synthesis op• Data kinds: none → video (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.synthesize_translation(shape=(64, 64), frames: 'int' = 32, amplitude_px=0.5, frequency_hz=4.0, fps=32.0, direction_deg=0.0, wavelength_px=(8.0, 16.0), contrast=0.4, offset=0.5, noise_sigma=0.0, seed: 'int' = 0) -> 'np.ndarray' (to call the implementation directly, import motionmag; motionmag.synthesize_translation(shape=(64, 64), frames: 'int' = 32, amplitude_px=0.5, frequency_hz=4.0, fps=32.0, direction_deg=0.0, wavelength_px=(8.0, 16.0), contrast=0.4, offset=0.5, noise_sigma=0.0, seed: 'int' = 0) -> 'np.ndarray'; from the registry, opsmotionmag.get("synthesize_translation"))
A clip whose displacement is known in closed form -> (T, H, W) video.
The scene is a stationary two-axis sinusoidal grating that is translated, frame by frame, by
d(t) = amplitude_px * sin(2*pi * frequency_hz * t / fps)
along *direction_deg* (0 deg = towards +x / increasing column). The translation is applied as a Fourier phase ramp, which for a pattern that is periodic on the grid is the *exact* band-limited shift — no interpolation kernel, no resampling error, so d(t) is ground truth to machine precision and sub-pixel amplitudes are meaningful.
wavelength_px is either one number (both axes) or (lambda_x, lambda_y). The default deliberately makes the two axes different octaves, and that is not cosmetic: if the horizontal and vertical gratings share a radial frequency they land in the *same* sub-band, whose local phase is then the phase of a sum of two moving components rather than of one. The phase of a sum is not linear in the displacement, so scaling it does not scale the motion — measured, a 64x64 clip built with a single wavelength on both axes magnified at alpha = 2 came out at 0.939 * (2 d) instead of 2 d, a 6.1 % error that does *not* shrink as d shrinks. Separating the octaves puts one component in each band and the relation becomes exact. This is the standard narrow-band condition of phase-based processing, made visible in the synthetic instead of hidden.
Each wavelength is snapped so that a whole number of cycles fits the frame (cycles = max(1, round(W / wavelength_px)), effective wavelength W / cycles); without that the pattern is not periodic on the grid and the Fourier shift would wrap a discontinuity across the border. With the default 64x64 frame and (8, 16) the snap is exact (8 and 4 cycles).
Values are not clipped into [0, 1]: clipping is a nonlinearity that would break the exact translation this function exists to provide. With the defaults the samples lie in [offset - contrast, offset + contrast].
*noise_sigma* adds zero-mean Gaussian sensor noise (after translation, drawn from numpy.random.default_rng(seed)) — the term that makes an SNR measurable at all.
This is the counterpart of photoncount.tcspc_simulate: a forward model good enough to close the loop on the analysis operators in this module.
• motion_magnification 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.
• motion_magnification — py -3.11 examples/motion_magnification.py
• poc_motion_magnification — py -3.11 examples/poc_motion_magnification.py
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
video as input)temporal_bandpass · temporal_band_power · band_snr · motion_magnify · phase_displacement · displacement_series
synthesis)—
*Provenance: motionmag.py — MOTIONMAG 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.