AIGC-常见图像质量评估MSE、PSNR、SSIM、LPIPS、FID、CSFD，余弦相似度----理论＋代码

持续更新和补充中…多多交流！

参考:
图像评价指标PNSR和SSIM
函数 structural_similarity
图片相似度计算方法总结

MSE和PSNR

MSE:

M S E = 1 m n ∑ i = 0 m − 1 ∑ j = 0 n − 1 [ I ( i , j ) − K ( i , j ) ] 2 MSE=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[I(i,j)-K(i,j)]^2 MSE=mn1​i=0∑m−1​j=0∑n−1​[I(i,j)−K(i,j)]2

import torch

def calculate_mse(original_img, enhanced_img):
    # 将图像转换为 PyTorch 的 Tensor
    original_img_tensor = torch.tensor(original_img, dtype=torch.float32)
    enhanced_img_tensor = torch.tensor(enhanced_img, dtype=torch.float32)
    
    # 计算像素值之差的平方
    diff = original_img_tensor - enhanced_img_tensor
    squared_diff = torch.square(diff)
    
    # 计算均方误差
    mse = torch.mean(squared_diff)
    
    return mse.item()  # 返回均方误差的值

# 示例用法
original_img = [0.1, 0.2, 0.3, 0.4]  # 原始图像像素值
enhanced_img = [0.15, 0.25, 0.35, 0.45]  # 处理后图像像素值

mse_value = calculate_mse(original_img, enhanced_img)
print("MSE 值为:", mse_value)

PSNR基于MSE进行计算:

P S N R = 10 ⋅ l o g 10 ( M A X I 2 M S E ) \begin{aligned} PSNR=10\cdot log_{10}(\frac{MAX_{I}^{2}}{MSE}) \end{aligned} PSNR=10⋅log10​(MSEMAXI2​​)​

import numpy as np

def calculate_mse(original_img, enhanced_img):
    mse = np.mean((original_img - enhanced_img) ** 2)
    return mse

MAX = 255  # 最大灰度级
original_img = np.array([[1, 2, 3], [4, 5, 6]])  # 原始图像
enhanced_img = np.array([[3, 4, 5], [6, 7, 8]])  # 处理后的图像

mse = calculate_mse(original_img, enhanced_img)
psnr = 10 * np.log10(MAX**2 / mse)
print("MSE:", mse)
print("PSNR:", psnr)

SSIM-结构相似性

SSIM（structural similarity）结构相似性，也是一种全参考的图像质量评价指标，它分别从亮度、对比度、结构三方面度量图像相似性。
S S I M ( x , y ) = [ l ( x , y ) α ⋅ c ( x , y ) β ⋅ s ( x , y ) γ ] SSIM(x,y)=[l(x,y)^\alpha\cdot c(x,y)^\beta\cdot s(x,y)^\gamma] SSIM(x,y)=[l(x,y)α⋅c(x,y)β⋅s(x,y)γ]

l ( x , y ) = 2 μ x μ y + C 1 μ x 2 + μ y 2 + C 1 l(x, y) = \frac{2\mu_x\mu_y + C_1}{\mu_x^2 + \mu_y^2 + C_1} l(x,y)=μx2​+μy2​+C1​2μx​μy​+C1​​是亮度相似度，

c ( x , y ) = 2 σ x σ y + C 2 σ x 2 + σ y 2 + C 2 c(x, y) = \frac{2\sigma_x\sigma_y + C_2}{\sigma_x^2 + \sigma_y^2 + C_2} c(x,y)=σx2​+σy2​+C2​2σx​σy​+C2​​是对比度相似度

s ( x , y ) = σ x y + C 3 σ x σ y + C 3 s(x, y) = \frac{\sigma_{xy} + C_3}{\sigma_x\sigma_y + C_3} s(x,y)=σx​σy​+C3​σxy​+C3​​是结构相似度，

公式中的 α ， β ， γ \alpha， \beta， \gamma α，β，γ是权重参数，用于控制每个相似度项的影响力。通常情况下，它们的值是 α = β = γ = 1 \alpha = \beta = \gamma = 1 α=β=γ=1。

代码: https://github.com/jorge-pessoa/pytorch-msssim

#针对?，?，?都为1的情况
import torch
import torch.nn.functional as F
from math import exp
import numpy as np
 
