1. A method of processing picture signals having interlaced field scanning, the method comprising the following stages: (a) selecting a time pair and a space pair of main points about a desired point in a line to be interpolated in a field being interpolated, the main points of said time pair having the same position in the images as the desired point, but being situated in the two fields occurring immediately before and immediately after the field being interpolated, while the main points of the space pair come from the field being interpolated, from respective ones of the two positions which are vertically adjacent to the position of the desired point; (b) calculating the "time" main difference between the signals at the two points in the time pair, and also the "space" main difference between the signals at the two points in the space pair; (c) selecting an interpolation function taking account of said main differences; and (d) calculating the interpolated signal of the desired point by means of said interpolation function; said method including the improvement whereby: stage (c) comprises, for each pair of main points: (c1) selecting auxiliary points situated on the same frame line as the main points and suitable for defining auxiliary pairs of points on either side of the desired point, while simultaneously selecting a space-time zone surrounding the desired point and including the two main points and the auxiliary points associated with said two main points; (c2) calculating auxiliary differences between the signals at the two points of each auxiliary pair; (c3) determining first level partial interpolation in that one of the directions between the main pair and the associated auxiliary pairs which gives the minimum difference; and (c4) determining a second level partial interpolation in the direction of the pair of main points concerned; and stage (d) comprises: (d1) for each pair of main points, hierarchical selection between first level partial interpolation and second level partial interpolation, as a function of the fact that said zone does not contain or does contain a local outline which is horizontal; and (d2) calculating the final interpolated luminance of the desired point from the partial interpolations each relating to pairs of main points.