How is the mass and semimajor axis of a directly imaged exoplanet found? I can't find information on this for the life of me. 

How do astronomers approximate the mass and semimajor axis of a directly imaged exoplanet? Would several photos need to be taken to find the period and find with Kepler's third law or can it be inferred through the temperature of the planet (or another method)? Also if you have any sources of this that would be great. 

Thanks
A single direct image of an exoplanets can give an estimate of the mass and orbital period of an exoplanet.

For the former, you need a model for how the luminosity of a giant exoplanet (which all the directly imaged ones are) evolves with time, as a function of mass, and an estimate of the age. One simply looks up what mass of planet would have cooled to its current luminosity at the age of the star that hosts the exoplanet. The luminosity measurement needs an accurate distance to the system and benefits from observations at multiple wavelengths. Realistically, these masses are uncertain by a factor of two at least, because of cooling model uncertainties.

Here is an example of this applied to various directly imaged exoplanets. Evolutionary tracks for various masses are shown in the luminosity versus age plane. Note the size of the age error bars and that is before you factor in uncertainty in the models (two flavours, "hot start" and "cold start" are shown as solid and dashed lines respectively - from Bonnefoy et al. 2013).



The semi-major axis can only be estimated (a lower limit), from a single image, and only then if you have a good distance to the star/planet system. The angular separation is converted to a projected linear separation.

A perfect example of the above is the estimate of the mass and orbit for the exoplanet GJ 504b (Kuzuhara et al. 2013).

With more images spread over an appreciable fraction of the planet's period one can be more accurate. The projection of the elliptical orbit can be mapped, yielding the orbital inclination and thus a better semi-major axis measurement. The orbital period can then also be roughly estimated and checked for consistency with Kepler's third law and an estimate of the stellar mass. Note though that currently imaged planets have orbital periods of at least decades.

Wang et al. (2016) give an example of this approach for beta Pic b. A dozen precise images constrain the semi-major axis to a few percent and give the total system (star plus planet, but dominated by the star) mass.