First-Order Optic Flow

First order flow only available Lower limit on the distance-scaled transverse velocity. Constraint on the immediacy of the surface patch. Constraint on the immediacy of the plane. Constraint on the spin. First order flow and tilt available The direction of the transverse velocity. The immediacy of the surface path. The immediacy of the plane. The spin. First order flow and the immediacy of the plane available The direction of the transverse velocity (4 solutions, coupled to tilt). The tilt (4 solutions, coupled to transverse velocity). The immediacy of the surface patch. The spin (two solutions). First order flow and spin available The direction of the transverse velocity (4 solutions, coupled to tilt). The tilt (4 solutions, coupled to transverse velocity). The immediacy of the surface patch (2 solutions). The immediacy of the plane (2 solutions). It is highly likely that a visual system will have some of this additional information available to it. The ambiguous solutions can be resolved with only coarse extra information. It is clear that first-order flow, for even a single surface patch, can contribute much of the information needed for the control of actions. Invariant properties of the motion parallax field due to the rigid movement of rigid bodies relative to an observer. These are the components of the deformation rate tensor in the D–S coordinate system. For the time being, we choose an image coordinate system which has its x-axis aligned with D and its y-axis aligned with S. Since we are working in a small patch round the fixed point, where the sphere is close to the tangent plane (Fig. 7), we then have Q D = x and Q S = y — that is, etc. We can substitute Eqs. 43 to 46 into Eqs. 31 to 34 to get (47) (48) (49) (50) The first three of these are identical to Eqs. 10 to 12. Fig. 4b shows that , so that Eq. 13 is equivalent to Eq. 50. Although we have chosen the x-y coordinates in our image along the D and S axes in order to link the equations, the relationships given by Eqs. 47 to 50 are independent of any particular choice of coordinate system: having established them, we can measure the differential flow using any axes we choose, and then use these equations to make the inferences discussed in Section 5. 7 Summary The nature of first-order differential …