A parallel noise-robust algorithm to recover depth information from radialflow fields

A parallel algorithm operating on the units ("neurons") of an artificial re tina is proposed to recover depth information in a visual scene from radial flow fields induced by ego motion along a given axis. The system consists of up to 600 radii with fewer than 65 radially arranged neurons on each rad ius. Neurons are connected only to their nearest neighbors, and they are ex cited as soon as a sufficiently strong gray-level change occurs. The time d ifference of two subsequently activated neurons is then used by the last-ex cited neuron to compute the depth information. All algorithmic calculations remain strictly local, and information is exchanged only between adjacent active neurons (except for the final read-out). This, in principle, permits parallel implementation. Furthermore, it is demonstrated that the calculat ion of the object coordinates requires only a single multiplication with a constant, which is dependent on only the retinal position of the active neu ron. The initial restriction to local operations makes the algorithm very n oise sensitive. In order to solve this problem, a prediction mechanism is i ntroduced. After an object coordinate has been determined, the active neuro n computes the time when the next neuronal excitation should take place. Th is estimated time is transferred to the respective next neuron, which will wait for this excitation only within a certain time window. If the excitati on fails to arrive within this window, the previously computed object coord inate is regarded as noisy and discarded. We will show that this predictive mechanism relies also on only a (second) single multiplication with anothe r neuron-dependent constant. Thus, computational complexity remains low, an d noisy depth coordinates are efficiently eliminated. Thus, the algorithm i s very fast and operates in real time on 128 x 128 images even in a serial implementation on a relatively slow computer. The algorithm is tested on sc enes of growing complexity, and a detailed error analysis is provided showi ng that the depth error remains very low in most cases. A comparison to sta ndard flow-field analysis shows that our algorithm outperforms the older me thod by far. The analysis of the algorithm also shows that it is generally applicable despite its restrictions, because it is fast and accurate enough such that a complete depth percept can be composed from radial flow field segments. Finally, we suggest how to generalize the algorithm, waiving the restriction of radial flow.