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Lens distortion correction

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I'm trying to write a shader to do distortion correction.http://docs.opencv.org/2.4/doc/tutorials/calib3d/camera_calibration/camera_calibration.html

Suppose there is just radial distortion. I have an input image with radial distortion and the output image will be the corrected image.

So for each pixel (x,y) in the output image, I want to sample the pixel in the input image that needs to move to (x,y). Intuitively, for radial distortion correction this is going to "pull" pixels inward toward the center of the image.

My question is at the boundaries, the texture coordinates are going to go out of bounds of the input image. I can use a black border color, but is this expected? Looking at the results from this post:Image lens distortion correction

it looks like the corrected image will have some radial black areas, but I just wanted to confirm.

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