  Solar filaments are magnetic structures often observed in the solar
atmosphere and consist of plasma that is cooler and denser than their
surroundings. They are visible for days -- and even weeks -- which suggests
that they are often in equilibrium with their environment before disappearing
or erupting. Several eruption models have been proposed that aim to reveal what
mechanism causes (or triggers) these solar eruptions. Validating these models
through observations represents a fundamental step in our understanding of
solar eruptions. We present an analysis of the observation of a filament
eruption that agrees with the torus instability model. This model predicts that
a magnetic flux rope embedded in an ambient field undergoes an eruption when
the axis of the flux rope reaches a critical height that depends on the
topology of the ambient field. We use the two vantage points of SDO and STEREO
to reconstruct the three-dimensional shape of the filament, to follow its
morphological evolution and to determine its height just before eruption. The
magnetograms acquired by SDO/HMI are used to infer the topology of the ambient
field and to derive the critical height for the onset of the torus instability.
Our analysis shows that the torus instability is the trigger of the eruption.
We also find that some pre-eruptive processes, such as magnetic reconnection
during the observed flares and flux cancellation at the neutral line,
facilitated the eruption by bringing the filament to a region where the
magnetic field was more vulnerable to the torus instability.
