Method of restoring the movements of a line of sight in terms of roll, pitch and yaw of an observation instrument during a picture shot of a duration of typically a few seconds per shot, said movements distorting each image in a frequency range up to high frequencies of a few hundred Hertz, according to which at least two images (14a, 14b) containing the same portion of a scene are formed, over the picture-shooting duration [Ti, Tf] on the basis of the instrument mounted on a moving carrier, the shots of these two images being offset in time by a substantially constant known value T and the said movements of the line of sight of the instrument in the course of the picture shot are determined by at least the following steps: a) a step of selecting and matching several homologous characteristic zones, each characteristic area being a portion of a scene of a few hundred pixels which contains radiometric, geometric or textural information, said characteristics areas being shot in the vicinity of instants respectively Tn and Tn + T (n=1 to N) distributed between Ti and Tf in the said images of the same portion of the scene so as to obtain a measurement of the position at the instants respectively Tn and Tn+T (n=1 to N) of the said homologous zones, or of at least a particular point of these zones, in each of the two images of the said portion, b) a step of calculating the angular variations of the line of sight of the instrument between the instants Tn and Tn+T (n=1 to N) by adjusting an image matching model, the said model giving for any point of a first image shot at the instant Tn (n=1 to N), an estimate of the position of its homologous point in a second image shot at the instant Tn+T as a function of parameters comprising in particular the orientation of the line of sight of the instrument at the instant Tn and the said angular variations of this line of sight between Tn and Tn + T; the adjustment of the model consisting in calculating the values of the said angular variations which minimize a function, for example a quadratic function, of the deviations between the position of the homologous zones of the second image that are predicted by the model, and the position of the said homologous zones of the second image as it is restored in step (a), and c) a step of reconstructing the movements of the line of sight over the time horizon [Ti, Tf] by integrating, filtering and possibly resampling the whole set of elementary variations reconstructed in step (b). a) a step of selecting and matching several homologous characteristic zones, each characteristic area being a portion of a scene of a few hundred pixels which contains radiometric, geometric or textural information, said characteristics areas being shot in the vicinity of instants respectively Tn and Tn + T (n=1 to N) distributed between Ti and Tf in the said images of the same portion of the scene so as to obtain a measurement of the position at the instants respectively Tn and Tn+T (n=1 to N) of the said homologous zones, or of at least a particular point of these zones, in each of the two images of the said portion, b) a step of calculating the angular variations of the line of sight of the instrument between the instants Tn and Tn+T (n=1 to N) by adjusting an image matching model, the said model giving for any point of a first image shot at the instant Tn (n=1 to N), an estimate of the position of its homologous point in a second image shot at the instant Tn+T as a function of parameters comprising in particular the orientation of the line of sight of the instrument at the instant Tn and the said angular variations of this line of sight between Tn and Tn + T; the adjustment of the model consisting in calculating the values of the said angular variations which minimize a function, for example a quadratic function, of the deviations between the position of the homologous zones of the second image that are predicted by the model, and the position of the said homologous zones of the second image as it is restored in step (a), and c) a step of reconstructing the movements of the line of sight over the time horizon [Ti, Tf] by integrating, filtering and possibly resampling the whole set of elementary variations reconstructed in step (b).