The chromatic appearance of a surface depends on its surrounding scene. A variety of mechanisms have been proposed to account for such phenomena, ranging from low-level gain control or adaptation processes that adjust for such properties as a scene's chromatic mean and covariance structure, to higher-level computations that compensate for the chromatic content of the illuminant. Despite their differences, a shared prediction of all such processes is that color induction should be limited to a full discounting of the surround or illuminant color--that is, an opponent color shift equal in magnitude to the chromatic bias of the surround or illuminant. Here, we report new forms of chromatic induction that can be significantly larger than predicted by all such models. We show that when the geometric and chromatic relationships between a target and its surround support a decomposition of an image into multiple layers, the induced color can significantly exceed the full discounting prediction. Similar phenomena are also observed with achromatic stimuli, suggesting that common processes of perceptual decomposition are involved in both forms of induction. These results demonstrate that information about the geometric and photometric relationship between a target and its surround is utilized by the mechanisms involved in color induction.