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I was thinking about this, but have yet to try it.

A normal panorama sweeps to capture a wide angle, what I want to achieve is the opposite: by moving the camera around a subject and stitching the resulting images together to create what I can only call a negative panorama (does this have a real name?).

I assume I would have to take a thin section from the middle of each image to counteract the FOV of the lens.

For example, an image in which you can see both sides of a car at once?

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This is called an inverse or object panorama. It produces a photo that looks similar to an unwrapped 3D model texture. It can certainly be done, but I'm not sure what software you'd use. – ElendilTheTall Aug 4 '12 at 9:45
This is someone I wanted to do forever! Hopefully someone will find a software to do it :) – Itai Aug 4 '12 at 12:59
A panorama is about a single perspective point. Pano brackets work to keep the lens nodal point at the same perspective as it is moved around. I'm guessing that what you want is that same single perspective as if from the inside, but imaging it from the outside, of the outside facing surface. You want the same thing as if the surface were transparent and could be shot from either inside or outside. Perspective would be the element to achieve. Since you can't get this from the outside, directly, the software would have to be emulating it and modifying the perspective. – Skaperen Aug 5 '12 at 5:01
Did you see "The Matrix" where the two were suspended in mid-air facing each other while the camera view swings around them? The "Bullet-Time effect" was used as a technique by firing many cameras in sequence and then viewing the common frames in sequence within a normal one-camera strip. – Stan Sep 9 '13 at 17:37
See also – user13451 Feb 8 '15 at 4:46

Instead of negative panorama you could call it a map projection of a tridimensional object (on a bidimensional plane). Similar to map making you would incur distortions of (some of) the geometrical quantities (angles, for instance).

Obviously all photographies are planar projections: the difference here is that you are "surrounding" your object with a cylinder, then cutting the projection from the interior on this cylinder longitudinally and mapping it to a plane. In a panorama you do the same but you project from the exterior towards the cylinder.

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Microsoft Research has developed a technique called Unwrap Mosaics that does this.

The input is a handheld video sequence with the camera circling the object. The software stitches the video frames into an unwrapped image that can be used as a texture map, or painted on.

The site linked above has video demonstrations and a paper presented at SIGGRAPH 2008 with a description of the algorithm. There is also a portion of the algorithm implemented in MATLAB.

Unfortunately the end to end software isn't available to the public at this time.

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You should take a look on article on Wikipedia, there is also free ios app Slit scan camera.

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I want to mention object movies. They have been made popular by the QuickTime VR file format, first released in 1994.

A quote (as of September 2013) from the web page of Object2VR, a software to create object movies:

Object2VR produces interactive 360° object movies. Object VR (virtual reality) movies are the result of a series of images taken of a subject from multiple angles and positions. To create an object movie, simply import an image series (a single row or multiple rows) and then export the movie as Flash, HTML5 and QuickTime VR formats to display on websites, kiosks and mobile devices.

To create the images you may put the camera on a tripod, and rotate the object on a turntable. There are dedicated hardware solutions, for example the XYimager products.

Wikipedia has an article on rotary views.

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Another approach might be to shoot a concave chrome hemisphere surrounding the object, like the inverse of shooting a chrome sphere when creating environment maps for image based lighting. The image of the object could be unwrapped into a single map which would show the object from surrounding perspectives.

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