Method and apparatus for gamut boundary determination

A method for finding a gamut boundary of an image forming device, the method comprising:

• identifying a set of points defining a gamut of the image forming device;
• selecting a parameter α and a parameter α2 for the gamut, the parameter α2 defining an α-shape and an α-surface enclosing a plurality of tetrahedra such that the plurality of tetrahedra belong to the α-shape;
• the parameter α defining a second α-surface, the parameter α is greater than the parameter α2, and the parameter α is no larger than necessary to guarantee that the α-surface has a minimum concave angle that is greater than a given angle;
• and
• computing the gamut boundary of the image forming device from the set of points and the parameter α.

Apparatus for calculating a color gamut volume from a color gamut comprising:

• a processing unit;
• a memory unit coupled to the processing unit;
• and
• a software means operative on the processing unit for:
• identifying an alpha shape associated with the color gamut, the alpha shape having a plurality of alpha surfaces deriving their shape based upon a real number parameter alpha greater than zero and less than infinity wherein a relatively low parameter alpha corresponds to a less convex shape than a relatively high parameter alpha, the alpha shape including a plurality of tetrahedra each having a volume and being defined by one of the alpha surfaces and a point interior to the alpha shape;
• and
• summing the volume of each of the plurality of tetrahedra to generate the color gamut volume.

Apparatus for finding a percentage of colors in an image having a gamut and capable of being rendered by an image forming unit, the apparatus comprising:

• a processing unit;
• a storage unit coupled to the processing unit;
• and
• a software means operative on the processing unit for:
• identifying a gamut boundary for the image;
• identifying a gamut boundary for the image forming unit;
• calculating the percentage of colors in the image capable of being rendered by the image forming unit from the gamut boundary for the image and the gamut boundary for the image forming unit by
• computing a first gamut volume associated with the gamut boundary of the image;
• computing a second gamut volume associated with the gamut boundary of the image forming unit;
• computing an intersection volume for the first gamut volume and the second gamut volume;
• and
• dividing the intersection volume by the first gamut volume.

A computer-readable medium having computer-executable instructions for performing a method comprising:

• computing a color image gamut volume;
• computing a plurality of gamut volumes, each of the plurality of gamut volumes associated with one of a plurality of image forming devices wherein the computing the plurality of gamut volumes for said each of the plurality of gamut volume includes
• identifying an α-shape associated with a color gamut, the α-shape including a plurality of tetrahedra and each of the plurality of tetrahedra having a volume;
• and
• summing the volume of each of the plurality of tetrahedra to generate the color image gamut volume;
• and
• identifying one of the plurality of gamut volumes having a gamut volume closest to the color image gamut volume.

A method for finding a gamut boundary of a color image, the method comprising:

• identifying a set of points larger than three in number defining a gamut of the color image;
• selecting a parameter α for generating an α-shape having a plurality of α-surfaces wherein each of the α-surfaces is defined by at least three of the set of points and the α-shape fits the set of points and bounds other points not included in the set of points, the parameter α is a real number greater than zero and less than infinity and a relatively low parameter α corresponds to an α-shape less convex than a relatively high parameter α;
• and
• computing the gamut boundary of the color image from the set of points and the parameter α.