 
# 计算一维的高斯分布向量
def gaussian(window_size, sigma):
    gauss = torch.Tensor([exp(-(x - window_size//2)**2/float(2*sigma**2)) for x in range(window_size)])
    return gauss/gauss.sum()
 
 
# 创建高斯核，通过两个一维高斯分布向量进行矩阵乘法得到
# 可以设定channel参数拓展为3通道
def create_window(window_size, channel=1):
    _1D_window = gaussian(window_size, 1.5).unsqueeze(1)
    _2D_window = _1D_window.mm(_1D_window.t()).float().unsqueeze(0).unsqueeze(0)
    window = _2D_window.expand(channel, 1, window_size, window_size).contiguous()
    return window
 
 
# 计算SSIM
# 直接使用SSIM的公式，但是在计算均值时，不是直接求像素平均值，而是采用归一化的高斯核卷积来代替。
# 在计算方差和协方差时用到了公式Var(X)=E[X^2]-E[X]^2, cov(X,Y)=E[XY]-E[X]E[Y].
# 正如前面提到的，上面求期望的操作采用高斯核卷积代替。
def ssim(img1, img2, window_size=11, window=None, size_average=True, full=False, val_range=None):
    # Value range can be different from 255. Other common ranges are 1 (sigmoid) and 2 (tanh).
    if val_range is None:
        if torch.max(img1) > 128:
            max_val = 255
        else:
            max_val = 1
 
        if torch.min(img1) < -0.5:
            min_val = -1
        else:
            min_val = 0
        L = max_val - min_val
    else:
        L = val_range
 
    padd = 0
    (_, channel, height, width) = img1.size()
    if window is None:
        real_size = min(window_size, height, width)
        window = create_window(real_size, channel=channel).to(img1.device)
 
    mu1 = F.conv2d(img1, window, padding=padd, groups=channel)
    mu2 = F.conv2d(img2, window, padding=padd, groups=channel)
 
    mu1_sq = mu1.pow(2)
    mu2_sq = mu2.pow(2)
    mu1_mu2 = mu1 * mu2
 
    sigma1_sq = F.conv2d(img1 * img1, window, padding=padd, groups=channel) - mu1_sq
    sigma2_sq = F.conv2d(img2 * img2, window, padding=padd, groups=channel) - mu2_sq
    sigma12 = F.conv2d(img1 * img2, window, padding=padd, groups=channel) - mu1_mu2
 
    C1 = (0.01 * L) ** 2
    C2 = (0.03 * L) ** 2
 
    v1 = 2.0 * sigma12 + C2
    v2 = sigma1_sq + sigma2_sq + C2
    cs = torch.mean(v1 / v2)  # contrast sensitivity
 
    ssim_map = ((2 * mu1_mu2 + C1) * v1) / ((mu1_sq + mu2_sq + C1) * v2)
 
    if size_average:
        ret = ssim_map.mean()
    else:
        ret = ssim_map.mean(1).mean(1).mean(1)
 
    if full:
        return ret, cs
    return ret
 
 
 
# Classes to re-use window
class SSIM(torch.nn.Module):
    def __init__(self, window_size=11, size_average=True, val_range=None):
        super(SSIM, self).__init__()
        self.window_size = window_size
        self.size_average = size_average
        self.val_range = val_range
 
        # Assume 1 channel for SSIM
        self.channel = 1
        self.window = create_window(window_size)
 
    def forward(self, img1, img2):
        (_, channel, _, _) = img1.size()
 
        if channel == self.channel and self.window.dtype == img1.dtype:
            window = self.window
        else:
            window = create_window(self.window_size, channel).to(img1.device).type(img1.dtype)
            self.window = window
            self.channel = channel
 
        return ssim(img1, img2, window=window, window_size=self.window_size, size_average=self.size_average)

还可以利用函数 structural_similarity

from skimage.metrics import structural_similarity as ssim
import numpy as np

# 创建两个示例图像
im1 = np.random.rand(256, 256)
im2 = np.random.rand(256, 256)

# 计算 SSIM，并使用一些可选参数
ssim_index, ssim_image = ssim(im1, im2,
                              win_size=11,
                              gradient=True,
                              data_range=1.0,
                              multichannel=False,
                              gaussian_weights=True,
                              full=True)

print(f"SSIM Index: {ssim_index}")
print(f"SSIM Image: \n{ssim_image}")
'''
def structural_similarity(*, im1, im2,
                         win_size=None, gradient=False, data_range=None,
                         multichannel=False, gaussian_weights=False,
                         full=False, **kwargs)
'''

