This paper is concerned with the derivation of a progression

of shadow-free image representations. First we show that

adopting certain assumptions about lights and cameras leads to a

1-d, grey-scale image representation which is illuminant invariant

at each image pixel. We show that as a consequence, images

represented in this form are shadow-free. We then extend this 1-d

representation to an equivalent 2-d, chromaticity representation.

We show that in this 2-d representation, it is possible to re-light

all the image pixels in the same way, effectively deriving a 2-d

image representation which is additionally shadow-free. Finally,

we show how to recover a 3-d, full colour shadow-free image

representation by first (with the help of the 2-d representation)

identifying shadow edges. We then remove shadow edges from

the edge-map of the original image by edge in-painting, and we

propose a method to re-integrate this thresholded edge map, thus

deriving the sought-after 3-d shadow-free image.