Biological Cybernetics

, Volume 97, Issue 4, pp 279–292 | Cite as

Geometry of the superior colliculus mapping and efficient oculomotor computation

  • Nicolas Tabareau
  • Daniel Bennequin
  • Alain Berthoz
  • Jean-Jacques Slotine
  • Benoît Girard
Original Paper


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.


Saccades Superior colliculus Spatio-temporal transformation Computational model 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Nicolas Tabareau
    • 1
  • Daniel Bennequin
    • 2
  • Alain Berthoz
    • 1
  • Jean-Jacques Slotine
    • 3
  • Benoît Girard
    • 1
  1. 1.UMR 7152, Laboratoire de Physiologie de la Perception et de l’ActionCNRS-Collège de FranceParisFrance
  2. 2.UMR 7586, Equipe Géométrie et DynamiqueUniversité Paris Diderot-CNRS, Paris, FranceParisFrance
  3. 3.Nonlinear Systems LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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