As examples, consider the human body in ambulatory motion or the human abdominal anatomy. First, both are made up of natural parts: such as torso, foot, and toe, or kidney, liver, and spleen. Second, to describe what we mean by "body" or "abdomen", we do not consider a single body or a single person's abdomen but rather describe a standard body or abdomen and then describe the deformation from the standard, and we describe the population of bodies or abdomens by statistics on these deformations. Third, we describe motion in terms of deformations. Fourth, since all such geometric entities must have N = at least many thousand primitives to describe them in enough detail, computation on objects and multi-objects require operations that are O(N), necessitating a multiscale representation, multiscale deformations, and multiscale statistics. I will describe a means of representing an instance of an entity, deformations, and their statistics that meets these requirements. I take the view that objects are the stuff in their interior, which is subject to local rotations (twistings & bendings), swellings & contractions, and displacements and that changes in inter-object and inter-object-part relations must be describable via such simple deformations. The object representation is called "m-reps", and the statistical approach needed to describe compositions of local rotations, swellings, and displacements generalizes normal linear statistics to nonlinear symmetric spaces. Examples of applications including segmentation of objects from images by posterior optimization of deformable models, discrimination of object classes according to object and object ensemble geometry, and graphics production of animated cines will be given.