FIDFrechlet Inception Distance（FID）

FID是基于Inception-V3模型（预训练好的图像分类模型）的feature vectors来计算真实图片与生成图片之间的距离，用高斯分布来表示，FID就是计算两个分布之间的Wasserstein-2距离。将真实图片和预测图片分别经过Inception模型中，得到2048维度（特征的维度）的embedding vector。把生成和真实的图片同时放入Inception-V3中，然后将feature vectors取出来用于比较。
d 2 = ∣ ∣ μ 1 − μ 2 ∣ ∣ 2 + T r ( C 1 + C 2 − 2 ∗ ( C 1 ∗ C 2 ) ) d^2 = ||\mu_1 -\mu_2||^2 + Tr(C_1 + C_2 - 2*\sqrt{(C_1 *C_2)}) d2=∣∣μ1​−μ2​∣∣2+Tr(C1​+C2​−2∗(C1​∗C2​) ​)

import numpy as np
from scipy.linalg import sqrtm

def calculate_fid(act1, act2):
    # 计算均值和协方差统计量
    mu1, sigma1 = act1.mean(axis=0), np.cov(act1, rowvar=False)
    mu2, sigma2 = act2.mean(axis=0), np.cov(act2, rowvar=False)
    
    # 计算均值之间的平方差之和
    ssdiff = np.sum((mu1 - mu2)**2.0)
    
    # 计算协方差之积的平方根
    covmean = sqrtm(sigma1.dot(sigma2))
    
    # 检查从sqrtm中移除的复数部分
    if np.iscomplexobj(covmean):
        covmean = covmean.real

    # 计算 FID 分数
    fid = ssdiff + np.trace(sigma1 + sigma2 - 2.0 * covmean)
    return fid

# 示例用法
act1 = np.random.rand(100, 10)  # 隐变量 act1
act2 = np.random.rand(100, 10)  # 隐变量 act2

fid_score = calculate_fid(act1, act2)
print("FID 分数为:", fid_score)

Inception score

Inception Score基于Inception-V3模型的分类概率来评估生成照片的质量，通过使用预训练的卷积神经网络（通常是Inception网络）来评估生成图像的质量和多样性。
K L   d i v e r g e n c e = p ( y ∣ x ) ∗ ( l o g ( p ( y ∣ x ) ) − l o g ( p ( y ) ) ) \mathrm{KL~divergence=p(y|x)*(log(p(y|x))-log(p(y)))} KL divergence=p(y∣x)∗(log(p(y∣x))−log(p(y)))

import numpy as np

def calculate_inception_score(p_yx, eps=1E-16):
    # 计算 p(y)：所有样本的平均值
    p_y = np.expand_dims(p_yx.mean(axis=0), 0)
    
    # 计算每个图像的 KL 散度
    kl_d = p_yx * (np.log(p_yx + eps) - np.log(p_y + eps))
    
    # 对类别求和
    sum_kl_d = kl_d.sum(axis=1)
    
    # 对所有图像的 KL 散度取平均值
    avg_kl_d = np.mean(sum_kl_d)
    
    # 撤销对数运算
    is_score = np.exp(avg_kl_d)
    
    return is_score

# 示例用法
p_yx = np.random.rand(100, 10)  # 概率分布 p(y|x)

is_score = calculate_inception_score(p_yx)
print("Inception Score 值为:", is_score)

LPIPS

论文:
The Unreasonable Effectiveness of Deep Features as a Perceptual Metric
代码:
LPIPS代码实现-Pytorch

LPIPS:学习感知图像块相似度(Learned Perceptual Image Patch Similarity, LPIPS)也称为“感知损失”(perceptual loss)，用于度量两张图像之间的差别，LPIPS 测量风格化图像和相应内容图像之间的内容保真度。它通过比较图像块的深层特征来工作，这些特征能够捕捉到人类视觉系统中对图像质量的感知。LPIPS的值越低表示两张图像越相似，反之，则差异越大。

