Method for displaying by an operator on a display unit, a multispectral image formed of a plurality of spectral images (11, 12, 13,...) of one and same scene that have been captured simultaneously in separate spectral bands respectively, the method comprising the following successive steps: /1/ within the multispectral image, selecting an analysis window corresponding to a portion of the scene and a plurality of target regions (T 1, T 2, T 3, T 4,...) in the analysis window, each target region being associated with a background region and separated from said background region by an intermediate region so that each target region is not adjacent with the background region that is associated with said target region; /2/ separately for each target region (T 1, T 2, T 3, T 4,...) in the analysis window, performing the following sub-steps: /2-1/ determining a Fisher projection based on intensity values of the spectral images, said Fisher projection being a linear combination of the spectral images (11, 12, 13,...) which optimises a contrast between the target region (T 1, T 2, T 3, T 4,...) and the background region that is associated with said target region; and /2-2/ applying the Fisher projection determined in sub-step /2-1/ to the intensity values of the spectral images (11, 12, 13,...) in the analysis window, so as to obtain a basic image of the scene portion that is contained in the analysis window for each target region (T 1, T 2, T 3, T 4,...) selected in step /1/; then /3/ combining the basic images in order to form a synthesis image relative to the scene portion that is contained in the analysis window; and /4/ displaying an image of the scene on the display unit, using in the analysis window the synthesis image that was obtained in step /3/, wherein a distinct background region (Bi) is associated with each target region (T 1, T 2, T 3, T 4,...), with an arrangement of said background regions such that none of the background regions overlaps with any one of the target regions, the process being characterised in that, in sub-step /2-1/ for each target region (T 1, T 2, T 3, T 4,...) of the analysis window, the Fisher projection is determined by weighting the intensity values of the spectral images (11, 12, 13,...), in the background region that is associated with said target region, with coefficients having values which are decreasing functions of a distance between the target region and a location in the background region to which the intensity values of the spectral images correspond. /1/ within the multispectral image, selecting an analysis window corresponding to a portion of the scene and a plurality of target regions (T 1, T 2, T 3, T 4,...) in the analysis window, each target region being associated with a background region and separated from said background region by an intermediate region so that each target region is not adjacent with the background region that is associated with said target region; /2/ separately for each target region (T 1, T 2, T 3, T 4,...) in the analysis window, performing the following sub-steps: /2-1/ determining a Fisher projection based on intensity values of the spectral images, said Fisher projection being a linear combination of the spectral images (11, 12, 13,...) which optimises a contrast between the target region (T 1, T 2, T 3, T 4,...) and the background region that is associated with said target region; and /2-2/ applying the Fisher projection determined in sub-step /2-1/ to the intensity values of the spectral images (11, 12, 13,...) in the analysis window, so as to obtain a basic image of the scene portion that is contained in the analysis window for each target region (T 1, T 2, T 3, T 4,...) selected in step /1/; then /2-1/ determining a Fisher projection based on intensity values of the spectral images, said Fisher projection being a linear combination of the spectral images (11, 12, 13,...) which optimises a contrast between the target region (T 1, T 2, T 3, T 4,...) and the background region that is associated with said target region; and /2-2/ applying the Fisher projection determined in sub-step /2-1/ to the intensity values of the spectral images (11, 12, 13,...) in the analysis window, so as to obtain a basic image of the scene portion that is contained in the analysis window for each target region (T 1, T 2, T 3, T 4,...) selected in step /1/; then /3/ combining the basic images in order to form a synthesis image relative to the scene portion that is contained in the analysis window; and /4/ displaying an image of the scene on the display unit, using in the analysis window the synthesis image that was obtained in step /3/,