It seems that lens match shading compresses vertices in the scene toward the center of the screen through perspective divide of modified w'. Vertices at the periphery need to be stretched to a greater degree toward the center so they need greater value of w', whereas the vertices at the center doesn't need to be stretched at all to maintain the original shading rate. As a result, the shading rate at the periphery decreases because less shading samples are taken at the peripheral regions after the perspective divide.

How does the approach choose the right value of A and B? If the warped image is too distorted, it seems that lenses might not recover the flat image. Does that means A and B are also dependent on the lens properties?

Is the (x, y) = (0, 0) point in the middle of the image?