Homography computation of a deformed square planar object

suppose you have a square planar object (a piece of paper). You take a photo of it. Generally speaking, it will appear deformed. Suppose you process the image and compute the four corners of the planar object. Given the four points, you can compute an homography.

But now suppose that the object undergoes some type of deformation. All we can say about the nature of the deformation is:

1. it is "smooth" ( the surface of the object will not form sharp angles)
2. the surface of the object will be always totally visible even after the deformation.

For example: you stick the square paper on the surface of a cylindrical object.

The question is: given only the fo开发者_开发知识库ur coordinates (in pixel) of the corners of the planar (deformed) object, can i compute the correct homography? That is, can i "remove" the effect of the deformation before computing the homograhy?

Even an "approximated" (read working ;) method would be really useful. Thanks.

Ps. I wish to add that i don't know, a priori, the content of the planar object. Infact, the algorithm i am writing computes the homography, unwarp the object and check its content. It is a 2D barcode, so i have a pair id/crc of numbers. If the crc extracted from the object is equal to the crc computed on the id then it is a valid barcode.

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A homography is by definition a plane-plane transform. If the barcode is small enough you could probably assume that the object it is attached to is piecewise planar. After rectifying the image of the barcode you could estimate a barrel distortion model.

If you want to remove the deformation first then you would have to estimate the surface first and then flatten it. That would be a lot more difficult.