Computing the relative motion of objects is an important navigation task that we routinely perform by relying on inherently unreliable biological cells in the retina. The non-linear and adaptive response of memristive devices make them excellent building blocks for realizing complex synaptic-like architectures that are common in the human retina. Here, we introduce a novel memristive thresholding scheme that facilitates the detection of moving edges. In addition, a double-layered 3-D memristive network is employed for modeling the motion computations that take place in both the Outer Plexiform Layer (OPL) and Inner Plexiform Layer (IPL) that enables the detection of on-center and off-center transient responses. Applying the transient detection results, it is shown that it is possible to generate an estimation of the speed and direction a moving object.