This article introduces a new psychophysical method for a performance-based view of color constancy, in which the task for the observer is to identify similar materials across illuminants despite possible appearance changes, and to simultaneously extract the relative colors of the illuminants.(15) The article also examines genei-ality conditions for the task. Physical and neural constraints on chromatic signals make it possible to use simple affineheuristic algorithms to solve the correspondence problem for most Lambertian surfaces in random spatial arrangements under different illuminants. For rough surfaces, where the relative amounts of interface and body reflections vary with source-object-sensor geometry, the algorithms solve the correspondence problem across illuminants for a constant source-object-sensor geometry, but are not successful for rough surfaces in different spatial arrangements under different illuminants. (C) 2000 John Wiley & Sons, Inc.