Explain why inferring object surface properties from image properties is, in general, an ill-posed problem: some of Hadamard's criteria for well-posed problems are not satisfied. In the case of inferring the colours of objects from images, how does knowledge of the properties of the illuminant affect the status of the problem and its solubility? More gen- erally, illustrate how addition of ancillary constraints or assumptions, even metaphysical assumptions, allows an ill-posed problem to be converted into a well-posed problem.