monogenic_signal — QUAT `riesz` op

• 資料種類:image2d → qimage

• 呼叫:import quatimage; quatimage.monogenic_signal(image, wavelength_px=8.0, bandwidth_octaves=1.0) -> 'np.ndarray'(或 opsquat.get("monogenic_signal"))

用法

某一尺度下影像的單演訊號。→ (H, W, 4)。

> 以下的詳細說明為原文 —— 摘要與標題已翻譯。

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.

詳細使用指南

• quaternion_monogenic 族使用指南

參考(範例資料・文獻)

• 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。

可執行的範例(實際呼叫該運算子並已驗證的樣例)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

型別可銜接的下一個運算子(可接受 `qimage` 作為輸入)

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

同類別(`riesz`)

riesz_transform · monogenic_amplitude · monogenic_phase · monogenic_orientation

*Provenance: quatimage.py — QUAT 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*

monogenic_signal — QUAT riesz op

用法