Abstract: A device gamut boundary surface in a device independent color space (DICS) is defined by a set of small triangles. Each triangle in the DICS corresponds to a triangle on the surface of a color cube in a device dependent color space (DDCS). The triangles in the DICS are derived based on a look-up table which can be obtained by measuring a set of color patches produced from the given device. A small set of carefully selected gamut boundary points or signals in the DICS are determined and their corresponding signals or points on the surface of the color cube in the DDCS are computed. These data are stored in a table called a gamut descriptor. Gamut descriptor signals or points can be determined by a convex polyhedral cone inclusion process and their corresponding signals in the DDCS can be determined by triangle interpolation. The gamut descriptor usually includes gamut boundary signals at a number of lightness layers along a series of predetermined hue angles.

Abstract: A convex interpolation apparatus and method to map source color signals in a n-dimensional color space to target color signals in a m-dimensional color space includes finding a set of sample signals in the source color space whose convex hull encloses the given signal; determining the coefficients needed to express the given signal as a convex combination of the set of sample signals; and interpolating the source signal to obtain a target signal in the target color space by using the coefficients and the sample signals is the target color space that correspond to the sample signals selected in the source color space. The sample signals in both color spaces can be lattice points or non-lattice points. A method and apparatus are also provided which can not only determine if a point is enclosed by a convex hull of a set of points in a n-dimensional space, but also simultaneously derive the coefficients needed to express the given point as a convex combination of the set of points.