Recent progresses in airborne light detection and ranging（LIDAR） technology allow rapid and inexpensive measurements of topography over large areas.This technology becomes a primary method for generating high-resolution digital terrain model（DTM） that is essential to numerous applications.LIDAR techniques represent a new and fruitful approach in the determination of digital surface model.LIDAR systems usually return a three-dimensional cloud of point measurements from reflective objects scanned by the laser beneath the flight path.One of the goals in processing LiDAR point cloud is to set up filtering methods in order to extract the digital terrain model automatically.There are a lot of methods of extracting DTM from LiDAR point cloud

but removing nonground points is still a challenging task.In order to generate a DTM

measurements from nonground features（buildings

vehicles and vegetation etc.） have to be removed.Mathematical morphology is based on set theory to extract features from an image and fits for signal analysis.It has been demonstrated that operation opening can remove objects on ground（vegetations

buildings

etc.） from LiDAR point cloud and reserve objects larger than structuring element.To find out a proper structuring element is very difficult.The larger window size of structuring element would over filter DTM and the smaller window would not filter all nonground objects.All nonground objects could be removed by one time opening operation theoretically if the structuring element is appropriate.Unfortunately there is no such structuring element in reality because of the complexity of terrain surface.This can be resolved by gradually increasing structuring element

which can filter objects on ground

but some terrain measurements also have been filtered at the same time.This results in too flat on terrain surface and the extracted DTM is lower than the real.In this paper

a restricted filter method is developed to solve the terrain details loss caused by over filtered.The overall process starts from an initial set of points

then gradually increases the structuring element which is restricted with elevation difference thresholds at the same time.Elevation difference threshold is set by undulation of terrain

and it can control result.The ratio of elevation difference of before and after opening to structuring element window size is k

which represents undulating grade.The larger the value of k is

the steeper the area is

and vice versa in order to reserve the terrain details

the threshold of k is set k

0

.Result value of filtered remains invariable when k

<

k

0

otherwise equals result value of opening.This procedure iterates while the window size of structuring element gradually increases.The times of iteration are determined by window size of and increasing style.The different size of nonground objects（vegetation

building etc.） are filtered by iteration and the details could be reserved.The feasibility and validity of the method is demonstrated with an example data of airborne laser scanning system developed by China.The results show that the filter can remove most of the nonground points effectively.