measure op• 資料種類:video → table
• 呼叫:import motionmag; motionmag.phase_displacement(video, f_lo, f_hi, fps, scales: 'int' = 4, orientations: 'int' = 4) -> 'dict'(或 opsmotionmag.get("phase_displacement"))
由局部相位得到的次像素位移場 -> `dict`。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The quantitative sibling of :func:motion_magnify: nothing is amplified and
nothing is re-rendered, the displacement itself is returned in pixels.
For each oriented sub-band, the temporal phase deviation `dphi(t)` (taken
against the band's temporal mean as the wrapped angle in `(-pi, pi]` —
never unwrapped in time, for the reason given in the design note above
`_AMP_FLOOR` — then band-passed) obeys
`dphi = -(kx*dx + ky*dy), where (kx, ky)` is the band's local
spatial frequency in radians per pixel — computed exactly as
`Im(conj(z) grad z)/|z|^2` with a spectral derivative, not from the band's
nominal centre. Each band contributes one linear constraint on the same
two unknowns, so the bands are combined per pixel by weighted least squares
with weights `|z|^2` (a band with no contrast gets no vote).
Returns ``{"dx": (T, H, W), "dy": (T, H, W), "weight": (H, W),
"valid": (H, W) bool, "rank": (H, W) int8, "fps": ..., "band_hz": ...,
"wrap_limit_px": ..., "reference_coherence": ...}`. dx/dy` follow
:mod:flow: `dx is column motion, dy` row motion, positive towards
increasing index, and both are zero-mean along time because the band-pass
removed DC.
`rank` says how much of the 2-D displacement the data could constrain at
each pixel: 2 = both components, 1 = the aperture problem (every band
with contrast there shares one orientation, so only the component along it
is observable — that component is returned and the unobservable direction is
exactly 0), 0 = no contrast at all, both zero. Measured on a purely
horizontal grating moving 0.3 px horizontally, every pixel is rank 1 and the
answer is `dx = 0.3000000000000001, dy = 0.0` exactly.
Accuracy and where it stops (measured, 64x64x64 clip at 32 fps, 8 px
horizontal grating, 4 Hz bin-centred, noiseless, defaults; the error is on
the peak of the recovered waveform):
============== ============== ============== ===================
true d (px) k*d (rad) measured (px) relative error
============== ============== ============== ===================
0.001 0.0008 0.00100000 8.7e-15
0.010 0.0079 0.01000000 3.1e-15
0.100 0.0785 0.10000000 1.8e-15
0.500 0.3927 0.50000000 6.7e-16
1.000 0.7854 1.00000000 4.4e-16
2.000 1.5708 2.00000000 6.7e-16
3.000 2.3562 3.00000000 5.9e-16
3.050 2.3954 3.05000000 2.9e-16
3.100 2.4347 1.72842712 4.4e-01 <- broken
4.000 3.1416 2.10461396 4.7e-01 <- broken
6.000 4.7124 2.35441757 6.1e-01 <- broken
============== ============== ============== ===================
Exact to rounding — and then it stops, abruptly, between 3.05 and 3.10 px.
That boundary is closed-form, and it is *not* the naive phase-wrap bound.
The temporal phase reference is the band's temporal mean `z_mean`, and for
a sinusoidal displacement of amplitude `A` that mean equals
`c * J0(k*A) — a Bessel function. At k*A = 2.4048`, the first zero of
`J0`, the reference amplitude passes through zero and its phase flips by
`pi; every deviation measured against it is then wrong by pi`. For the
8 px grating that is `A = 2.4048/(2*pi/8) = 3.0619` px, which is exactly
where the table breaks. `reference_coherence` in the return is
`|z_mean| / mean_t|z|, i.e. |J0(k*A)|` blended over the bands, and it
falls monotonically from 1.00000 at 0.001 px to 0.50252 at the 3.05 px edge
— a runtime warning that the reference is going degenerate.
Beyond that sits the harder bound `|k*d| < pi` (half a band wavelength,
reported as `wrap_limit_px` from the measured local frequencies), which no
phase-based method can pass with a single band.
Under noise the accuracy is set by the noise, not by the method: on the same
clip with `A = 0.5` px, additive sigma = 0.001 / 0.01 / 0.05 gives
relative errors 2.2e-04 / 1.8e-03 / 1.9e-03.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者・年份)與用途見上面的族使用指南。
• 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
table 作為輸入)measure)*Provenance: motionmag.py — MOTIONMAG 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.