On the other hand, the signals of biological EMDs encode the image velocity in a nonlinear and ambiguous way. Their responses peak at a certain velocity and decrease for velocities beyond this optimum [8]. Further properties of at least basic EMD models make this motion detection scheme only a poor velocity sensor: (1) The response amplitudes of basic versions of the EMD depend on the global spatial frequency composition of the input image [9]. (2) The global contrast of the moving image changes the response of basic EMDs in a quadratic way [10,11]. (3) The time-dependent responses of individual EMDs show pronounced fluctuations that depend on the specific details of the pattern analysed by the EMD; these pattern-dependent fluctuations can be reduced by spatial integration over many EMDs looking at neighbouring points of the image [12].

(4) Even the time course of spatially integrated EMD outputs depends not only on pattern velocity but also on acceleration and higher-order temporal derivatives [10,13].Control systems for mobile robots often combine the biologically inspired concept of flow-specific large-field integration with computer-vision algorithms for local velocity estimation that do not show the strong contrast and pattern dependence of EMDs [14,15]. Systems using biologically inspired EMDs were also proposed and successfully tested in simulation [16] and in hardware [17] but are limited to environments with a restricted range of textural properties [18,19].

Compared to the performance of models employing basic EMD variants, the responses of motion-sensitive neurons in the brain of insects, such as flies, after which EMDs were modelled, are much Anacetrapib less sensitive to the pattern structure and contrast. In particular, they show the quadratic dependency on image contrast only for very low contrast values. For higher contrast values, the response does not increase with increasing contrast and the neuronal responses become less sensitive to the local contrast variations of the stimulus patterns [10,20�C22]. This relative contrast independence is not the consequence of signal saturation Dacomitinib at the level of the wide-field motion sensitive neuron, because the response can still be modulated by changing the image velocity, but of processing in the peripheral visual system [23].

To reduce the dependence of EMDs on local pattern contrast and, thus, to approximate the responses of their biological equivalents, various augmentations of EMDs were proposed. These range from simple saturating static nonlinearities incorporated into the motion detection process [10,21] to a sophisticated combination of nonlinearities and temporal filters [18,24].