I need to obtain a grid of bare ground elevation (removing all edifices, trees, roads and man-made elements) for quantitative geomorphological analysis from a high resolution (1 m) DSM obtained by orthoimages (not from LIDAR). Is there any suggestion you can provide me to filter my original grid?
This filtering process is usually performed on a lidar point cloud and not an interpolated derivative. It is unlikely that you will have satisfactory results attempting to filter the DSM. I would highly recommend tracking down the original lidar data.
You could attempt to treat your DSM as a point cloud by converting it to points and then running a filter intended for lidar point clouds. Depending on the algorithm, you may get a suitable result for generating a bare earth DEM. However, it may end up oversmoothed and not supporting the current resolution of your DSM.
Some recommended "free" lidar filtering software: