As animals navigate and interact with their environment, the image projected on their retina is constantly moving due to both self-motion and external motion of objects. Thus understanding how the retina processes moving objects is of crucial importance. This task is made difficult by the many non-linearities present in the retinal circuit. Previous works showed that retina ganglion cells extract specific non-linear features from moving objects and send this information to the brain. For example, direction selective cells respond maximally to motion in a ”preferred” direction and not in the opposite ”null” direction. But the dynamical features so far studied were always related to the object position, velocity or direction of motion. In most of those studies moving objects were thus treated as either points or edges in space and time. But moving object are in general extended and not uniform. They are made of different textures that cover their different parts. Yet it is not clear how the retina represents these textures. To study this, we recorded mouse retina ganglion cells during the presentation of moving bars to which we added small white-noise perturbations. We then used these responses to estimate a stimulus specific “local Receptive Field” across the time of the bar sweep. In this way, we can determine which changes in the stimulus will maximally change the response of the neuron and which ones will leave it invariant. By performing this estimation of a local RF for several points in time, we show that the selectivity of ganglion cells can be modulated in time by an object crossing their receptive field and that different ganglion cell types are selective to different parts of a moving object. We then show that this differential selectivity can be reproduced with a single sub-unit model architecture that allows non-linear spatio-temporal integration across the ganglion cell’s receptive field. Our model predicts that a crucial role in determining which part of a moving object a certain cell will be selective to is played by the subunit rectification threshold, suggesting a specific and plausible implementation for such a complex parallel computation.