Curvature and Perspective
There are various reasons you might want to perform a perspective transform on an image, but in the case of road images taken from our front-facing camera on a car, why are we interested in doing a perspective transform?
Because it is more straightforward to take a gradient on a top-down view of the road image.
Because ultimately we want to measure the curvature of the lines, and to do that, we need to transform to a top-down view.
Because transforming the perspective removes the effect of curvature from our measurement.
Because transforming the perspective removes the effect of shadows and color differences from our road image.