Crater detection is accomplished by means of Hough transform, applied to binary images, which is obtained by edge detection and thresholding from grey value images. Because the ordinary Hough transform is very time consuming, the problem must be reduced. Starting from minimum mean square estimation linear (matched) filters are obtained representing the radon transform, which is equivalent to the Hough transform. Because the filter coefficients can be calculated in advance and may be saved in a filter bank, the computation of the Hough accumulator array can be speeded up considerably. The computational amount can be reduced further, if the accumulator array is projected from the (a,b,r)-space to the (a,b)-space. In order to do that, a special method is presented, which uses a priori information about the possible circle (or crater) radii. Coarse estimation of the circle center coordinates by this method defines limited regions where the full Hough transform can be applied with a much lower amount of computation. The method presented here was applied to simulated images and to Mars images obtained by the VIKING Mars orbiters.