# The Wyckoff Principle

• The Wyckoff principle is based on the fact that differently exposed images of the same scene or object capture different information due to the differences in exposure. Consider, for example, these four images of the same scene: an open doorway leading off into a long dark corridor (captured with a Personal Imaging camera, but the Wyckoff principle applies to equally well to ordinary hand-held 35mm cameras, HandyCams, etc.).

The above image shows the open doorway, upon which there is direct sunlight shining. Since I am looking at the white sign on the door, my camera has adjusted itself to expose this nicely. The door and wall are visible, but the inside of the corridor to the right is dark.

As I look to the right, the camera's automatic exposure brightens up the image so that now I can no longer read the sign. However, it's still not bright enough for me to see down into the dark hallway.

Now as I turn my head further to the right, I can begin to see just a little of the hallway.

As I look straight down the hallway, my camera's gain increases to properly expose what's in the center of it's field of view. I can see a person standing in the hallway (Charles Wyckoff, inventor of XR film). However, the dark brown door to the left apears as completely white --- so white in fact, that we can no longer tell that it is a door.
The entire dataset from this looking around is available to other researchers for illustrating/testing the Wyckoff principle
• Another similar dataset is also available. Here is a lookpainting generated, using the Wyckoff principle, from that dataset.

Notice how the sign on the door is very clear, and, at the same time, we can see down into the dark corridor.
• Joint parameter estimation in both domain and range of functions in same orbit of projective-Wyckoff group This paper pertains to creating high resolution radiance maps, by combining differently exposed pictures of the same subject matter in order to extend dynamic range. (Based on an earlier 1993 paper published in IS&T.)
• A wearker result, for when the pictures differ ONLY IN EXPOSURE (e.g. when all the pictures are taken from the same camera position and orientation, as for example when the camera is mounted on a tripod and a number of pictures are taken with different shutter speeds) is described in the paper Being Undigital...
• A simple example of how the Wyckoff priniple can be applied to just two images (that's the minimum number required).
• Here's another example of a Wyckoff set, consisting of some pictures taken at the cyberman opening at the Royal theatre. You can view or download the entire dataset from here.

--Steve Mann

I am a faculty member at University of Toronto; you may want to visit my official faculty WWW page at http://www.eecg.toronto.edu/~mann

Contact info: Professor Steve Mann, University of Toronto, Department of Electrical Engineering, 10 King's College Road, Toronto, Ontario, M5S 3G4 mann@eecg.toronto.edu.

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