The invention relates to an image processing method for preserving the edges of objects reproduced in an intensity image and for reducing the noise, including the steps of acquisition of the intensity image in the form of a multidimensional matrix of points (2-D, 3-D), determination of the intensity gradient at each point, defined by its direction ((.theta..sub.p) and its modulus (.parallel.G.sub.p.parallel.), and the passage at each point of a recursive spatial filter having an anisotropic kernel and providing a degree of smoothing which is greater in the direction perpendicular to the direction of the gradient than in the direction of the intensity gradient. The kernel is spherical on the scanning lines which are not normal to the intensity gradient and it is shaped as a flattened sphere whose major dimension extends in the direction of lines normal to the intensity gradient in a scanned point. The invention also relates to a medical X-ray imagine apparatus for carrying out this method.