Method for transforming color signals

Claim 1

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output color signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output color signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output color signal component, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output color signal components, which are stored in the look-up table and which are close to the target output color signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output color signal components stored in the look-up table as lattice points in a three-dimensional output color signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output color signal space, (c3) originating said three linearly independent vectors from said origin, a local coordinate system being thereby constituted in said three-dimensional output color signal space, (c4) transforming a difference between the target output color signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output color signal space, (c5) updating said origin and said three linearly independent vectors by utilizing said local coordinates in said three-dimensional output color signal space, (c6) repeating steps (c3)-(c5), a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output color signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output color signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output color signal component.

Claim 2

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output color signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output color signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output color signal component, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output color signal components, which are stored in the look-up table and which are close to the target output color signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output color signal components stored in the look-up table as lattice points in a three-dimensional output color signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output color signal space, (c3) originating said three linearly independent vectors from said origin, a local coordinate system being thereby constituted in said three-dimensional output color signal space, (c4) transforming a difference between the target output color signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output color signal space, (c5) updating said origin and said three linearly independent vectors by utilizing said local coordinates in said three-dimensional output color signal space, (c6) repeating steps (c3)-(c5), a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output color signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output color signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output color signal component.

Claim 5

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output color signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output color signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output color signal component, which is not stored in the look-up table, with a linear interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output color signal components, which are stored in the look-up table and which are close to the target output color signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output color signal components stored in the look-up table as lattice points in a three-dimensional output color signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output color signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output color signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output color signal component, in said local coordinate system in said three-dimensional output color signal space, (c5) approximating each of the values of i+diq i , j+djq j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated original, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6), and until an updated original and an updated displacement have become respectively equal to a predecessor origin (i, j, k) and a predecessor displacement in said three-dimensional output color signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i q j q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 6

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output color signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output color signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output color signal component, which is not stored in the look-up table, with a linear interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output color signal components, which are stored in the look-up table and which are close to the target output color signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output color signal components stored in the look-up table as lattice points in a three-dimensional output color signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output color signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output color signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output color signal component, in said local coordinate system in said three-dimensional output color signal space, (c5) approximating each of the values of i+diq i , j+djq j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated original, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6), and until an updated original and an updated displacement have become respectively equal to a predecessor origin (i, j, k) and a predecessor displacement in said three-dimensional output color signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i q j q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 11

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a corresponding plurality of three-dimensional output chromaticity signal components, each of which is obtained with one of the three-dimensional input signals components; (b) transforming a target output chromaticity signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output chromaticity signal component, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output chromaticity signal components, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output chromaticity signal components, which are stored in the look-up table and which are close to the target output chromaticity signal component, the linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output chromaticity signal components stored in the look-up table as lattice points in a three-dimensional output chromaticity signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output chromaticity signal space, (c3) originating said three linearly independent vectors from said origin, thereby constructing a local coordinate system in said three-dimensional output chromaticity signal space, (c4) transforming a difference between the target output chromaticity signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output chromaticity signal space, (c5) updating said origin and said three vectors by utilizing said local coordinates in said three-dimensional output chromaticity signal space, (c6) repeating steps (c3)-(c5), a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output chromaticity signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output chromaticity signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output chromaticity signal components.

Claim 12

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a corresponding plurality of three-dimensional output chromaticity signal components, each of which is obtained with one of the three-dimensional input signals components; (b) transforming a target output chromaticity signal component into a three-dimensional input signal component of said plurality of three-dimensional input signal components by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output chromaticity signal component, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output chromaticity signal components, which is not stored in the look-up table, with an interpolating process from a plurality of the three-dimensional input signal components corresponding to a plurality of the three-dimensional output chromaticity signal components, which are stored in the look-up table and which are close to the target output chromaticity signal component, the linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output chromaticity signal components stored in the look-up table as lattice points in a three-dimensional output chromaticity signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output chromaticity signal space, (c3) originating said three linearly independent vectors from said origin, thereby constructing a local coordinate system in said three-dimensional output chromaticity signal space, (c4) transforming a difference between the target output chromaticity signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output chromaticity signal space, (c5) updating said origin and said three vectors by utilizing said local coordinates in said three-dimensional output chromaticity signal space, (c6) repeating steps (c3)-(c5), a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output chromaticity signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output chromaticity signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output chromaticity signal components.

