riesz opimage2d → qimageimport fullseye as fs; fs.ledger.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray' (実装を直接呼ぶなら import quatimage; quatimage.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray'、台帳から引くなら opsquat.get("monogenic_signal"))The monogenic signal of an image at one scale. → (H, W, 4).
Felsberg & Sommer (2001). The image is band-passed by a log-radial raised
cosine centred at 1/wavelength_px cycles/pixel with half-width
bandwidth_octaves, and the result is packed with its Riesz pair as the
quaternion (band-pass image, R1, R2, 0). From that single object
:func:monogenic_amplitude, :func:monogenic_phase and
:func:monogenic_orientation read the local contrast, the local phase and
the local orientation — the 2-D analogue of what |z| and arg z give
a 1-D analytic signal, with orientation as the extra degree of freedom that
only exists in 2-D.
The band-pass is applied before the Riesz kernels because the Riesz multiplier has a jump at DC: without a band that excludes DC the “local phase” of the image mean is undefined, not merely noisy.
A grating exactly at the band centre passes with gain 1, so for
contrast * cos(2*pi*(u0*x+v0*y) + p) the amplitude is contrast
everywhere, the phase is the grating’s own phase, and the orientation is
atan2(v0, u0) mod pi. Measured on a 64x64 frame with an 8 px grating of
unit contrast and phase 0.7: amplitude mean exactly 1.0 with a spread of
8.9e-16 across the frame, phase error 5.3e-15 rad, orientation error
0.0 rad.
Honest limit. The phase is well defined only where the amplitude is; in a
flat region the amplitude is at the rounding floor and the phase is the angle
of numerical dust. Nothing here suppresses that — the amplitude map is the
confidence map and it is returned in the same object, so a caller can mask on
it. The operators that consume the signal (:func:riesz_displacement,
:func:riesz_motion_magnify) do mask, with the same relative thresholds
:mod:motionmag uses, so their numbers are comparable.
Raises ValueError: image is not a finite real (H, W) array;
wavelength_px is not > 2 (a shorter wavelength is past Nyquist and the
band would be empty); bandwidth_octaves is not > 0; the band contains
no frequency bin of this frame size.
py -3.11 examples/quaternion_monogenic.pyqimage を入力に取れる)quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation
riesz)riesz_transform · monogenic_amplitude · monogenic_phase · monogenic_orientation
Provenance: quatimage.py — QUAT operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.