Closed form non-iterative watermark embedding

An apparatus comprising:

• memory for storing data representing imagery;
• one or more electronic processors configured for:
• transforming the data representing imagery into a Lab color space;
• determining a visibility change for local image areas attributable to adding a color channel encoded signal, the determining a visibility change utilizing a luminance and a color contrast sensitivity functions associated with the transformed data in the Lab color space, in which the determining a visibility change yields a determined visibility change, in which the determining a visibility change utilizes an ellipsoid model of the Lab space, the ellipsoid model comprising a larger radius in the a-b plane relative to a radius in the L plane;
• generating luminance (L), a channel (a), and b channel (b) embedding weights to minimize the determined visibility change, in which the generating (L), (a), and (b) embedding weights yields (L), (a), and (b) generated embedding weights, in which embedding weights for the a channel and the b channel are generated with an approximation of an intersection of a line through the ellipsoid model origin and an ellipse in the a-b plane;
• and
• altering the data representing imagery with the (L), (a), and (b) generated embedding weights in an embedding color space, the (L), (a), and (b) generated embedding weights collectively conveying the encoded signal within the imagery, the altering yielding altered imagery comprising the encoded signal.

A non-transitory computer readable medium on which is stored instructions, which when executed by one or more electronic processors, perform a method comprising:

• obtaining data representing imagery;
• transforming the data representing imagery into a Lab color space;
• determining a visibility change for local image areas attributable to adding a color channel encoded signal, said determining a visibility change utilizing a luminance and a color contrast sensitivity function associated with the transformed data in the Lab color space, in which said determining a visibility change yields a determined visibility change in which the determining utilizes an ellipsoid model of the Lab space, the ellipsoid model comprising a larger radius in the a-b plane relative to a radius in the L plane;
• determining luminance (L), a channel (a), and b channel (b) embedding weights to minimize the determined visibility change, in which said determining (L), (a), and (b) embedding weights yields (L), (a), and (b) determined embedding weights, in which embedding weights for the a channel and the b channel are determined with an approximation of an intersection of a line through the ellipsoid model origin and an ellipse in the a-b plane;
• and
• applying the (L), (a), and (b) determined embedding weights per pixel in an embedding color space, the (L), (a), and (b) determined embedding weights collectively conveying the encoded signal within the imagery, said applying yielding altered imagery comprising the encoded signal.