Tissot’s Indicatrix

Creating a flatmap from a folded cortical surface always introduces some distortion. This is similar to what happens when a map of the globe is flattened into a 2-D map like a Mercator projection. For the cortical surface the amount and type of distortion will depend on the curvature of the surface (i.e. whether it is on a gyrus or a sulcus) and on the distance to the nearest cut.

In general, we recommend examining data both in flattened and original 3-D space using the interactive webGL viewer, but it is also informative to visualize the distortion directly.

One method to show distortion is to visualize how geodesic discs, which contain all of the points within some geodesic distance of a central point, appear on the flattened cortical surface.

This technique is traditionally used to characterize and visualize distortions introduced by flattening the globe onto a map:

plot tissots indicatrix

Out:

Generating tissots_indicatrix surface info...
/home/travis/virtualenv/python3.7.1/lib/python3.7/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:318: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
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/home/travis/virtualenv/python3.7.1/lib/python3.7/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:318: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
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import cortex
import matplotlib.pyplot as plt

tissot = cortex.db.get_surfinfo("S1", "tissots_indicatrix", radius=10, spacing=30)
tissot.cmap = 'plasma'

cortex.quickshow(tissot, with_labels=False, with_rois=False, with_colorbar=False)

plt.show()

Total running time of the script: ( 0 minutes 49.312 seconds)

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