1. A method for stabilizing images of a scene acquired by an observation device of an imaging system, the method comprising: a step for acquiring gyrometric measurements by at least one gyrometric sensor secured to the observation device; a step for performing an image processing of a stream of successive images, the step for performing the image processing comprising: determining approximate shifts undergone between the successive images by using the gyrometric measurements; determining fine shifts undergone between the successive images by using the approximate shifts and the image stream; evaluating the fine shifts, integrating an auto-evaluation method aimed at estimating reliability of the image processing; if the image processing is estimated not to be reliable, the approximate shifts are favored; and if the image processing is estimated to be reliable, the fine shifts are favored, a step for applying the favored shifts to the image stream so as to stabilize it.