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The Cyclopean View

- The Problem

One of the most amazing properties of human stereo vision is the fusion of the left and right views of a scene into a single cyclopean one. Since both eyes look at the world from two slightly different perspectives, our brain can not simply overlay the two images. The images just don't match:

Right Image with Fixationspot
Right Image
Left Image with Fixationspot
Left Image

The fixation marks in the stereo images above indicate the current fixation point; the simple overlay of the two images shows double contours in most image areas - except for the current fixation point.
Overlay of left & right image
Overlay

However - this is not what humans normally perceive. They fuse the two stereo images into a percept which is qualitatively very different from the two monocular components (Wheatstone, 1883). If you alternately close your left or your right eye, you will notice how your view switches between left and right perspective, and, probably, an additional perspective which is located somehow between these two views: it's the cyclopean image.

- The Facts

It is know for some time (Hering 1897, but already Abu Ali Al-Hazan ibn Al-Hazan ibn Al-Haytham around 1000) that under normal viewing conditions, the world appears to us as seen from a virtual eye placed midway between the left and right eye positions. The geometry of this cyclopean eye is depicted here:

Cyclopean View Geometry

This simple geometrical arrangement has an important consequence: since the world appears different from any of these viewpoints, the image we perceive of the world is never recorded directly by any sensory array, but constructed by our neural hardware!

Here's an example: the wooden block in the following stereo image is depicted in the images either from the left or from the right; but if you cross-fuse the images, you should perceive the wooden block from a position straight ahead:

Right Image of Robothand
Right Image
Left Image of Robothand
Left Image

Stereo image courtesy of Kiel Cognitive Systems Group

- How it might be done

As we have seen, left and right retinal images are not identical (that's why we can calculate the depth of a scene in the first place), and a simple superposition of the two images would lead to diplopia for most parts of the image. Proper fusion requires the alignment of the two monocular views to some common image coordinate system, which in turn requires the disparities for all image parts to be known. Thus, to achieve proper fusion, one has to solve the correspondence problem.

In coherence-based stereo, disparity calculations and fusion are performed simultaneously. As a matter of fact, the cyclopean view can be simply read out of the network.

Comparing the connections in the network for coherence-based stereo with the cyclopean view geometry,

Network and Cyclopean View Geometry
one sees that the left and right data lines in the network can be associated with the lines of sight emanating from the left and right eye. But: the disparity stacks in the network split the angle between the left and right data lines in half - and that corresponds in three-dimensional space exactly to the cyclopean view direction!

Now, successful disparity calculations are marked in the network by a small set of coherently coding units in each disparity stack. Therefore, a simple average over the inputs of all these coherently coding units creates the cyclopean view:

Cyclopean View (+ movie)
Cyclopean View
Simple overlay of stereo images
Overlay - for comparison

Note again that the simple overlay of the stereo images (right display) is diplopic in most image parts. And, the cyclopean image has a perspective straightahead, which is different from the two input images (see above). The cyclopean view is a view constructed by the coherence-network; it was never taken by any camera.

With natural scenery, the change of perspective seen in the above example is not so dramatic, but it's still present. And it is important if you want to sample 3d-space through vergence-movements

Using all the data available in the coherence-network, it is possible to create all virtual views between the two real eye-positions.

Motion between
 eye-positions

If you click on the above image, you can see a small movie (1.3M/click here for a smaller (252k) .mpg-movie) simulating a virtual camera-movement from the left to the right eye-position and back.

Another funny application of this process is the reconstruction of the original stereo pair from a color-anaglpyh. If you are interested, you can create, via the worldwide web, the cyclopean image of any stereopair by clicking here.


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