monogenic_signal — QUAT `riesz` op

• 데이터 종류: image2d → qimage

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

사용법

어느 스케일에서의 이미지의 모노제닉 신호. → (H, W, 4).

> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.

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.

자세한 사용 가이드

• quaternion_monogenic 패밀리 가이드

참고(샘플 데이터·문헌)

• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.

• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.

• 알고리즘의 정전(저자·연도)과 용도는 위의 패밀리 사용 가이드에 적혀 있습니다.

실행 가능한 예제(이 연산자를 실제로 호출하는 검증된 샘플)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

타입이 이어지는 다음 연산자(`qimage` 를 입력으로 받는 것)

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

같은 카테고리(`riesz`)

riesz_transform · monogenic_amplitude · monogenic_phase · monogenic_orientation

*Provenance: quatimage.py — QUAT 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*

monogenic_signal — QUAT riesz op

사용법