The apparatus comprises a camera (10) with a digital sensor read by a mechanism of the rolling shutter type delivering video data (Scam) line by line. An exposure control circuit (22) adjusts dynamically the exposure time (texp) as a function of the level of illumination of the scene that is captured. A gyrometer unit (12) delivers a gyrometer signal (Sgyro) representative of the instantaneous variations of attitude (φ, θ, ψ) of the camera, and a processing circuit (18) that receives the video data (Scam) and the gyrometer signal (Sgyro) delivers as an output video data processed and corrected for artefacts introduced by vibrations specific to the apparatus. An anti-wobble filter (24) dynamically modifies the gain of the gyrometer signal as a function of the exposure time (texp), so as to reduce the gain of the filter when the exposure time increases, and vice versa.