Recent instrumentation has demonstrated that the solar atmosphere supports omnipresent transverse waves, which could play a key role in energizing the solar corona. Large-scale studies are required in order to build up an understanding of the general properties of these transverse waves. To help facilitate this, we present an automated algorithm for identifying and tracking features in solar images and extracting the wave properties of any observed transverse oscillations. We test and calibrate our algorithm using a set of synthetic data, which includes noise and rotational effects. The results indicate an accuracy of 1%-2% for displacement amplitudes and 4%-10% for wave periods and velocity amplitudes. We also apply the algorithm to data from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory and find good agreement with previous studies. Of note, we find that 35%-41% of the observed plumes exhibit multiple wave signatures, which indicates either the superposition of waves or multiple independent wave packets observed at different times within a single structure. The automated methods described in this paper represent a significant improvement on the speed and quality of direct measurements of transverse waves within the solar atmosphere. This algorithm unlocks a wide range of statistical studies that were previously impractical.