure. Made dynamical via matrix models, they describe rich physical
systems including noncommutative gauge theory and emergent gravity. Refining
the construction in [1], we construct a semi-classical limit through an
immersed submanifold of complex projective space based on quasi-coherent
states. We observe the phenomenon of oxidation, where the resulting
semi-classical space acquires spurious extra dimensions. We propose to remove
this artifact by passing to a leaf of a carefully chosen foliation, which
allows to extract the geometrical content of the noncommutative spaces. This is
demonstrated numerically via multiple examples.
