This dissertation presents novel real-time shadow algorithms to enable efficient filtering of Shadow Maps in order to increase the image quality and overall coherence characteristics. This is achieved by expressing the shadow test as a sum of products where the parameters of the shadow test are separated from each other. Ordinary Shadow Maps are then subject to a transformation into new so called basis-images which can, as opposed to Shadow Maps, be linearly filtered. The convolved basis images are equivalent to a pre-filtered shadow test which are used to reconstruct anti-aliased as well as physically plausible all frequency shadows.