步骤:从 l l l层提取特征堆(feature stack)并在通道维度中进行单位规格化(unit-normalize)。利用向量 W l W_l Wl​来放缩激活通道数,最终计算 L 2 L_2 L2​距离。 最后在空间上平均，在通道上求和。 d ( x , x 0 ) = ∑ l 1 H l W l ∑ h , w ∣ ∣ w l ⊙ ( y ^ h w l − y ^ 0 h w l ) ∣ ∣ 2 2 d(x,x_0)=\sum_l\frac1{H_lW_l}\sum_{h,w}||w_l\odot(\hat{y}_{hw}^l-\hat{y}_{0hw}^l)||_2^2 d(x,x0​)=l∑​Hl​Wl​1​h,w∑​∣∣wl​⊙(y^​hwl​−y^​0hwl​)∣∣22​

d ( x , x 0 ) d(x, x_0) d(x,x0​)：表示图像块 x x x 和 x 0 x_0 x0​ 之间的感知距离，即它们在感知上的差异度量。

l l l：表示特征堆中的层（layer）索引，用于指代不同的深度特征表示。

H l ， W l H_l，W_l Hl​，Wl​：表示特征堆中第 l l l 层的高度（height）和宽度（width）。

h , w h, w h,w：分别表示特征堆中第 l l l 层的高度和宽度索引，用于遍历特征图中的每个位置。

w l w_l wl​：表示用于缩放特征通道的权重向量，对应于特征堆中第 l l l 层的通道数。

y ^ h w l \hat{y}_{hw}^l y^​hwl​：表示特征堆中第 l l l 层的特征表示的一个元素，对应于在位置 ( h , w ) (h, w) (h,w) 处的特征向量。

y ^ 0 h w l \hat{y}_{0hw}^l y^​0hwl​：表示特征堆中第 l l l 层的参考特征表示的一个元素，对应于在位置 ( h , w ) (h, w) (h,w) 处的参考特征向量。

import torch  
import lpips  

use_gpu = False  
spatial = True  #返回感知距离的空间地图

# 创建线性校准的 LPIPS 模型
loss_fn = lpips.LPIPS(net='alex', spatial=spatial)  # 使用 AlexNet 架构创建 LPIPS 模型
# loss_fn = lpips.LPIPS(net='alex', spatial=spatial, lpips=False)  # 使用不同网络配置的 LPIPS 模型

if use_gpu:
    loss_fn.cuda()  # 如果 use_gpu 为 True，则将 LPIPS 模型移动到 GPU 上

# 示例中使用虚拟张量
root_path = r'D:\Project\results\faces'  # 存储图像的根路径
img0_path_list = []  # 存储文件名中包含 '_generated' 的图像路径列表
img1_path_list = []  # 存储文件名中包含 '_real' 的图像路径列表

# 循环遍历图像路径（代码已注释，不会执行）
for root, _, fnames in sorted(os.walk(root_path, followlinks=True)):
    for fname in fnames:
        path = os.path.join(root, fname)
        if '_generated' in fname:
            img0_path_list.append(path)
        elif '_real' in fname:
            img1_path_list.append(path)

distances = []  # 存储计算得到的图像对之间的感知距离
for i in range(len(img0_path_list)):
    dummy_img0 = lpips.im2tensor(lpips.load_image(img0_path_list[i]))  # 加载并将图像转换为张量
    dummy_img1 = lpips.im2tensor(lpips.load_image(img1_path_list[i]))  # 加载并将图像转换为张量
    
    if use_gpu:
        dummy_img0 = dummy_img0.cuda()  # 将图像张量移动到 GPU
        dummy_img1 = dummy_img1.cuda()  # 将图像张量移动到 GPU
    
    dist = loss_fn.forward(dummy_img0, dummy_img1)  # 计算图像对之间的感知距离
    distances.append(dist.mean().item())  # 将平均距离添加到 distances 列表中

print('Average Distances: %.3f' % (sum(distances) / len(img0_path_list)))  # 打印平均感知距离

CSFD

代码：https://github.com/jiwoogit/StyleID
论文：https://jiwoogit.github.io/StyleID_site/

Content Feature Structural Distance-CFSD内容特征结构距离。在风格迁移评估中，内容保真度通常依赖于LPIPS距离，该指标使用了在ImageNet数据集上预训练的AlexNet模型的特征空间，这使得LPIPS对纹理有偏见。图像的风格信息可能会影响LPIPS分数，因为它偏向于纹理特征。为了减少风格信息对评估的影响，作者引入了CFSD，这是一种只考虑图像块之间空间相关性的新距离度量。

CFSD的计算步骤：

CFSD公式：

C F S D = 1 h w ∑ i = 1 h w D K L ( S i c ∣ ∣ S i c s ) , \mathrm{CFSD}=\frac{1}{hw}\sum_{i=1}^{hw}D_{\mathrm{KL}}(S_{i}^{c}||S_{i}^{cs}), CFSD=hw1​i=1∑hw​DKL​(Sic​∣∣Sics​),

#StyleID\evaluation\eval_artfid.py
def compute_patch_simi(path_to_stylized, path_to_content, batch_size, device, num_workers=1):
    """Computes the distance for the given paths.

