Two-dimensional Hilbert transforms

Two-dimensional Hilbert Transforms'

Two-dimensional transforms for device color calibration

Color device calibration is traditionally performed using one-dimensional per-channel tone-response corrections (TRCs). While one-dimensional TRCs are attractive in view of their low implementation complexity and efficient real-time processing of color images, their use severely restricts the degree of control that can be exercised along various device axes. A typical example is that 1-D TRCs i...

Camera Color Correction Using Two-Dimensional Transforms

For digital camera systems, transforming from the native camera RGB signals into an intermediate working space is often required, with common examples involving transformations into XYZ or the sRGB. For scene-linear camera signals, by far the most common approach utilizes 3x3 matrices. For color pipelines designed for Rec709 displays, matrix-based input transforms are capable of producing reaso...

Two-dimensional block transforms and their properties

For two-dimensional (2-D) digital filters implemented by a block recursive equation, explicit relations between their frequency characteristics and those of scalar filter are obtained. Specifically, these include the relation between the discrete-time Fourier transform (DTFT) of the block recursive equation and that of the scalar 2-D difference equation, and the relation between the block matri...

On the Two Dimensional Bilinear Hilbert Transform

We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.