motion op• Datenarten: video → table
• Aufruf: import quatimage; quatimage.riesz_motion_magnify(video, alpha, f_lo, f_hi, fps, scales: 'int' = 4) -> 'dict' (oder opsquat.get("riesz_motion_magnify"))
Skaliert die Bewegung eines Clips im Band um *alpha* auf dem Riesz-Weg. → dict.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
The Riesz-pyramid magnifier of Wadhwa et al. (2014), and the direct
counterpart of `motionmag.motion_magnify: same contract, same alpha`
convention (a displacement gain — 1 is the identity, 2 doubles the
motion, -1 reverses it), same honesty block, different decomposition.
Each radial sub-band is turned into a monogenic signal, projected onto the
band's temporal-mean orientation to give a complex analytic signal `z`, and
the temporal phase deviation `angle(z * conj(z_mean))` is band-passed and
multiplied by `alpha - 1`. The band is then re-rendered as
`I*cos(shift) - R_proj*sin(shift) — the real part of z * exp(i*shift)`
— and the bands are summed. Because the radial filters are an *amplitude*
partition of unity, that sum is the reconstruction: at `alpha = 1` the
output equals the input to 5.55e-16 (measured on a 64x64x64 clip;
`motionmag.motion_magnify` gives 7.77e-16 on the same clip).
The gain really is the gain. Measuring the magnified clip's displacement with
the *independent* steerable estimator `motionmag.displacement_series`, on a
single-grating clip of true amplitude 0.1 px:
======== ========================== ==========================
alpha Riesz measured gain steerable measured gain
======== ========================== ==========================
0.0 0.000000000000 0.000000000000
2.0 2.000000000000 2.000000000000
4.0 4.000000000000 4.000000000000
-1.0 -1.000000000000 -1.000000000000
20.0 20.000000000000 20.000000000000
======== ========================== ==========================
— twelve decimal places, for both, including the reversal.
Returns the same shape of dict `motionmag.motion_magnify` returns —
``{"video", "alpha", "band_hz", "fps", "scales", "snr_in", "snr_out",
"image_snr_change_db", "motion_snr_out_db", "motion_snr_change_db",
"band_power_ratio", "phase_shift_max_rad", "phase_shift_rms_rad",
"linear_regime", "reference_coherence"}`` — and it is the same dict because
the SNR block is computed by calling `motionmag.band_snr` rather than
re-deriving it. Two magnifiers that disagree about how to measure their own
cost cannot be compared, so they share the measurement.
Magnification never improves the motion SNR, here as there: scaling the
in-band phase scales the in-band noise by the same factor. What degrades is
the image SNR. Measured on the shared 64x64x64 / 32 fps / 0.2 px / 4 Hz
synthetic under sigma = 0.01 noise, band 3-5 Hz, against
`motionmag.motion_magnify` on the identical clip:
====== ================== ================== ============== ==============
alpha image change (dB) image change (dB) band ratio band ratio
Riesz steerable Riesz steerable
====== ================== ================== ============== ==============
2 -4.8611 -4.8260 0.937704 0.935433
4 -10.3616 -10.3504 0.861162 0.858130
8 -15.3515 -15.5097 0.629948 0.628597
====== ================== ================== ============== ==============
The two magnifiers cost essentially the same — within 0.16 dB and 0.3 % of
band-power linearity at every gain. So the choice between them is not
about magnification quality; it is about the displacement measurement (where
the Riesz route has a 13 % failure mode on multi-orientation texture, see
:func:riesz_displacement) and about cost (this one is 2.09x faster on the
same clip: 0.1034 s against 0.2163 s, best of 7).
Raises `ValueError: *video* is not a valid (T, H, W)` clip or is
over :data:MAX_PYRAMID_ELEMENTS; `|alpha| is over :data:MAX_ALPHA`;
the pass-band is empty, reaches DC, or exceeds Nyquist; *scales* is outside
`[1, MAX_SCALES]`.
• Leitfaden zur Familie quaternion_monogenic
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
table als Eingabe)—
motion)riesz_displacement · riesz_displacement_series
*Provenance: quatimage.py — QUAT Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.