    Args:
        path_to_stylized (str): Path to the stylized images.
        path_to_style (str): Path to the style images. [注：这里应该为 path_to_content，修正为 path_to_content]
        batch_size (int): Batch size for computing activations.
        content_metric (str): Metric to use for content distance. Choices: 'lpips', 'vgg', 'alexnet' [注：缺少 content_metric 参数]
        device (str): Device for computing activations.
        num_workers (int): Number of threads for data loading.

    Returns:
        (float) FID value. [注：文档中写的是 FID value，但函数名为 compute_patch_simi，可能存在混淆，需要核对和确认]

    """
    device = torch.device('cuda') if device == 'cuda' and torch.cuda.is_available() else torch.device('cpu')

    # 根据路径获取图像路径并排序以匹配样式化图像与对应的内容图像
    stylized_image_paths = get_image_paths(path_to_stylized, sort=True)
    content_image_paths = get_image_paths(path_to_content, sort=True)

    # 确保样式化图像和内容图像数量相等
    assert len(stylized_image_paths) == len(content_image_paths), 'Number of stylized images and number of content images must be equal.'

    # 定义图像转换方法
    style_transforms = ToTensor()
    
    # 创建样式化图像的数据集和数据加载器
    dataset_stylized = ImagePathDataset(stylized_image_paths, transforms=style_transforms)
    dataloader_stylized = torch.utils.data.DataLoader(dataset_stylized,
                                                      batch_size=batch_size,
                                                      shuffle=False,
                                                      drop_last=False,
                                                      num_workers=num_workers)

    # 创建内容图像的数据集和数据加载器
    dataset_content = ImagePathDataset(content_image_paths, transforms=style_transforms)
    dataloader_content = torch.utils.data.DataLoader(dataset_content,
                                                     batch_size=batch_size,
                                                     shuffle=False,
                                                     drop_last=False,
                                                     num_workers=num_workers)
    
    # 初始化用于计算距离的度量类
    metric = image_metrics.PatchSimi(device=device).to(device)

    dist_sum = 0.0
    N = 0
    pbar = tqdm(total=len(stylized_image_paths))
    
    # 遍历样式化图像和内容图像的批次
    for batch_stylized, batch_content in zip(dataloader_stylized, dataloader_content):
        # 在不计算梯度的上下文中进行操作，节省内存和计算资源
        with torch.no_grad():
            # 计算当前批次的距离
            batch_dist = metric(batch_stylized.to(device), batch_content.to(device))
            N += batch_stylized.shape[0]
            dist_sum += torch.sum(batch_dist)

        pbar.update(batch_stylized.shape[0])

    pbar.close()

    return dist_sum / N

def compute_cfsd(path_to_stylized, path_to_content, batch_size, device, num_workers=1):
    """Computes CFSD for the given paths.

    Args:
        path_to_stylized (str): Path to the stylized images.
        path_to_content (str): Path to the content images.
        batch_size (int): Batch size for computing activations.
        device (str): Device for computing activations.
        num_workers (int): Number of threads for data loading.

    Returns:
        (float) CFSD value.
    """
    print('Compute CFSD value...')

    # 计算 Patch Similarity，该函数返回样式化图像和内容图像的距离值
    simi_val = compute_patch_simi(path_to_stylized, path_to_content, 1, device, num_workers)
    
