monogenic_signal — QUAT `riesz` op

• データ種: image2d → qimage

• 呼び出し: import quatimage; quatimage.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray' (または opsquat.get("monogenic_signal"))

使い方

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

:func:monogenic_amplitude, :func:monogenic_phase and

:func: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.

Closed form

-----------

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 (:func:riesz_displacement,

:func:riesz_motion_magnify) do mask, with the same relative thresholds

:mod: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.

詳しい使い方ガイド

• quaternion_monogenic 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)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

型が繋がる次の op(`qimage` を入力に取れる)

quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation

同カテゴリ(`riesz`)

riesz_transform · monogenic_amplitude · monogenic_phase · monogenic_orientation

*Provenance: quatimage.py — QUAT 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)。*

monogenic_signal — QUAT riesz op

使い方