In a star-planet system, Kepler's third law determines that both the planet and its host star orbit the system's center of mass in a strict periodic regime. In multi-planet systems, however, multi-body interactions impart a non-Keplerian regime which causes orbits to deviate from strict periodicity. In transit photometry, these deviations are manifested as transit timing variations (TTVs). The features of a TTV signal are a function of planetary masses and orbital parameters, and are therefore useful for exoplanet characterization, especially for constraining planet masses. The case is more complicated for small exoplanets, whose transits may be in the signal-to-noise range where timing constraint is challenging or impossible, and the TTV of a discrete transit cannot be determined. Therefore, a global model which fits the TTV signal of the entire lightcurve at once is a favourable method to constrain the masses of small transiting exoplanets in multi-planet systems. For this purpose, I develop a non-linear, photodynamical fitting algorithm which fits a global TTV model in the photometric domain for a given system. With this tool I then infer planetary masses of small transiting exoplanets in multi-planet systems from Kepler's complete data set, and constrain their mass-radius relation.