Claim 15

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a corresponding plurality of three-dimensional output chromaticity signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output chromaticity signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating a three-dimensional input signal component corresponding to the target output chromaticity signal component, which is not stored in the look-up table, with a linear interpolating process from a plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output chromaticity signal components, which are stored in the look-up table and which are close to the target output chromaticity signal component, said linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output chromaticity signal components stored in the look-up table as lattice points in a three-dimensional output chromaticity signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output chromaticity signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output chromaticity signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output chromaticity signal component, in said local coordinate system in said three-dimensional output chromaticity signal space, (c5) approximating each of the values of i+diq i , j+djq j and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing a direction of the displacement di if q i is negative, reversing a direction the displacement dj if q j negative, and reversing a direction the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated original and an updated displacement have become respectively equal to the predecessor original and the predecessor displacement in said three-dimensional output chromaticity signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dk, k) and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 16

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a corresponding plurality of three-dimensional output chromaticity signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output chromaticity signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating a three-dimensional input signal component corresponding to the target output chromaticity signal component, which is not stored in the look-up table, with a linear interpolating process from a plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output chromaticity signal components, which are stored in the look-up table and which are close to the target output chromaticity signal component, said linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output chromaticity signal components stored in the look-up table as lattice points in a three-dimensional output chromaticity signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output chromaticity signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output chromaticity signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output chromaticity signal component, in said local coordinate system in said three-dimensional output chromaticity signal space, (c5) approximating each of the values of i+diq i , j+djq j and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing a direction of the displacement di if q i is negative, reversing a direction the displacement dj if q j negative, and reversing a direction the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated original and an updated displacement have become respectively equal to the predecessor original and the predecessor displacement in said three-dimensional output chromaticity signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dk, k) and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 21

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three -dimensional input signal components, and a plurality of corresponding three -dimensional output optical density signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output optical density signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output optical density signal component, which is not stored in the look-up table, with an interpolating process using the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output optical density signal components, which are stored in the look-up table and which are close to the target output optical density signal component, said linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional output signal space, and designating the plurality of the three-dimensional output optical density signal components stored in the look-up table as lattice points in a three-dimensional output optical density signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output optical density signal space, (c3) originating said three linearly independent vectors from said original, thereby constructing a local coordinate system being in said three-dimensional output optical signal space, (c4) transforming a difference between the target output optical density signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output optical density signal space, (c5) updating said origin and said three linearly independent vectors by utilizing said local coordinates in said three-dimensional output optical density signal space, (c6) repeating steps (c3)-(c5) a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output optical density signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output optical density signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output optical density signal components.

Claim 22

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three -dimensional input signal components, and a plurality of corresponding three -dimensional output optical density signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output optical density signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output optical density signal component, which is not stored in the look-up table, with an interpolating process using the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output optical density signal components, which are stored in the look-up table and which are close to the target output optical density signal component, said linear interpolating process including (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional output signal space, and designating the plurality of the three-dimensional output optical density signal components stored in the look-up table as lattice points in a three-dimensional output optical density signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output optical density signal space, (c3) originating said three linearly independent vectors from said original, thereby constructing a local coordinate system being in said three-dimensional output optical signal space, (c4) transforming a difference between the target output optical density signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output optical density signal space, (c5) updating said origin and said three linearly independent vectors by utilizing said local coordinates in said three-dimensional output optical density signal space, (c6) repeating steps (c3)-(c5) a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output optical density signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output optical density signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output optical density signal components.

Claim 25

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components, which change in steps and which are fed into a color image output apparatus, and a plurality of corresponding three-dimensional output optical density signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output optical density signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating this three-dimensional input signal component corresponding to the target output optical density signal component which is not stored in the look-up table, with a linear interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output optical density signal components, which are stored in the look-up table and which are close to the target output optical density signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output optical density signal components stored in the look-up table as lattice points in a three-dimensional output optical density signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output optical density signal space, where each of i, j, and k represents a lattice point position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output optical density signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output optical density signal component, in said local coordinate system in said three-dimensional output optical density signal space, (c5) approximating each of the values of i+diq i , j+dj j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, a new k, respectively and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated original and an updated displacement have respectively equal a predecessor origin and a predecessor displacement in said three-dimensional output optical density signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j,k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 26

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components, which change in steps and which are fed into a color image output apparatus, and a plurality of corresponding three-dimensional output optical density signal components, each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output optical density signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating this three-dimensional input signal component corresponding to the target output optical density signal component which is not stored in the look-up table, with a linear interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output optical density signal components, which are stored in the look-up table and which are close to the target output optical density signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space, and designating the plurality of the three-dimensional output optical density signal components stored in the look-up table as lattice points in a three-dimensional output optical density signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output optical density signal space, where each of i, j, and k represents a lattice point position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output optical density signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k), and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output optical density signal component, in said local coordinate system in said three-dimensional output optical density signal space, (c5) approximating each of the values of i+diq i , j+dj j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, a new k, respectively and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated original and an updated displacement have respectively equal a predecessor origin and a predecessor displacement in said three-dimensional output optical density signal space, and (c8) interpolating a resultant input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j,k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 31

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output signal components, which describe colors and each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output signal component, which is not stored in the look-up table, with an interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output signal components, which are stored in the look-up table and which are close to the target output signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space and designating the plurality of the three-dimensional output signal components stored in the look-up table as lattice points a three-dimensional output signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output signal space, (c3) designating said three linearly independent vectors from said origin, thereby constructing a local coordinate system being in said three-dimensional output signal space, (c4) transforming a difference between the target output signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output signal space, (c5) updating said origin and said three vectors by utilizing said local coordinates in said three-dimensional output signal space, (c6) repeating steps (c3)-(c5) a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output signal components.

