Geometry of the superior colliculus mapping and efficient oculomotor computation

Abstract

Numerous brain regions encode variables using spatial distribution of activity in neuronal maps. Their specific geometry is usually explained by sensory considerations only. We provide here, for the first time, a theory involving the motor function of the superior colliculus to explain the geometry of its maps. We use six hypotheses in accordance with neurobiology to show that linear and logarithmic mappings are the only ones compatible with the generation of saccadic motor command. This mathematical proof gives a global coherence to the neurobiological studies on which it is based. Moreover, a new solution to the problem of saccades involving both colliculi is proposed. Comparative simulations show that it is more precise than the classical one.

The Conformal Camera in Modeling Active Binocular Vision

“…The mappings w = ln(z ± a) − ln a give an accepted approximation of the retinotopic structure in V1 and SC areas [15,30], where a > 0 removes logarithmic singularity and ±a indicates either the left or right brain hemisphere, depending on its sign. On the other hand, the DPFT that provides the data model for image representation can be efficiently computed by FFT in log-polar coordinates given by the complex logarithmic mapping w = ln z.…”

Effect of Microstimulation of the Superior Colliculus on Visual Space Attention

“…According to Cynader and Berman (1972), the fovea is represented anteriorly; the peripheral visual field, posteriorly; the lower visual field, laterally; and the upper visual field, medially. Inasmuch as visuotopic inputs to the colliculus are superimposed on an oculomotor map (Tabareau, Bennequin, Berthoz, Slotine, & Girard, 2007;Skaliora, Doubell, Holmes, Nodal, & King, 2004;Wallace, McHaffie, & Stein, 1997;Baleydier & Mauguiere, 1978), it may be that projections from V4 provide visual feature information, which could trigger orienting oculomotor reactions to spatially localized regions based on unexpected form, color, or texture (Zénon & Krauzlis, 2012). These authors (Zénon & Krauzlis, 2012) found that, although inactivation of the SC led to attention-like deficits, it did not diminish the attention-related modulation within extrastriate visual cortex.…”

Traffic sign detection with VG-RAM weightless neural networks

“…Before a saccadic movement, cells in the SC are activated and a winner-takes-it-all behavior leads to the selection of a point in the visual field retinotopically mapped in the SC-this point is the target of the saccade [14]. The mapping from the retina to SC follows a log-polar function [13]. Figure 1 shows the log-polar transform of an image, centered on the point (x c , y c )-this point corresponds to the center of attention in the visual field.…”

“…The images captured by the eyes are transformed into electrical impulses by the retina and, through the optic nerve, are projected into the SC and other cerebral areas [12]. The neural projection from the retina to SC follows a retinotopic mapping, i.e., neighboring regions in the retina are projected onto neighboring regions of the SC [13]. Before a saccadic movement, cells in the SC are activated and a winner-takes-it-all behavior leads to the selection of a point in the visual field retinotopically mapped in the SC-this point is the target of the saccade [14].…”