Characterizing human retinotopic mapping with conformal geometry: A preliminary study

Duyan Ta, Jie Shi, Brian Barton, Alyssa Brewer, Zhong Lin Lu, Yalin Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


Functional magnetic resonance imaging (fMRI) has been widely used to measure the retinotopic organization of early visual cortex in the human brain. Previous studies have identified multiple visual field maps (VFMs) based on statistical analysis of fMRI signals, but the resulting geometry has not been fully characterized with mathematical models. Here we test whether VFMs V1 and V2 obey the least restrictive of all geometric mappings; that is, whether they are anglepreserving and therefore maintain conformal mapping. We measured retinotopic organization in individual subjects using standard traveling-wave fMRI methods. Visual stimuli consisted of black and white, drifting checkerboards comprising rotating wedges and expanding rings to measure the cortical representations of polar angle and eccentricity, respectively. These representations were then projected onto a 3D cortical mesh of each hemisphere. By generating a mapped unit disk that is conformal of the VFMs using spherical stereographic projection and computing the parameterized coordinates of the eccentricity and polar angle gradients, we computed Beltrami coefficients to check whether the mapping from the visual field to the V1 and V2 cortical representations is conformal. We find that V1 and V2 exhibit local conformality. Our analysis of the Beltrami coefficient shows that selected regions of V1 and V2 that contain reasonably smooth eccentricity and polar angle gradients do show significant local conformality, warranting further investigation of this approach for analysis of early and higher visual cortex. These results suggest that such a mathematical model can be used to characterize the early VFMs in human visual cortex.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2014
Subtitle of host publicationImage Processing
ISBN (Print)9780819498274
StatePublished - Jan 1 2014
EventMedical Imaging 2014: Image Processing - San Diego, CA, United States
Duration: Feb 16 2014Feb 18 2014

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2014: Image Processing
Country/TerritoryUnited States
CitySan Diego, CA


  • Beltrami coefficient
  • Conformal geometry
  • Functional magnetic resonance imaging
  • Retinotopic mapping
  • Visual field maps

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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