This paper presents two methods for separating moving objects from their background in time-varying imagery by use of moving edges. (where, a moving edge is a boundary point of moving objects) The one is a region growing method which is for extracting the region moving objects, the other is a boundary detection method which uses a graph search algorithm to find the boundary of moving objects. The proposed methods have solved various problems which the existing algorithms may have. That is, the new methods are capable of extracting the region or boundary of moving objects under various circumstances. They work well in the state of complex background, fast or slow motion, rotation and motion along the optical axis if dynamic image is not in the state of very low contrast between moving objects and their background.