  Kepler Mission's single-band photometry suffers from astrophysical false
positives, the most common of background eclipsing binaries (BEBs) and
companion transiting planets (CTPs). Multi-color photometry can reveal the
color-dependent depth feature of false positives and thus exclude them. In this
work, we aim to estimate the fraction of false positives that are unable to be
classified by Kepler alone but can be identified with their color-dependent
depth feature if a reference band (z, Ks and TESS) were adopted in follow-up
observation. We build up physics-based blend models to simulate multi-band
signals of false positives. Nearly 65-95% of the BEBs and more than 80% of the
CTPs that host a Jupiter-size planet will show detectable depth variations if
the reference band can achieve a Kepler-like precision. Ks band is most
effective in eliminating BEBs exhibiting any depth sizes, while z and TESS band
prefer to identify giant candidates and their identification rates are more
sensitive to photometric precision. Provided the radius distribution of planets
transiting the secondary star in binary systems, we derive formalism to
calculate the overall identification rate for CTPs. By comparing the likelihood
distribution of the double-band depth ratio for BEB and planet models, we
calculate the false positive probability (FPP) for typical Kepler candidates.
Additionally, we show that the FPP calculation helps distinguish the planet
candidate's host star in an unresolved binary system. The analysis framework of
this paper can be easily adapted to predict the multi-color photometry yield
for other transit surveys, especially for TESS.
