概念
在数学上，Frechet Distance用于计算两个“多元”正态分布之间的距离。对于“单变量”正态分布，Frechet距离为\(d(X,Y)=(μ_X−μ_Y)^2+(σ_X−σ_Y)^2\)
FID用来计算生成图片与真实图片的特征向量之间的距离，分数越低两组图片越相似。这些分数结合了每个合成图像的条件类别预测的置信度（质量）和预测类别的边际概率的积分（多样性）。
FID 越低表示图像质量越好； 相反，较高的分数表示图像质量较低，并且该关系可能是线性的。
计算
\[d^2 = ||mu_1 – mu_2||^2 + Tr(C_1 + C_2 – 2*sqrt(C_1*C_2))\]
- mu：生成图与真实图向量元素的均值
- C：生成图与真实图向量的协方差矩阵，也称为sigma
代码
# example of calculating the frechet inception distance in Keras for cifar10
import numpy
from numpy import cov
from numpy import trace
from numpy import iscomplexobj
from numpy import asarray
from numpy.random import shuffle
from scipy.linalg import sqrtm
from keras.applications.inception_v3 import InceptionV3
from keras.applications.inception_v3 import preprocess_input
from keras.datasets.mnist import load_data
from skimage.transform import resize
from keras.datasets import cifar10
# scale an array of images to a new size
def scale_images(images, new_shape):
images_list = list()
for image in images:
# resize with nearest neighbor interpolation
new_image = resize(image, new_shape, 0)
# store
images_list.append(new_image)
return asarray(images_list)
# calculate frechet inception distance
def calculate_fid(model, images1, images2):
# calculate activations
act1 = model.predict(images1)
act2 = model.predict(images2)
# calculate mean and covariance statistics
mu1, sigma1 = act1.mean(axis=0), cov(act1, rowvar=False)
mu2, sigma2 = act2.mean(axis=0), cov(act2, rowvar=False)
# calculate sum squared difference between means
ssdiff = numpy.sum((mu1 - mu2)**2.0)
# calculate sqrt of product between cov
covmean = sqrtm(sigma1.dot(sigma2))
# check and correct imaginary numbers from sqrt
if iscomplexobj(covmean):
covmean = covmean.real
# calculate score
fid = ssdiff + trace(sigma1 + sigma2 - 2.0 * covmean)
return fid
# prepare the inception v3 model
model = InceptionV3(include_top=False, pooling='avg', input_shape=(299,299,3))
# load cifar10 images
(images1, _), (images2, _) = cifar10.load_data()
shuffle(images1)
images1 = images1[:10000]
print('Loaded', images1.shape, images2.shape)
# convert integer to floating point values
images1 = images1.astype('float32')
images2 = images2.astype('float32')
# resize images
images1 = scale_images(images1, (299,299,3))
images2 = scale_images(images2, (299,299,3))
print('Scaled', images1.shape, images2.shape)
# pre-process images
images1 = preprocess_input(images1)
images2 = preprocess_input(images2)
# calculate fid
fid = calculate_fid(model, images1, images2)
print('FID: %.3f' % fid)