Formulation of Border-Ownership Assignment in Area V2 as an Optimization Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10636)


Border-ownership (BO) assignment, or the assignment of borders to an occluding object, is a primary step in visual perception. Physiological experiments have revealed the existence of neurons in area V2 that respond selectively to objects placed on a specific side of their response field. Although existing models can reproduce this phenomenon, they are not based on a clear computational theory. For this study, we formulated BO assignment as a well-defined optimization problem. We hypothesize that information related to BO assignment can be expressed as a conservative vector field. This conservative vector field is proposed as the gradient of a scalar field that carries information related to the depth order of the overlapping object. Conservative vector fields have zero curl (rotation). Using this theorem, we construct and solve an optimization problem. Numerical simulations demonstrate that a model based on our derived algorithm solves BO assignment for problems of perceived order and occlusion. Deduced neural networks provide insight into possible characteristics of lateral connections in area V2.


Computational model Perception Depth order Middle vision 



This work was partially supported by JSPS KAKENHI (16K00204).


  1. 1.
    Nakayama, K., Shimojo, S., Silverman, G.H.: Stereoscopic depth: Its relation to image segmentation, grouping, and the recognition of occluded objects. Perception 18, 55–68 (1989)CrossRefGoogle Scholar
  2. 2.
    Zhou, H., Friedman, H.S., von der Heydt, R.: Coding of border ownership in monkey visual cortex. J. Neurosci. 20(17), 6594–6611 (2000)Google Scholar
  3. 3.
    Qiu, F.T., von der Heydt, R.: Figure and ground in the visual cortex: V2 combines stereoscopic cues with gestalt rules. Neuron 47(1), 155–166 (2005)CrossRefGoogle Scholar
  4. 4.
    Li, Z.: Border ownership from intracortical interactions in visual area V2. Neuron 47(1), 143–153 (2005)CrossRefGoogle Scholar
  5. 5.
    Sakai, K., Nishimura, H., Shimizu, R., Kondo, K.: Consistent and robust determination of border ownership based on asymmetric surrounding contrast. Neural Netw. 33, 257–274 (2012)CrossRefGoogle Scholar
  6. 6.
    Craft, E., Schütze, H., Niebur, E., von der Heydt, R.: A neural model of figure-ground organization. J. Neurophysiol. 97(6), 4310–4326 (2007)CrossRefGoogle Scholar
  7. 7.
    Poggio, T., Torre, V., Koch, C.: Computational vision and regularization theory. Nature 317, 314–319 (1985)CrossRefGoogle Scholar
  8. 8.
    Qiu, F.T., von der Heydt, R.: Neural representation of transparent overlay. Nat. Neurosci. 10(3), 283–284 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Graduate School of Information SystemsThe University of Electro-CommunicationsTokyoJapan

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