Rubber Checkerboards
Sunday, June 26, 2011 at 10:37PM
Bob Gerber

Just a few thoughts to share today; let's consider the usefulness of the idea of a matrix or checkerboard when we think about the relationship between a small region of the visual scene and a corresponding region of the retina.  You saw that I made extensive use of this checkerboard metaphor in my last post.  You will see it again in future posts.  

We know that the lens "projects" an image of the outside scene onto the retina.  If you did the blind spot test earlier in this blog, you learned that there really is a correspondence between objects in the real world -- like the black spot on the test sheet -- and specific locations on the retina.  Remember that you had to move your head in order to move the retinal image of the black spot until the image fell upon the "blind spot" in the eye you tested.  

In the early introductory portion of the Stephen Palmer Vision Science book, he portrays the organization of information from the retina in what I have called a "checkerboard" -- in his specific example it was a matrix with 24 rows and 17 columns.  He demonstrated, at least to my satisfaction, that this is ONE useful way to portray the spatial mapping of photoreceptor data to the portions of the brain that use that data.  Useful as it may be, he certainly does not suggest that a matrix or what I call a checkerboard is anything more than a metaphor.  

He later shows that the actual data would pose significant problems for this checkerboard metaphor.  The reason is pretty simple.  Consider the one important property of any checkerboard -- a matrix of evenly spaced rows and columns.   Although the rows and columns in a matrix or checkerboard are evenly distributed -- the distribution of the actual photoreceptors on the surface of the retina is certainly not even.  

The central foveal region of the retina has a very high density of photoreceptors within a 20-degree visual cone around the central line of sight of each eye.  In order to fit the information from this high-density region of photoreceptors into our evenly spaced checkerboard, we would need a “rubber checkerboard” that could bulge to permit us to pack in the additional information.  This phenomenon is called "cortical magnification."  It is called "cortical" because the magnification effect first matters when the information from the eyes arrives at the primary visual cortex in the very back of your skull.  [Oops, I slipped and mentioned a specific part of the brain.]  ;-)

The images below are my very rough attempt to visually depict "cortical magnification."   You probably recognize the left-hand image from the landing page of this website.  Imagine that you are standing where the camera was that produced the image of my "virtual world headquarters" lobby.  The image on the left is what you would see.  The image on the right is exactly the same view but I have tried to distort the image as if you had packed extra information from the high-density foveal region into a bulging rubber checkerboard.  The optical diameter of the bulge is about 20 degrees.

 

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