fullseye

monogenic_signal — QUAT riesz op

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

参考(サンプルデータ・文献)

実行できる例(この op を実際に呼ぶ検証済みサンプル)

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)。

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.