Reading out Binocular Energy Population Codes for Short-latency Disparity-vergence Eye Movements

Fig 1: (left) Simulated experimental setup where the eyes verge on planes at different depth. (right) The LONG and SHORT signals used to drive vergence, and the T0 signal to switch between LONG and SHORT modes.

The ability of the human brain to fuse the images projected on the left and right retinas, in order to achieve depth perception, depends directly on the ability to produce and to keep a stable fixation, i.e. to act as both the eyes fixate the same point in the word. This task is carried out by vergence eye movements (Fig.1 left).
Experimental evidences show that, although depth perception and vergence eye movements are based on the activity of complex cells of the primary visual cortex, the brain adopts specific and separate mechanisms to combine binocular information and carry out the two distinct tasks. We define as fusibility range (FR) the range where a distributed population of disparity detectors is able to fuse the left and right retinal images and hence to compute a disparity map. In each image location the decoding of the population can be achieved through a centre of mass strategy where each cell response is weighted by its preferred disparity, and thus taking a decision on the disparity values. Vergence control models that are based on a distributed population of disparity detectors, usually require first the computation of the disparity map, thus limiting the functionality of the vergence system inside the FR. The model we developed, mimicking the behaviour of the cells in the Medial Superior Temporal area [Takemura et al., Journal of Neurophysiology, 85:2245-2266, 2001], combines the population responses without taking a decision, but extracting a disparity-vergence response that allows us to nullify the disparity in the fovea, even if the stimulus presented is far beyond the FR. The disparity-vergence response is obtained by a weighted sum of the population response, where the weights are computed by minimizing a functional that embeds two very specific goals: (1) to obtain signals proportional to horizontal disparities, (2) to make these signals be insensitive to the presence of vertical disparities. The desired feature of the horizontal disparity tuning curve for vergence is an odd symmetry with a linear segment passing smoothly through zero disparity, which defines a critical servo range over which changes in the stimulus horizontal disparity elicit roughly proportional changes in the amount of the horizontal vergence angle. On the basis of the Dual Mode theory [Hung et al., IEEE Trans. on Biomedical Engineering, 33:1021-1028, 1986], the model provides two distinct vergence control mechanisms: a fast mode enabled in the presence of large disparities, and a slow mode enabled in the presence of small disparities (cfr LONG and SHORT signals in Fig.1 right). Moreover we extract an additive signal T0, sensitive to zero disparity, that automatically switches between LONG and SHORT, depending on the disparities present in the scene.
The model, tested in a simple virtual environment characterized by a frontoparallel plane with a random dot texture (Fig.1 left), produces the correct change of vergence for both a steady plane and a plane moving in depth, even when in the scene are present disparities larger than the FR. Thus, the model is able, first, to bring back the disparities of the scene inside the FR, in order to grant the effectiveness of the disparity map, and then, to keep the fixation point stable on the surface of the object in fovea.