How do I convert a "flat" image into a "spherical" image?

I want to make a soccer ball (or possibly a tennis ball) as a projectile. How would I go about mapping a texture, like this, which does not map well to a sphere:


to something like this, which does map well to a sphere?

Note: It would be also nice various sports balls were already included in UE4, perhaps they could be added, or someone could make and sell them on the market place.