高光谱图像重构常用评价指标及其Python实现

高光谱图像重构评价指标及其Python实现

高光谱图像重构的评价指标通常有三项。其中部分指标从普通图像变化而来，部分指标只有高光谱图像独有。本文拟从以下两个角度介绍高光谱图像评价指标，并列出基于Python语言的skimage库的对应实现方法。

1）从普通图像重构评价指标到高光谱图像重构评价指标

2）从普通图像重构评价指标代码到高光谱图像重构评价指标代码

一、MSE

MSE计算两组数据的均方误差，是最常用的评价相似度的准则，包括但不限于图像、信号。

Skimage库中对应的函数原型：

skimage.measure.compare_mse(im1, im2)

Parameters:	im1, im2 : ndarray Image. Any dimensionality.
Returns:	mse : float The mean-squared error (MSE) metric.

想要测度其他距离，参考compare_nrmse函数

http://scikit-image.org/docs/stable/api/skimage.measure.html#compare-nrmse

二、PSNR与MPSNR

1. PSNR

PSNR全称是Compute the peak signal to noise ratio。用于计算原始图像与重构图像之间的峰值信噪比。在图像超分辨率等任务中尤为常用，如同错误率之于分类任务，PSNR是图像重构任务事实上的基准评价准则。

skimage.measure.compare_psnr(im_true, im_test, data_range=None, dynamic_range =None )

Parameters:	im_true : ndarray Ground-truth image. im_test : ndarray Test image. data_range : int The data range of the input image (distance between minimum and maximum possible values). By default, this is estimated from the image data-type.
Returns:	psnr : float The PSNR metric.

2. MPSNR

MPSNR用于计算两幅高光谱图像之间的平均峰值信噪比。MPSNR计算方法很简单，只需要分别计算不同波段的PSNR，取均值就可以了。

def mpsnr(x_true, x_pred):
    """

    :param x_true: 高光谱图像：格式：(H, W, C)
    :param x_pred: 高光谱图像：格式：(H, W, C)
    :return: 计算原始高光谱数据与重构高光谱数据的均方误差
    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
    """
    n_bands = x_true.shape[2]
    p = [compare_psnr(x_true[:, :, k], x_pred[:, :, k], dynamic_range=np.max(x_true[:, :, k])) for k in range(n_bands)]
    return np.mean(p)

三、SSIM与MSSIM

1. SSIM用于计算两幅图像之间的平均结构相似度。

skimage.measure.compare_ssim(X, Y, win_size=None, gradient=False, data_range=None, multichannel=False, gaussian_weights=False, full=False, dynamic_range=None, **kwargs)

Parameters:	X, Y : ndarray Image. Any dimensionality. win_size : int or None The side-length of the sliding window used in comparison. Must be an odd value. If gaussian_weights is True, this is ignored and the window size will depend on sigma. gradient : bool, optional If True, also return the gradient. data_range : int, optional The data range of the input image (distance between minimum and maximum possible values). By default, this is estimated from the image data-type. multichannel : bool, optional If True, treat the last dimension of the array as channels. Similarity calculations are done independently for each channel then averaged. gaussian_weights : bool, optional If True, each patch has its mean and variance spatially weighted by a normalized Gaussian kernel of width sigma=1.5. full : bool, optional If True, return the full structural similarity image instead of the mean value.
Returns:	mssim : float The mean structural similarity over the image. grad : ndarray The gradient of the structural similarity index between X and Y [R327]. This is only returned if gradient is set to True. S : ndarray The full SSIM image. This is only returned if full is set to True.
Other Parameters:
	use_sample_covariance : bool if True, normalize covariances by N-1 rather than, N where N is the number of pixels within the sliding window. K1 : float algorithm parameter, K1 (small constant, see [R326]) K2 : float algorithm parameter, K2 (small constant, see [R326]) sigma : float sigma for the Gaussian when gaussian_weights is True.

2. MSSIM

MSSIM用于计算两幅高光谱图像之间的平均结构相似度。MSSIM计算方法很简单，只需要分别计算不同波段的SSIM指数，取均值就可以了。

def mssim(x_true,x_pred):
    """
        :param x_true: 高光谱图像：格式：(H, W, C)
        :param x_pred: 高光谱图像：格式：(H, W, C)
        :return: 计算原始高光谱数据与重构高光谱数据的结构相似度
    """
    SSIM = compare_ssim(X=x_true, Y=x_pred, multichannel=True)
    return SSIM

四、SAM

SAM这个概念只存在于多/高光谱图像，普通图像没有这个概念。SAM又称光谱角相似度，用于度量原始高光谱数据与重构高光谱数据之间的光谱相似度。

def sam(x_true, x_pred):
    """
    :param x_true: 高光谱图像：格式：(H, W, C)
    :param x_pred: 高光谱图像：格式：(H, W, C)
    :return: 计算原始高光谱数据与重构高光谱数据的光谱角相似度
    """
    assert x_true.ndim ==3 and x_true.shape == x_pred.shape
    sam_rad = np.zeros(x_pred.shape[0, 1])
    for x in range(x_true.shape[0]):
        for y in range(x_true.shape[1]):
            tmp_pred = x_pred[x, y].ravel()
            tmp_true = x_true[x, y].ravel()
            sam_rad[x, y] = np.arccos(tmp_pred / (norm(tmp_pred) * tmp_true / norm(tmp_true)))
    sam_deg = sam_rad.mean() * 180 / np.pi
    return sam_deg

五、相关资料

0. 文中用到的代码

https://github.com/JiJingYu/tensorflow-exercise/tree/master/HSI_evaluate

1. 文中提到的函数的文档

http://scikit-image.org/docs/stable/api/skimage.measure.html#compare-mse

2. PSNR维基百科链接

https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio

3. SSIM参考文献

[R326] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13, 600-612. https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf , DOI:10.1.1.11.2477

[R327] Avanaki, A. N. (2009). Exact global histogram specification optimized for structural similarity. Optical Review, 16, 613-621. http://arxiv.org/abs/0901.0065 , DOI:10.1007/s10043-009-0119-z