  Among the most fascinating and hotly-debated areas in contemporary
astrophysics are the means by which planetary systems are assembled from the
large rotating disks of gas and dust which attend a stellar birth. Although
important work has already been, and is still being done both in theory and
observation, a full understanding of the physics of planet formation can only
be achieved by opening observational windows able to directly witness the
process in action. The key requirement is then to probe planet-forming systems
at the natural spatial scales over which material is being assembled. By
definition, this is the so-called Hill Sphere which delineates the region of
influence of a gravitating body within its surrounding environment. The Planet
Formation Imager project (PFI) has crystallized around this challenging goal:
to deliver resolved images of Hill-Sphere-sized structures within candidate
planet-hosting disks in the nearest star-forming regions. In this contribution
we outline the primary science case of PFI. For this purpose, we briefly review
our knowledge about the planet-formation process and discuss recent
observational results that have been obtained on the class of transition disks.
Spectro-photometric and multi-wavelength interferometric studies of these
systems revealed the presence of extended gaps and complex density
inhomogeneities that might be triggered by orbiting planets. We present
detailed 3-D radiation-hydrodynamic simulations of disks with single and
multiple embedded planets, from which we compute synthetic images at
near-infrared, mid-infrared, far-infrared, and sub-millimeter wavelengths,
enabling a direct comparison of the signatures that are detectable with PFI and
complementary facilities such as ALMA. From these simulations, we derive some
preliminary specifications that will guide the array design and technology
roadmap of the facility.