Claim 32

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output signal components, which describe colors and each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output signal component, which is not stored in the look-up table, with an interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output signal components, which are stored in the look-up table and which are close to the target output signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space and designating the plurality of the three-dimensional output signal components stored in the look-up table as lattice points a three-dimensional output signal space, (c2) setting a certain appropriate origin and three linearly independent vectors in said three-dimensional output signal space, (c3) designating said three linearly independent vectors from said origin, thereby constructing a local coordinate system being in said three-dimensional output signal space, (c4) transforming a difference between the target output signal component and said origin into local coordinates in said local coordinate system in said three-dimensional output signal space, (c5) updating said origin and said three vectors by utilizing said local coordinates in said three-dimensional output signal space, (c6) repeating steps (c3)-(c5) a plurality of times, thereby determining a new local coordinate system and new coordinates in said three-dimensional output signal space, and (c7) taking a point, which is in a local coordinate system in said three-dimensional input signal space, the local coordinate system corresponding to said new local coordinate system in said three-dimensional output signal space, and which is represented by said new coordinates, as a resultant three-dimensional input signal component, which corresponds to the target output signal components.

Claim 35

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output signal components, which describe colors and each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output signal component, which is not stored in the look-up table, with a linear interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output signal components, which are stored in the look-up table and which are close to the target output signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space and designating the plurality of the three-dimensional output signal components stored in the look-up table as lattice points in a three-dimensional output signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k) and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output signal component, in said local coordinate system in said three-dimensional output signal space, (c5) approximating each of the values of i+diq i , j+djq j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated origin and an updated displacement have become respectively equal to the predecessor origin and the predecessor displacement in said three-dimensional output signal space, and (c8) interpolating an input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.

Claim 36

A method for transforming a color signal, comprising the steps of: (a) creating a look-up table storing a plurality of three-dimensional input signal components and a plurality of corresponding three-dimensional output signal components, which describe colors and each of which is obtained with one of the three-dimensional input signal components; (b) transforming a target output signal component into a three-dimensional input signal component by referring to the look-up table; and (c) interpolating the three-dimensional input signal component corresponding to the target output signal component, which is not stored in the look-up table, with a linear interpolating process from the plurality of the three-dimensional input signal components corresponding to the plurality of the three-dimensional output signal components, which are stored in the look-up table and which are close to the target output signal component, said linear interpolating process including, (c1) designating the plurality of the three-dimensional input signal components stored in the look-up table as lattice points in a three-dimensional input signal space and designating the plurality of the three-dimensional output signal components stored in the look-up table as lattice points in a three-dimensional output signal space, (c2) setting an origin (i, j, k) and a displacement (di, dj, dk) in said three-dimensional output signal space, where each of i, j, and k represents the lattice point step position with respect to one of three-dimensional directions, wherein i, j, k=1, 2, 3, . . . , and di, dj, dk=1 or -1, (c3) constructing a local coordinate system in said three-dimensional output signal space by using a point (i, j, k), a point (i+di, j, k), a point (i, j+dj, k) and a point (i, j, k+dk), (c4) calculating a representation vector q=(q i , q j , q k ), which represents the target output signal component, in said local coordinate system in said three-dimensional output signal space, (c5) approximating each of the values of i+diq i , j+djq j , and k+dkq k to an integer, (c6) updating said origin (i, j, k) with respective integers from step (c5) equalling a new i, a new j, and a new k, and carrying out a displacement updating process such that, when a representation vector q is calculated by using said updated origin, reversing the displacement di if q i is negative, reversing the displacement dj if q j is negative, and reversing the displacement dk if q k is negative, (c7) repeating steps (c2)-(c6) until an updated origin and an updated displacement have become respectively equal to the predecessor origin and the predecessor displacement in said three-dimensional output signal space, and (c8) interpolating an input signal component point, which is represented by the representation vector q=(q i , q j , q k ), with a linear interpolating process from four points (i, j, k), (i+di, j, k), (i, j+dj, k), and (i, j, k+dk) in a local coordinate system, which is constituted by said four points in said three-dimensional input signal space.