变形方形平面物体的单应性计算
假设你有一个方形平面物体（一张纸）。你给它拍张照片。一般来说，会显得变形。假设您处理图像并计算平面对象的四个角。给定这四个点，您可以计算单应性。
但现在假设该物体经历了某种类型的变形。关于变形的本质，我们只能说：
- 它是“光滑的”（物体表面不会形成锐角），
- 即使在变形之后，物体的表面也将始终完全可见。
例如：将正方形纸贴在圆柱形物体的表面上。
问题是：仅给定平面（变形）对象的角的四个坐标（以像素为单位），我可以计算正确的单应性吗？也就是说，我可以在计算单应性之前“消除”变形的影响吗？
即使是“近似”（阅读工作；）方法也会非常有用。 谢谢。
诗。 我想补充一点，我先验地不知道平面物体的内容。事实上，我正在编写的算法计算单应性、反扭曲对象并检查其内容。它是一个二维条形码，所以我有一对 id/crc 数字。如果从对象中提取的 crc 等于在 id 上计算的 crc，则它是有效的条形码。
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:
- it is "smooth" ( the surface of the object will not form sharp angles)
- 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 four 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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根据定义，单应性是平面-平面变换。如果条形码足够小，您可能会假设它所附着的物体是分段平面的。校正条形码图像后，您可以估计桶形失真模型。
如果你想先消除变形，那么你必须先估计表面，然后将其展平。那会困难很多。
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.