Coronal waves are large-scale disturbances often driven by coronal mass ejections (CMEs). We investigate a spectacular wave event on 7 March 2012, which is associated with an X5.4 flare (SOL2012-03-07). By using a running center-median (RCM) filtering method for the detection of temporal variations in extreme ultraviolet (EUV) images, we enhance the EUV disturbance observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) onboard the PRoject for Onboard Autonomy 2 (PROBA2). In coronagraph images, a halo front is observed to be the upper counterpart of the EUV disturbance. Based on the EUV and coronagraph images observed from three different perspectives, we have made three-dimensional (3D) reconstructions of the wave surfaces using a new mask-fitting method. The reconstructions are compared with those obtained from forward-fitting methods. We show that the mask fitting method can reflect the inhomogeneous coronal medium by capturing the concave shape of the shock wave front. Subsequently, we trace the developing concave structure and derive the deprojected wave kinematics. The speed of the 3D-wave nose increases from a low value below a few hundred $mathrm{km,s^{-1}}$ to a maximum value of about 3800 $mathrm{km,s^{-1}}$, and then slowly decreases afterwards. The concave structure starts to decelerate earlier and has significantly lower speeds than those of the wave nose. We also find that the 3D-wave in the extended corona has a much higher speed than the speed of EUV disturbances across the solar disk.
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