python - 使用最小二乘法进行颜色校正

Question

我尝试过使用最小二乘法对图像进行色彩校正。我不明白为什么它不起作用，这应该是颜色校准的标准方法。

首先，我以 CR3 格式提取上图，将其转换为 RGB 空间，然后使用 OpenCV boundingRect 和 inRange 函数裁剪出四个色 block ，将这四个色 block 保存在一个名为 coloursRect 的数组中。使用 vstack 以便存储每个像素颜色的数组从 3d 转换为 2d。因此，例如，colour0 存储“红色补丁”的每个像素的 RGB 值。

colour0 = np.vstack(coloursRect[0])
colour1 = np.vstack(coloursRect[1])
colour2 = np.vstack(coloursRect[2])
colour3 = np.vstack(coloursRect[3])

lstsq_a = np.array(np.vstack((colour0,colour1,colour2,colour3)))

然后我在 RGB 中声明原始引用颜色。

r_ref = [240,0,22]
y_ref = [252,222,10]
g_ref = [30,187,22]
b_ref = [26,0,165]
ref_patches = [r_ref,y_ref,g_ref, b_ref]

每个引用颜色的数量根据实际图像色 block 中的像素数量乘以，例如，r_ref 乘以 colour0 数组的长度。 (我知道这是一种糟糕的数据处理方式，但理论上应该可行)

lstsq_b_0to255 = np.array(np.vstack(([ref_patches[0]]*colour0.shape[0],[ref_patches[1]]*colour1.shape[0],[ref_patches[2]]*colour2.shape[0],[ref_patches[3]]*colour3.shape[0]))) 

计算最小二乘法，并与图像相乘。

lstsq_x_0to255 = np.linalg.lstsq(lstsq_a, lstsq_b_0to255)[0]


img_shape = img.shape
img_s = img.reshape((-1, 3))
img_corr_s = img_s @ lstsq_x_0to255
img_corr = img_corr_s.reshape(img_shape).astype('uint8')

但是这种颜色校正方法不起作用并且图像中的颜色不正确。我可以知道是什么问题吗？

编辑:使用 RGB 而不是 HSV 作为引用颜色

Answer 1

忽略图像 ICC 配置文件未在此处正确解码的事实，这是给定引用 RGB 值并使用 Colour 的预期结果:

import colour
import numpy as np


# Reference values a likely non-linear 8-bit sRGB values.
# "colour.cctf_decoding" uses the sRGB EOTF by default.
REFERENCE_RGB = colour.cctf_decoding(
    np.array(
        [
            [240, 0, 22],
            [252, 222, 10],
            [30, 187, 22],
            [26, 0, 165],
        ]
    )
    / 255
)

colour.plotting.plot_multi_colour_swatches(colour.cctf_encoding(REFERENCE_RGB))

IMAGE = colour.cctf_decoding(colour.read_image("/Users/kelsolaar/Downloads/EKcv1.jpeg"))

# Measured test values, the image is not properly decoded as it has a very specific ICC profile.
TEST_RGB = np.array(
    [
        [0.578, 0.0, 0.144],
        [0.895, 0.460, 0.0],
        [0.0, 0.183, 0.074],
        [0.067, 0.010, 0.070],
    ]
)

colour.plotting.plot_image(
    colour.cctf_encoding(colour.colour_correction(IMAGE, REFERENCE_RGB, TEST_RGB))
)

in this module可用的主要功能如下:

def least_square_mapping_MoorePenrose(y: ArrayLike, x: ArrayLike) -> NDArray:
    """
    Compute the *least-squares* mapping from dependent variable :math:`y` to
    independent variable :math:`x` using *Moore-Penrose* inverse.

    Parameters
    ----------
    y
        Dependent and already known :math:`y` variable.
    x
        Independent :math:`x` variable(s) values corresponding with :math:`y`
        variable.

    Returns
    -------
    :class:`numpy.ndarray`
        *Least-squares* mapping.

    References
    ----------
    :cite:`Finlayson2015`

    Examples
    --------
    >>> prng = np.random.RandomState(2)
    >>> y = prng.random_sample((24, 3))
    >>> x = y + (prng.random_sample((24, 3)) - 0.5) * 0.5
    >>> least_square_mapping_MoorePenrose(y, x)  # doctest: +ELLIPSIS
    array([[ 1.0526376...,  0.1378078..., -0.2276339...],
           [ 0.0739584...,  1.0293994..., -0.1060115...],
           [ 0.0572550..., -0.2052633...,  1.1015194...]])
    """

    y = np.atleast_2d(y)
    x = np.atleast_2d(x)

    return np.dot(np.transpose(x), np.linalg.pinv(np.transpose(y)))


def matrix_augmented_Cheung2004(
    RGB: ArrayLike,
    terms: Literal[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22] = 3,
) -> NDArray:
    """
    Perform polynomial expansion of given *RGB* colourspace array using
    *Cheung et al. (2004)* method.

    Parameters
    ----------
    RGB
        *RGB* colourspace array to expand.
    terms
        Number of terms of the expanded polynomial.

    Returns
    -------
    :class:`numpy.ndarray`
        Expanded *RGB* colourspace array.

    Notes
    -----
    -   This definition combines the augmented matrices given in
        :cite:`Cheung2004` and :cite:`Westland2004`.

