color op• 資料種類:qimage → qimage
• 呼叫: import fullseye as fs; fs.ledger.quat_color_rotate(qimage, axis_rgb, angle_rad) -> 'np.ndarray'(要直接呼叫實作,import quatimage; quatimage.quat_color_rotate(qimage, axis_rgb, angle_rad) -> 'np.ndarray';從台帳取用則 opsquat.get("quat_color_rotate"))
把每個像素的顏色繞 RGB 軸旋轉:q x conj(q)。→ (H, W, 4)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The operation a complex pixel cannot express. axis_rgb is a direction in RGB space and angle_rad the rotation about it; the rotor q = cos(a/2) + sin(a/2) * axis is built with pose_quat.axis_angle_to_quat and the conjugation is applied to the vector part of every pixel, leaving the scalar part untouched (a conjugation cannot move it).
The conjugation is applied through the 3x3 matrix from pose_quat.quat_to_hom_mat3d rather than by two per-pixel Hamilton products, because for a (512, 512) image that is 500k quaternion multiplications versus one einsum. The two are the *same map*, measured:
against per-pixel pose_quat.quat_rotate_point_3d the agreement is 4.44e-16, the round trip rotate(rotate(q, ax, a), ax, -a) returns q to 2.22e-16, and the colour magnitude is preserved to 2.22e-16.
The matrix identity is also the honest limit of the *capability* claim. SO(3) and the unit quaternions are isomorphic, so a 3x3 orthogonal colour matrix does exactly this and nothing is lost by using one — measured against an explicit Rz(30 deg), the agreement is 2.22e-16. What a quaternion buys is 4 numbers instead of 9, exact closure under composition, and slerp. Measured over 100,000 random small rotations composed in sequence, the quaternion (renormalised each step, 4 divisions) drifts from unit norm by 0.0 while the matrix (composed by multiplication, not re-orthonormalised) drifts to |R^T R - I| = 4.33e-14.
That advantage is real but it is nearly nothing, and an earlier revision of this file oversold it by four orders of magnitude. The same measurement then read 4.4e-10 for the matrix, which looked like a decisive argument for quaternions. It was not an argument about quaternions at all: it was the pose_quat defect described below, feeding a slightly non-orthogonal matrix into every one of the 100,000 steps. With that fixed the honest figure is 4.33e-14, i.e. ordinary rounding over 100k products. The lesson is the repository's own: a number that flatters the thing you are building is the one to re-measure first.
What a *channelwise* pipeline — three independent scalar filters, which is what running the complex ops on R, G and B separately means — cannot do is this operation at all: it never mixes channels, so it cannot turn red towards green. Pure red rotated 90 degrees about the blue axis comes back as (-2.2e-16, 1.0, 0.0); no per-channel gain can put anything in the green channel, because it starts at zero. That is the comparison in tests/test_quatimage.py, and it is the one that is decisive.
pose_quat used to normalise as n / (norm + 1e-12). A zero axis then returned [cos(a/2), 0, 0, 0], which quat_to_hom_mat3d re-normalised to the identity: a rotation request silently became a no-op. Worse, at angle_rad = pi that same path produced [0, 0, 0, 0], whose normalisation was 0/(0+1e-12) = 0 and whose matrix was again the identity — a *180-degree* colour rotation silently becoming a copy. Both were reported and have since been fixed in pose_quat itself (zero length now raises; axis_angle_to_quat(0, 0, 1, pi) now returns exactly [0, 0, 0, 1] with norm 1, where it used to return norm 0.9999999999990).
This operator nevertheless keeps both of its own guards — _require_direction on the axis, and an explicit unit-norm assertion on the finished rotor (tolerance _UNIT_TOL). A check that only holds while a dependency behaves is not a check, and the caller of this module should get this module's error message. A genuine pi rotation still works:
pure red about the blue axis gives (-1.0, 1.2e-16, 0.0).
Raises ValueError: *qimage* is not a valid (H, W, 4) field; *axis_rgb* is not a finite non-zero 3-vector; *angle_rad* is not a finite real scalar; the constructed rotor is not unit norm.
• 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。
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
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
color)*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)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.