Summary form only give. Teleological modeling, a developing approach for creating abstractions and mathematical representations of physically realistic time-dependent objects, is described. In this approach, geometric constraint-properties, mechanical properties of objects, the parameters representing an object, and the control of the object are incorporated into a single conceptual framework. A teleological model incorporates time-dependent goals of behavior of purpose as the primary abstraction and representation of what the object is. A teleological implementation takes a geometrically incomplete specification of the motion, position, and shape of an object, and produces a geometrically complete description of the object's shape and behavior as a function of time. Teleological modeling techniques may be suitable for consideration in computer vision algorithms by extending the current notions about how to make mathematical representations of objects. Teleological descriptions can produce compact representations for many of the physically derivable quantities controlling the shapes, combining-operations, and constraints which govern the formation and motion of objects