    References
    ----------
    :cite:`Cheung2004`, :cite:`Westland2004`

    Examples
    --------
    >>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
    >>> matrix_augmented_Cheung2004(RGB, terms=5)  # doctest: +ELLIPSIS
    array([ 0.1722481...,  0.0917066...,  0.0641693...,  0.0010136...,  1...])
    """

    RGB = as_float_array(RGB)

    R, G, B = tsplit(RGB)
    tail = ones(R.shape)

    existing_terms = np.array([3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22])
    closest_terms = as_int(closest(existing_terms, terms))
    if closest_terms != terms:
        raise ValueError(
            f'"Cheung et al. (2004)" method does not define an augmented '
            f"matrix with {terms} terms, closest augmented matrix has "
            f"{closest_terms} terms!"
        )

    if terms == 3:
        return RGB
    elif terms == 5:
        return tstack(
            [
                R,
                G,
                B,
                R * G * B,
                tail,
            ]
        )
    elif terms == 7:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                tail,
            ]
        )
    elif terms == 8:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R * G * B,
                tail,
            ]
        )
    elif terms == 10:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                tail,
            ]
        )
    elif terms == 11:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                tail,
            ]
        )
    elif terms == 14:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**3,
                G**3,
                B**3,
                tail,
            ]
        )
    elif terms == 16:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**2 * G,
                G**2 * B,
                B**2 * R,
                R**3,
                G**3,
                B**3,
            ]
        )
    elif terms == 17:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**2 * G,
                G**2 * B,
                B**2 * R,
                R**3,
                G**3,
                B**3,
                tail,
            ]
        )
    elif terms == 19:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**2 * G,
                G**2 * B,
                B**2 * R,
                R**2 * B,
                G**2 * R,
                B**2 * G,
                R**3,
                G**3,
                B**3,
            ]
        )
    elif terms == 20:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**2 * G,
                G**2 * B,
                B**2 * R,
                R**2 * B,
                G**2 * R,
                B**2 * G,
                R**3,
                G**3,
                B**3,
                tail,
            ]
        )
    elif terms == 22:
        return tstack(
            [
                R,
                G,
                B,
                R * G,
                R * B,
                G * B,
                R**2,
                G**2,
                B**2,
                R * G * B,
                R**2 * G,
                G**2 * B,
                B**2 * R,
                R**2 * B,
                G**2 * R,
                B**2 * G,
                R**3,
                G**3,
                B**3,
                R**2 * G * B,
                R * G**2 * B,
                R * G * B**2,
            ]
        )


def matrix_colour_correction_Cheung2004(
    M_T: ArrayLike,
    M_R: ArrayLike,
    terms: Literal[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22] = 3,
) -> NDArray:
    """
    Compute a colour correction matrix from given :math:`M_T` colour array to
    :math:`M_R` colour array using *Cheung et al. (2004)* method.

    Parameters
    ----------
    M_T
        Test array :math:`M_T` to fit onto array :math:`M_R`.
    M_R
        Reference array the array :math:`M_T` will be colour fitted against.
    terms
        Number of terms of the expanded polynomial.

    Returns
    -------
    :class:`numpy.ndarray`
        Colour correction matrix.

    References
    ----------
    :cite:`Cheung2004`, :cite:`Westland2004`

    Examples
    --------
    >>> prng = np.random.RandomState(2)
    >>> M_T = prng.random_sample((24, 3))
    >>> M_R = M_T + (prng.random_sample((24, 3)) - 0.5) * 0.5
    >>> matrix_colour_correction_Cheung2004(M_T, M_R)  # doctest: +ELLIPSIS
    array([[ 1.0526376...,  0.1378078..., -0.2276339...],
           [ 0.0739584...,  1.0293994..., -0.1060115...],
           [ 0.0572550..., -0.2052633...,  1.1015194...]])
    """

    return least_square_mapping_MoorePenrose(
        matrix_augmented_Cheung2004(M_T, terms), M_R
    )


def colour_correction_Cheung2004(
    RGB: ArrayLike,
    M_T: ArrayLike,
    M_R: ArrayLike,
    terms: Literal[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22] = 3,
) -> NDArray:
    """
    Perform colour correction of given *RGB* colourspace array using the
    colour correction matrix from given :math:`M_T` colour array to
    :math:`M_R` colour array using *Cheung et al. (2004)* method.

    Parameters
    ----------
    RGB
        *RGB* colourspace array to colour correct.
    M_T
        Test array :math:`M_T` to fit onto array :math:`M_R`.
    M_R
        Reference array the array :math:`M_T` will be colour fitted against.
    terms
        Number of terms of the expanded polynomial.

    Returns
    -------
    :class:`numpy.ndarray`
        Colour corrected *RGB* colourspace array.

    References
    ----------
    :cite:`Cheung2004`, :cite:`Westland2004`

    Examples
    --------
    >>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
    >>> prng = np.random.RandomState(2)
    >>> M_T = prng.random_sample((24, 3))
    >>> M_R = M_T + (prng.random_sample((24, 3)) - 0.5) * 0.5
    >>> colour_correction_Cheung2004(RGB, M_T, M_R)  # doctest: +ELLIPSIS
    array([ 0.1793456...,  0.1003392...,  0.0617218...])
    """

    RGB = as_float_array(RGB)
    shape = RGB.shape

    RGB = np.reshape(RGB, (-1, 3))

    RGB_e = matrix_augmented_Cheung2004(RGB, terms)

    CCM = matrix_colour_correction_Cheung2004(M_T, M_R, terms)

    return np.reshape(np.transpose(np.dot(CCM, np.transpose(RGB_e))), shape)

我可能会推荐直接使用Colour，因为有多种方法可以根据训练集给出不同的结果。话虽这么说，但鉴于您实际上只有 4 种彩色且没有非彩色，我不会期待很好的结果。此类校准的最低推荐图表是具有 24 个色 block 的 ColorChecker Classic。