watermark::SpectralWatermark Class

Detailed Description

The class comment in the header gives the five steps. This file keeps the reasons for the choices, because each one was measured against the testWatermark distortions on the 1538-vertex test cube:

- A vertex graph is only stable if the welder rejoins cracked corners. The per-corner noise of the test (0.5 % of the diagonal, 14 % of an edge per coordinate) plus the per-corner moves of the vertex displacement layer split vertices apart. A weld with about ten wrong vertices in 1538 scrambles the coefficients: the median coefficient error went from 0.004 to 0.05 scale units, ten times the noise. The welder below gives the exact topology for 40 of 40 noise seeds at 0.4 %, 38 of 40 at 0.5 %, 26 of 40 at 0.55 % and none at 0.6 %. - Rotation invariance needs a frame, and the cube defeats a PCA frame (its inertia is isotropic). The polar factor of the coefficients of eigenvectors 1-3 does not: they are large (about 14 for the cube) and far apart, so noise turns the frame by about 2.5e-4 rad. - Blind detection needs no estimate of the host, so this uses dither modulation (QIM) and not additive spread spectrum. The old code correlated coefficient magnitudes with a ±1 sequence; the host magnitudes swamp that sum, so it could never decode.