1. A method of stabilizing the images of a scene, acquired by means of an observation device of an imaging system, comprising; a step of digital processing of a stream of successive images; a step of acquiring gyrometric measurements by means of at least one gyrometric sensor secured to the observation device, of using these gyrometric measurements to determine approximate shifts undergone between successive images, and in that the image processing step comprises: i. a sub-step of using the approximate shifts and the image stream acquired to determine so-called fine shifts undergone between successive images and, ii. a sub-step of evaluating the fine shifts, and iii. a sub-step of merging the approximate shifts and the fine shifts with a view to applying merged shifts to the image stream so as to stabilize it.