It is possible to add a third dimension to a 2D image, although it probably won't have the desired effect. You start by calculating a height map based on the brightness or hue of the 2D image. The height map will add the third dimension, where e.g. the bright areas are higher than the dark areas. In general, most images will have a bright object in the foreground and a darker background so the result will still look very good, although it could also give some weird effects to other images.
Of course, there is another alternative to store 3D images in a @D image format, but this requires the use of something similar to the Alpha channel. Normally, alpha channels are used for transparency, but a similar channel could be used as height map, indicating which parts of the image should be lifted and how much the lift should be. Normal applications would still recognize them as 2D images but specialized software will be able to use this height map, thus adding depth to every pixel.