How to set up a binocular rivalry experiment, that splits a single image in two separately controlled ones?

The question is about the actual physical setup and steps needed to take in order to experiment with the phenomena. I found a tutorial on jove.com, "How to Create and Use Binocular Rivalry", and it also has a dedicated explanatory article.

However, the experiment I want to make is tricky in the following sense.

A regular binocular rivalry experiment has two separate images set up, and normally the image features are controlled in a way that is suitable to exhibit a whatever the experimenters want.

In the case that I want to make, images are not separate, they are basically left and right parts of a single image that is usually viewed as a single image as well. With the experiment I will control left and right halves of that single image separately, but I do want to present halves to different eyes. The particular problem is that I want to calibrate the physical setup so that the physical boundary between images is not exactly visible. So it means I can't just split left and right - the border between the images in the eyes of the observer has to be as small as possible.

Under this condition, how to calibrate the binocular setup then?

UPDATE: As advised in comments, I should say that the example stimulus is the two halves of one single face. The boundary between halves should not be seen to not potentially distract the observer or influence his perception elsewise.

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This is interesting. But the first thing I don't understand about this is what will be in the "other" half of the images. White? Black? 50% Grey? Because, you know, there is no "empty", visually, there has to be something, and that will be an image in itself. So what kind of image do you want to split, and what are you trying to research? –  what Sep 21 '13 at 22:05
Sry for being ambiguously abstract, I should've explained right away that halves of the image are halves of the face. The face is the same, but halves express different emotion. Curiosity here is about whether I would get the regular switching between percepts or something else. The trick here is to calibrate it in the way that would not let the observer to see the border between the left/right halves because then it can destroy the perceptual effect. –  Leonid Fedorov Sep 23 '13 at 13:41