In this work, we analyse and compare several linear and nonlinear colo
ur representation spaces at different physiological levels, show the r
elationships between spaces and discuss the mathematical properties th
ey should exhibit. At the photoreceptor level, we examine the cone exc
itation and the cone contrast spaces. We discuss the second-stage spac
es, usually known as ATD-spaces, paying particular attention to Boynto
n's space and including a nonlinear space, the opponent modulation spa
ce. In addition, we approach third-stage transformations, which might
take place at the cortical level. Finally, we analyse a perceptual ATD
-type space, discussing how it might be derived as a third-stage trans
formation of an LGN-based ATD-space.