Limits...
Modeling magnification and anisotropy in the primate foveal confluence.

Schira MM, Tyler CW, Spehar B, Breakspear M - PLoS Comput. Biol. (2010)

Bottom Line: We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface.The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas.Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.

View Article: PubMed Central - PubMed

Affiliation: School of Psychiatry and The Black Dog Institute, University of New South Wales, Sydney Australia. mschira@science.unsw.edu.au

ABSTRACT
A basic organizational principle of the primate visual system is that it maps the visual environment repeatedly and retinotopically onto cortex. Simple algebraic models can be used to describe the projection from visual space to cortical space not only for V1, but also for the complex of areas V1, V2 and V3. Typically a conformal (angle-preserving) projection ensuring local isotropy is regarded as ideal and primate visual cortex is often regarded as an approximation of this ideal. However, empirical data show systematic deviations from this ideal that are especially relevant in the foveal projection. The aims of this study were to map the nature of anisotropy predicted by existing models, to investigate the optimization targets faced by different types of retino-cortical maps, and finally to propose a novel map that better models empirical data than other candidates. The retino-cortical map can be optimized towards a space-conserving homogenous representation or a quasi-conformal mapping. The latter would require a significantly enlarged representation of specific parts of the cortical maps. In particular it would require significant enlargement of parafoveal V2 and V3 which is not supported by empirical data. Further, the recently published principal layout of the foveal singularity cannot be explained by existing models. We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface. The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas. Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.

Show MeSH

Related in: MedlinePlus

Predicted and measured areal magnification.(a) As predicted by the classical Log-Polar model, using parameters from [35] (b) The Double-Sech model, (c) Empirical data from [3] (crosses), [15] (circles) and [27] (diamonds).
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2813258&req=5

pcbi-1000651-g006: Predicted and measured areal magnification.(a) As predicted by the classical Log-Polar model, using parameters from [35] (b) The Double-Sech model, (c) Empirical data from [3] (crosses), [15] (circles) and [27] (diamonds).

Mentions: Explicit linear magnification curves were estimated from both models and compared to empirical data (Figure 6). Both models result in fairly accurate predictions from 12° to 3°. However, more central than 3°, the classical Log-Polar model fails to predict the empirical data, suggesting in particular a very specific enlargement of V3 that is absent in the data. The Double-Sech model, on the other hand, predicts a constant relation of magnification between V1, V2 and V3 throughout the visual field, providing a fairly accurate prediction of magnification from 12° down to 0.75°. However, central to 0.75° the empirical data show that V3 and V2 are larger than V1, a property that is not captured by either of the present models.


Modeling magnification and anisotropy in the primate foveal confluence.

Schira MM, Tyler CW, Spehar B, Breakspear M - PLoS Comput. Biol. (2010)

Predicted and measured areal magnification.(a) As predicted by the classical Log-Polar model, using parameters from [35] (b) The Double-Sech model, (c) Empirical data from [3] (crosses), [15] (circles) and [27] (diamonds).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2813258&req=5

pcbi-1000651-g006: Predicted and measured areal magnification.(a) As predicted by the classical Log-Polar model, using parameters from [35] (b) The Double-Sech model, (c) Empirical data from [3] (crosses), [15] (circles) and [27] (diamonds).
Mentions: Explicit linear magnification curves were estimated from both models and compared to empirical data (Figure 6). Both models result in fairly accurate predictions from 12° to 3°. However, more central than 3°, the classical Log-Polar model fails to predict the empirical data, suggesting in particular a very specific enlargement of V3 that is absent in the data. The Double-Sech model, on the other hand, predicts a constant relation of magnification between V1, V2 and V3 throughout the visual field, providing a fairly accurate prediction of magnification from 12° down to 0.75°. However, central to 0.75° the empirical data show that V3 and V2 are larger than V1, a property that is not captured by either of the present models.

Bottom Line: We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface.The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas.Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.

View Article: PubMed Central - PubMed

Affiliation: School of Psychiatry and The Black Dog Institute, University of New South Wales, Sydney Australia. mschira@science.unsw.edu.au

ABSTRACT
A basic organizational principle of the primate visual system is that it maps the visual environment repeatedly and retinotopically onto cortex. Simple algebraic models can be used to describe the projection from visual space to cortical space not only for V1, but also for the complex of areas V1, V2 and V3. Typically a conformal (angle-preserving) projection ensuring local isotropy is regarded as ideal and primate visual cortex is often regarded as an approximation of this ideal. However, empirical data show systematic deviations from this ideal that are especially relevant in the foveal projection. The aims of this study were to map the nature of anisotropy predicted by existing models, to investigate the optimization targets faced by different types of retino-cortical maps, and finally to propose a novel map that better models empirical data than other candidates. The retino-cortical map can be optimized towards a space-conserving homogenous representation or a quasi-conformal mapping. The latter would require a significantly enlarged representation of specific parts of the cortical maps. In particular it would require significant enlargement of parafoveal V2 and V3 which is not supported by empirical data. Further, the recently published principal layout of the foveal singularity cannot be explained by existing models. We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface. The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas. Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.

Show MeSH
Related in: MedlinePlus