We describe motion coding algorithms for use with the arbitrary shaped objects of emerging video coding standards. These algorithms exploit the temporal redundancy of the object shape description under conditions of concentrated diverse motion. In Variable Sized Block Matching (VSBM), the ambiguity of small area matching is reduced by coalescing blocks to yield accurate motion information over larger blocks. The technique is extended to exploit irregularly shaped areas of uniform motion within a small object. This Modified VSBM (MVSBM) can be enhanced by coding areas of identical motion within the spatial structure of the object. This spatial structure itself has temporal redundancy that can be reduced by inter-frame differential coding. For the MPEG-4 test sequences "Stefan" and "Children" the total amount of data required to specify motion shows improvements of 20% and 17% respectively.