COLOR MANAGEMENT- P9: ICC White Papers are one of the formal deliverables of the International Color Consortium, the other being the ICC specification itself – ISO 15076: Image technology color management – Architecture, profile format, and data structure. The White Papers undergo an exhaustive internal development process, followed by a formal technical review by the membership and a ballot for approval by the ICC Steering Committee. | 224 Profile Construction and Evaluation Figure Power law with exponent g 0 It is not obvious how or even whether a CMM should process data when g is zero or negative. The profile is almost certainly corrupt or in error in such a case. There is clearly no point in defining a constant or decreasing function which will be clipped over the entire domain. The CMM developer may choose in such a case to reject the profile or to replace Figure Power law with exponent g 1 2 Use of the parametricCurveType 225 the parametric curve with the identity function y x which amounts to setting g 1 or some other default. Ideally profile creators should abide by the condition g 0 and CMM developers should treat any occurrences of negative and zero values as errors and take appropriate action. The Power-Law Argument Function type 0 is just the basic power law described above y fo x xg x Fo y y1 g. In the other types the argument to the power law is not simply x but a linear expression in x. In types 1 2 3 and 4 the argument which we will call s takes the form s ax b where a and b are additional parameters. The power law is then sg. Since there is no practical restriction on the parameter values s can take on any value as x varies between 0 and 1. If s is negative sg can be imaginary or complex. It will be real for integer g but g cannot be restricted to integer values. In such a situation a CMM might choose to take the real part of the expression. Alternatively it could take the absolute magnitude. It could arbitrarily set the expression to zero or one. Another option is simply to require s to be non-negative. In types 1 2 3 and 4 the domain is divided into two segments and the power law is employed only in the higher segment. For instance the definition of type 1 is y f1 x 0 0 x b a sg b a x 1. In normal usage a will be positive and b will be negative so that the segment boundary b a occurs at a positive value of x. The function is identically zero in the lower segment .
