It is a useful competence to see motion relative to the head or to the external world, although those quantities are not directly given on the retina. The same holds for judgement of the shape of an object. We argue that the required transformations can be, and are done independent of the associated direction transformations. This involves perceptual channels with retinal apertures but non-retinocentric motion- or shape- sensitivity. In order to arrive at units that perform such a mixed transformation, the substructure of the retinotopic receptive field needs to be dynamically adjusted, using extra-retinal signals (or equivalent measures like vertical disparity). Here we show that detectors tuned to disparity-curvature X retinal-direction can extract (metric) object curvature from the retinal disparity field in one step. We point out the correspondence to a previously proposed model of heading detection, which contains detectors that become tuned to head-centric flow by dynamically changing their preferred structure of the flowfield in a retinal aperture, depending on the eye movement.