synthesize_translation — MOTIONMAG `synthesis` op

• データ種: なし → video(引数だけで決まる op —— 画像やデータの入力を取らない)

• 呼び出し: 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' (または opsmotionmag.get("synthesize_translation"))

使い方

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.

詳しい使い方ガイド

• motion_magnification ファミリガイド

参考(サンプルデータ・文献)

• サンプルデータカタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• 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

型が繋がる次の op(`video` を入力に取れる)

temporal_bandpass · temporal_band_power · band_snr · motion_magnify · phase_displacement · displacement_series

同カテゴリ(`synthesis`)

—

*Provenance: motionmag.py — MOTIONMAG 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)。*

synthesize_translation — MOTIONMAG synthesis op

使い方