A single profile of a solid object contains much information about the shape of the object. Viewing the changing profiles of a moving object provides even greater information about the shape of the object. Few computational models of this process have been applied to the human ability to recover the shape and motion of solid objects from their changing profiles. We propose a theory that relates measurable quantities of changing two-dimensional (2-D) profiles to structural properties of three-dimensional (3-D) surfaces in motion. The relevance of this theory to human perception is shown by relating theoretical predictions to existing psychophysical results as well as additional demonstrations of human recovery of shape from profiles.