vortex_blur animation

Description: AVI animation demonstrating the effects of blurring a
             vortex or "pinwheel" pattern of orientation preference
             [1,2], similar to the patterns found in V1 via optical
             recording [3,4] and electrophysiology [5].


This animation demonstrates the effects of blurring on orientation
preference mappings, also known as "orientation pinwheels" maps. In
this animation, an initial synthetic orientation preference mapping is
low-pass filtered by a sequence of blurring kernels of the Cauchy
distribution type parameterized by the full-width at half-maximum
(FWHM).

The color code for the mapping is similar to those found in the
literature, where each color corresponds to a set of orientation
angles from 0 to 180 degrees. A pinwheel or "vortex" center can be
identified as those points around which the full 180 degrees of
orientation preference is represented. Vortex centers where the
orientation wraps around in a clockwise sense are labeled as positive
chirality centers (white dots) and vortex centers where the
orientation wraps in a counterclockwise sense are labeled as negative
chirality centers (black squares).

As predicted, applying a low-pass filter to the orientation map
results in vortex annihilation---nearby vortices of opposite chirality
become blended into one another until they cancel each other out.
During the annihilation process, two vortex centers slowly approach
each other as the blurring kernel size increases, thus annihilation is
necessarily accompanied by systematic vortex center movement.

To aid the visualization, a Voronoi diagram is computed for each stage
in the blurring process. The Voronoi cell corresponding to each vortex
center represents the region of the orientation map that is closer to
a particular vortex center than any other. Note that vortex centers
annihilate exactly when the pair collides with their shared Voronoi
edge.

In addition, the zero-crossings of both the real and imaginary part of
the "polar representation" of the orientation response appear in the
animation as solid and dashed black lines, respectively. Note that the
vortex centers align with intersections of the two families of
zero-crossings.

The approximate dimensions of the displayed orientation map is
2.5x2.5mm, and the initial or "real" inter-vortex distance (RIVD) is
assumed to be 450 microns.




  References:
  ===========

 [1] A. Rojer and E. L. Schwartz. Cat and monkey cortical columnar
     patterns modeled by bandpass-filtered 2D white noise. Biological
     Cybernetics, 62:381-391, 1990.

 [2] E. L. Schwartz and A. S. Rojer. Cortical hypercolumns and the
     topology of random orientation maps. Proceedings of 12th
     International Conference on Pattern Recognition, pages 150-5
     vol.2, 1994.

 [3] G. G. Blasdel and G. Salama. Voltage-sensitive dyes reveal a
     modular organization in monkey striate cortex. Nature,
     321(6070):579-585, 5-11 June 1986.

 [4] T. Bonhoeffer and A. Grinvald. The layout of iso-orientation
     domains in area 18 of cat visual cortex: optical imaging reveals
     a pinwheel-like organization. Journal of Neuroscience,
     13(10):4157-4180, October 1993.

 [5] N. V. Swindale, J. A. Matsubara, and M. S. Cynader. Surface
     organization of orientation and direction selectivity in cat area
     18. Journal of Neuroscience, 7(5):1414-1427, May 1987.