When a moving object cuts in front of a moving observer at a 90 degrees angle, the observer correctly perceives that the object is traveling along a perpendicular path just as if viewing the moving object from a stationary vantage point. Although the observer's own (self-)motion affects the object's pattern of motion on the retina, the visual system is able to factor out the influence of self-motion and recover the world-relative motion of the object (Matsumiya and Ando, 2009). This is achieved by using information in global optic flow (Rushton and Warren, 2005; Warren and Rushton, 2009; Fajen and Matthis, 2013) and other sensory arrays (Dupin and Wexler, 2013; Fajen et al., 2013; Dokka et al., 2015) to estimate and deduct the component of the object's local retinal motion that is due to self-motion. However, this account (known as "flow parsing") is qualitative and does not shed light on mechanisms in the visual system that recover object motion during self-motion. We present a simple computational account that makes explicit possible mechanisms in visual cortex by which self-motion signals in the medial superior temporal area interact with object motion signals in the middle temporal area to transform object motion into a world-relative reference frame. The model (1) relies on two mechanisms (MST-MT feedback and disinhibition of opponent motion signals in MT) to explain existing data, (2) clarifies how pathways for self-motion and object-motion perception interact, and (3) unifies the existing flow parsing hypothesis with established neurophysiological mechanisms.