Color conversion using barycentric projections
View Patent ↗A method and apparatus for interpolating values for a color space from an input color value. A unit hypercube enclosing the input value is generated based on values from a look up table. A set of boundary conditions are then imposed on the unit hypercube. To perform the actual interpolation, an initial barycentric projection is performed from a selected vertex of the unit hypercube through the input value onto a boundary of the unit hypercube. If the projection satisfies one of the boundary conditions, an interpolated value is calculated using the projection by back substitution. If the initial projection does not satisfy a boundary condition, an intermediate value is generated from the previous projection and successive barycentric projections are performed using respectively different vertices of the unit hypercube through intermediate values onto a boundary of the unit hypercube until a projection satisfies one of the boundary conditions.
1. A method of determining an interpolated value for a color space, comprising:
generating a unit hypercube enclosing an input value;
imposing a set of boundary conditions on the unit hypercube;
performing barycentric projections from respectively different vertices of the unit hypercube through the input value or intermediate value onto a boundary of the unit hypercube until a projection satisfies one of the boundary conditions; and
determining the interpolated value by back substitution using the barycentric projections.
2. The method of claim 1 , wherein the boundary conditions include a discrete boundary condition.
3. The method of claim 2 , wherein the discrete boundary condition is associated with a vertex of the unit hypercube.
4. The method of claim 1 , wherein the boundary conditions include a continuous boundary condition.
5. The method of claim 4 , wherein the continuous boundary condition is associated with a facet of the hypercube.
6. The method of claim 1 , wherein:
the boundary conditions include a first continuous boundary condition associated with a first facet of the unit hypercube and a second continuous boundary condition associated with a second facet of the unit hypercube; and
the continuous boundary conditions agree at an intersection of the first facet and the second facet.
7. The method of claim 1 , further comprising determining a simplex enclosing the input value, wherein:
the simplex is enclosed by the hypercube; and
a barycentric projection is performed using a vertex of the simplex.
8. The method of claim 1 , wherein when performing a barycentric projection from respectively different vertices of the unit hypercube through the intermediate value onto a boundary of the unit hypercube, the intermediate value is determined from a previous barycentric projection.
9. A computer-readable medium which stores computer-executable instructions, said computer-executable instructions for determining an interpolated value for a color space, the computer-executable instructions causing a computer to perform a method according to any of claims 1 to 8 .
10. An apparatus for determining an interpolated value for a color space, the apparatus comprising:
a program memory for storing instructions executable to perform a method according to any of claims 1 to 8 ; and
a processor coupled to the program memory for executing the instructions stored in said program memory.