There are transformations that you can apply to achieve some of what you're after, but there's not enough information in the source photo to come up with the final photo. For example, look at the heads of the two bolts. In the final photo, you can see that they're hexagonal, with round washers. But in the source photo you're looking at them from the side, so you have no way to know what shape they are: they could be round or hexagonal or square. Furthermore, there's extra information that you need to hide: in the source photo you see the edge of the sign, but this needs to be hidden when you change the viewing angle so that you're looking at the sign straight on.

For a whiteboard, however, the problem is much simpler because the surface is very flat and the thickness of the pen strokes is negligible. That is, the image on the whiteboard exists in a single plane. You can therefore use an affine transformation to stretch the image vertically, compress the bottom horizontally, and stretch the top horizontally. It should work pretty well provided you get enough resolution from your camera.