    # 将距离值保留四位小数
    simi_dist = f'{simi_val.item():.4f}'
    return simi_dist

#evaluation\image_metrics.py
class PatchSimi(nn.Module):

    def __init__(self, device=None):
        # 初始化函数
        super(PatchSimi, self).__init__()
        # 加载预训练的 VGG19 模型，并移到指定设备上进行评估
        self.model = models.vgg19(pretrained=True).features.to(device).eval()
        # 指定层名称和替换名称的映射
        self.layers = {"11": "conv3"}
        # 图像归一化的均值和标准差
        self.norm_mean = (0.485, 0.456, 0.406)
        self.norm_std = (0.229, 0.224, 0.225)
        # KL 散度损失函数
        self.kld = torch.nn.KLDivLoss(reduction='batchmean')
        
        self.device = device

    def get_feats(self, img):
        features = []
        # 遍历 VGG19 模型的各层并提取特征
        for name, layer in self.model._modules.items():
            img = layer(img)
            if name in self.layers:
                features.append(img)
        return features
    
    def normalize(self, input):
        # 图像归一化处理
        return transforms.functional.normalize(input, self.norm_mean, self.norm_std)

    def patch_simi_cnt(self, input):
        b, c, h, w = input.size()
        # 转置和重塑特征
        input = torch.transpose(input, 1, 3)
        features = input.reshape(b, h*w, c).div(c)
        feature_t = torch.transpose(features, 1, 2)
        # 计算内容图像的特征相似度
        patch_simi = F.log_softmax(torch.bmm(features, feature_t), dim=-1)
        return patch_simi.reshape(b, -1)

    def patch_simi_out(self, input):
        b, c, h, w = input.size()
        # 转置和重塑特征
        input = torch.transpose(input, 1, 3)
        features = input.reshape(b, h*w, c).div(c)
        feature_t = torch.transpose(features, 1, 2)
        # 计算样式化图像的特征相似度
        patch_simi = F.softmax(torch.bmm(features, feature_t), dim=-1)
        return patch_simi.reshape(b, -1)

    def forward(self, input, target):
        src_feats = self.get_feats(self.normalize(input))
        target_feats = self.get_feats(self.normalize(target))
        init_loss = 0.
        # 计算各层的 KL 散度并求和作为初始损失值
        for idx in range(len(src_feats)):
            init_loss += F.kl_div(self.patch_simi_cnt(src_feats[idx]), self.patch_simi_out(target_feats[idx]), reduction='batchmean')

余弦相似度

cos ⁡ ( θ ) = ∑ i = 1 n ( x i × y i ) ∑ i = 1 n ( x i ) 2 × ∑ i = 1 n ( y i ) 2 = a ∙ b ∣ ∣ a ∣ ∣ × ∣ ∣ b ∣ ∣ \begin{aligned} \begin{array}{c}\\{\cos( \theta )}\\\end{array} =\quad\frac{\sum_{i = 1}^{n} ( x_{i} \times y_{i} )}{\sqrt{\sum_{i = 1}^{n} ( x_{i} )^{2}} \times \sqrt{\sum_{i = 1}^{n} ( y_{i} )^{2}}} = \frac{\mathrm{a} \bullet \mathrm{b}}{| | \mathrm{a} | | \times | | \mathrm{b} | |} \end{aligned} cos(θ)​=∑i=1n​(xi​)2 ​×∑i=1n​(yi​)2 ​∑i=1n​(xi​×yi​)​=∣∣a∣∣×∣∣b∣∣a∙b​​

# -*- coding: utf-8 -*-
# !/usr/bin/env python
# 余弦相似度计算
from PIL import Image
from numpy import average, dot, linalg
# 对图片进行统一化处理
def get_thum(image, size=(64, 64), greyscale=False):
    # 利用image对图像大小重新设置, Image.ANTIALIAS为高质量的
    image = image.resize(size, Image.ANTIALIAS)
    if greyscale:
        # 将图片转换为L模式，其为灰度图，其每个像素用8个bit表示
        image = image.convert('L')
    return image
# 计算图片的余弦距离
def image_similarity_vectors_via_numpy(image1, image2):
    image1 = get_thum(image1)
    image2 = get_thum(image2)
    images = [image1, image2]
    vectors = []
    norms = []
    for image in images:
        vector = []
        for pixel_tuple in image.getdata():
            vector.append(average(pixel_tuple))
        vectors.append(vector)
        # linalg=linear（线性）+algebra（代数），norm则表示范数
        # 求图片的范数
        norms.append(linalg.norm(vector, 2))
    a, b = vectors
    a_norm, b_norm = norms
    # dot返回的是点积，对二维数组（矩阵）进行计算
    res = dot(a / a_norm, b / b_norm)
    return res
image1 = Image.open('010.jpg')
image2 = Image.open('011.jpg')
cosin = image_similarity_vectors_via_numpy(image1, image2)
print('图片余弦相似度', cosin)