python - keras和scipy不同的2D卷积结果

Question

在尝试调试我的神经网络时，我发现有些结果难以理解。我尝试使用 scipy (1.3.0) 进行离线计算，但我得到的结果与使用 的 keras (2.3.1) 不同tensorflow (1.14.0) 后端。这是一个最小的可重现示例:

from keras.layers import Conv2D, Input
from keras.models import Model
import numpy as np
from scipy.signal import convolve2d

image = np.array([[-1.16551484e-04, -1.88735046e-03, -7.90571701e-03,
        -1.52302440e-02, -1.55315138e-02, -8.40757508e-03,
        -2.12123734e-03, -1.49851941e-04],
       [-1.88735046e-03, -3.05623915e-02, -1.28019482e-01,
        -2.46627569e-01, -2.51506150e-01, -1.36146188e-01,
        -3.43497843e-02, -2.42659380e-03],
       [-7.90571701e-03, -1.28019482e-01, -5.06409585e-01,
        -6.69258237e-01, -6.63918257e-01, -5.31925797e-01,
        -1.43884048e-01, -1.01644937e-02],
       [-1.52302440e-02, -2.46627569e-01, -6.69258296e-01,
         2.44587708e+00,  2.72079444e+00, -6.30891442e-01,
        -2.77190477e-01, -1.95817426e-02],
       [-1.55315138e-02, -2.51506120e-01, -6.63918316e-01,
         2.72079420e+00,  3.01719952e+00, -6.19484246e-01,
        -2.82673597e-01, -1.99690927e-02],
       [-8.40757508e-03, -1.36146188e-01, -5.31925797e-01,
        -6.30891442e-01, -6.19484186e-01, -5.57167232e-01,
        -1.53017864e-01, -1.08097391e-02],
       [-2.12123734e-03, -3.43497805e-02, -1.43884048e-01,
        -2.77190447e-01, -2.82673597e-01, -1.53017864e-01,
        -3.86065207e-02, -2.72730505e-03],
       [-1.49851941e-04, -2.42659380e-03, -1.01644937e-02,
        -1.95817426e-02, -1.99690927e-02, -1.08097391e-02,
        -2.72730505e-03, -1.92666746e-04]], dtype='float32')

kernel = np.array([[ 0.04277903 ,  0.5318366  ,  0.025291916],
       [ 0.5756132  , -0.493123   ,  0.116359994],
       [ 0.10616145 , -0.319581   , -0.115053006]], dtype='float32')

print('Mean of original image', np.mean(image))

## Scipy result

res_scipy = convolve2d(image, kernel.T, mode='same')

print('Mean of convolution with scipy', np.mean(res_scipy))

## Keras result

def init(shape, dtype=None):
    return kernel[..., None, None]
im = Input((None, None, 1))
im_conv = Conv2D(1, 3, padding='same', use_bias=False, kernel_initializer=init)(im)
model = Model(im, im_conv)

model.compile(loss='mse', optimizer='adam')

res_keras = model.predict_on_batch(image[None, ..., None])

print('Mean of convolution with keras', np.mean(res_keras))

当可视化结果时，我发现它们实际上是对称的(围绕中心取模一点偏移的点对称)。 .

我尝试了一些经验主义的东西，比如转置内核，但它没有改变任何东西。

---

编辑感谢@kaya3 的评论，我意识到将内核旋转 180 度就可以了。但是，我仍然不明白为什么我需要这样做才能获得相同的结果。

Answer 1

神经网络(和图像处理)中通常所说的卷积并不完全是convolution的数学概念，这就是convolve2d工具，但与 correlation 类似，由 correlate2d 实现:

res_scipy = correlate2d(image, kernel.T, mode='same')