Recent neurophysiological evidence suggests the ability to interpret biological motion is facilitated by a neuronal "mirror system" which maps visual inputs to the pre-motor cortex. If the common architecture and circuitry of the cortices is taken to imply a common computation across multiple perceptual and cognitive modalities, this visual-motor interaction might be expected to have a unified computational basis. Two essential tasks underlying such visual-motor cooperation are shown here to be simply expressed and directly solved as transformation-discovery inverse problems: (a) discriminating and determining the pose of a primed 3D object in a real-world scene, and (b) interpreting the 3D configuration of an articulated kinematic object in an image. The recently developed map-seeking method provides tractable, cortically-plausible solution to these and a variety of other inverse problems which can be posed as the discovery of a composition of transformations between two patterns. The method relies on an ordering property of superpositions and on decomposition of the transformation spaces inherent in the generating processes of the problem.