Few studies have addressed the question of desynchronization. One study by von der Malsburg and Schneider  introduced a common inhibitor to desynchronize two segments. Their method of synchronization, however, depends on long-range connections, and thus suffers the deficiency mentioned earlier. Schillen and König  introduced desynchronizing lateral connections with fixed delays to segment two objects. These desynchronizing connections have a short range, and two objects cannot be segmented if their distance is not small. Also it is not clear how these models perform with a scene of more than two objects. The lack of an effective mechanism for desynchronization greatly limits the utility of neural oscillations to address perceptual organization (see Terman and Wang  for more discussions).
In addition to their analysis on synchronization, Terman and Wang  also provide a general solution to the problem of desynchronization. They defined a new class of oscillatory networks: Locally Excitatory Globally Inhibitory Oscillator Networks (LEGION, Wang and Terman ), where inhibition is exerted by a global inhibitor which receives input from each unit of the network, and sends inhibition back to each unit. They proved that LEGION exhibits a mechanism called selective gating, whereby an oscillator jumping up to the active phase (high value) rapidly recruits the oscillators stimulated by the same pattern, while preventing other oscillators from jumping up. With the selective gating mechanism, the network rapidly achieves both synchronization within each group of oscillators corresponding to the same pattern and desynchronization between different groups. Here, desynchronization between two blocks means that they never stay in the active phase at the same time. Starting with random initial conditions, the overall time the system takes to achieve both synchronization and desynchronization is no greater than m cycles of oscillations, where m is the number of patterns simultaneously presented to the network. Campbell and Wang (in press) also addressed desynchronization, and their simulations show that a network of Wilson-Cowan oscillators with a global unit can exhibit desynchronization among groups of oscillators, each of which is a synchronous body.
We regard the rates of synchrony and desynchrony as particularly important, not only because speed is critical for real time scene segmentation but also of the considerations of neural plausibility. It is known that human subjects can identify an object in a visual scene in about 100 ms (  Irving Biederman, personal communication 1994). This suggests that both synchrony and desynchrony must be achieved in just a few cycles if 40 Hz oscillations are taken to be the underlying mechanism. Physiological recordings of synchronous oscillations also suggest that synchrony seems to be a transient event, lasting for only a few cycles [5,44,48].