Solar coronal mass ejections (CMEs) are large-scale eruptions of plasma and magnetic field from the Sun into the corona and interplanetary space. They are the most significant drivers of adverse space weather at Earth and other locations in the heliosphere, so it is important to understand the physics governing their eruption and propagation. However the diffuse morphology and transient nature of CMEs makes them difficult to identify and track using traditional image processing techniques. Furthermore, the true three-dimensional geometry of CMEs has remained elusive due to the limitations of coronagraph plane-of-sky images with restricted fields-of-view. For these reasons the Solar Terrestrial Relations Observatory (STEREO) was launched as a twin-spacecraft mission to y in orbits ahead and behind the Earth in order to triangulate independent observations of CME structure. It is the first time CMEs have been observed from vantage points off the Sun-Earth line and each spacecraft carries an instrument suite designed to image from the low solar corona out to the orbit of Earth in order to observe and study CME propagation towards Earth. In this thesis the implementation of multiscale image processing techniques to identify and track the CME front through coronagraph images is detailed. An ellipse characterisation of the CME front is used to determine the CME kinematics and morphology with increased precision as compared to techniques used in current CME catalogues, and efforts are underway to automate this procedure for applying to a large number of CME observations for future analysis. It was found that CMEs do not simply undergo constant acceleration, but rather tend to show a higher acceleration early in their propagation. The angular width of CMEs was also found to change as they propagate, normally increasing with height from the Sun. However these results were derived from plane-of-sky measurements with no correction for how the true CME geometry and direction affect the kinematics and morphology observed. With the advent of the unique dual perspectives of the STEREO spacecraft, the multiscale methods were extended to an elliptical tie pointing technique in order reconstruct the front of a CME in three dimensions. Applying this technique to the Earth-directed CME of 12 December 2008 allowed an accurate determination of its true kinematics and morphology, and the CME was found to undergo early acceleration, non-radial motion, angular width expansion, and aerodynamic drag in the solar wind as it propagated towards Earth. This study and its conclusions are of vital importance to the fields of space weather monitoring and forecasting.

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