riesz op• Data kinds: image2d → qimage
• Call: import fullseye as fs; fs.ledger.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray' (to call the implementation directly, import quatimage; quatimage.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray'; from the registry, 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 monogenic_amplitude, monogenic_phase and 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 (riesz_displacement, riesz_motion_magnify) do mask, with the same relative thresholds 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.
• quaternion_monogenic family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
qimage as input)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. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.