python - MaxPooling2D、Conv2D、UpSampling2D层的输出大小是如何计算的？

Question

我正在学习卷积自动编码器，并且正在使用 keras 构建图像降噪器。
以下代码适用于构建模型:

denoiser.add(Conv2D(32, (3,3), input_shape=(28,28,1), padding='same')) 
denoiser.add(Activation('relu'))
denoiser.add(MaxPooling2D(pool_size=(2,2)))

denoiser.add(Conv2D(16, (3,3), padding='same'))
denoiser.add(Activation('relu'))
denoiser.add(MaxPooling2D(pool_size=(2,2)))

denoiser.add(Conv2D(8, (3,3), padding='same'))
denoiser.add(Activation('relu'))

################## HEY WHAT NO MAXPOOLING?

denoiser.add(Conv2D(8, (3,3), padding='same'))
denoiser.add(Activation('relu'))
denoiser.add(UpSampling2D((2,2)))

denoiser.add(Conv2D(16, (3,3), padding='same'))
denoiser.add(Activation('relu'))
denoiser.add(UpSampling2D((2,2)))

denoiser.add(Conv2D(1, (3,3), padding='same'))

denoiser.compile(optimizer='adam', loss='mean_squared_error', metrics=['accuracy'])
denoiser.summary()

并给出以下总结:

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_155 (Conv2D)          (None, 28, 28, 32)        320       
_________________________________________________________________
activation_162 (Activation)  (None, 28, 28, 32)        0         
_________________________________________________________________
max_pooling2d_99 (MaxPooling (None, 14, 14, 32)        0         
_________________________________________________________________
conv2d_156 (Conv2D)          (None, 14, 14, 16)        4624      
_________________________________________________________________
activation_163 (Activation)  (None, 14, 14, 16)        0         
_________________________________________________________________
max_pooling2d_100 (MaxPoolin (None, 7, 7, 16)          0         
_________________________________________________________________
conv2d_157 (Conv2D)          (None, 7, 7, 8)           1160      
_________________________________________________________________
activation_164 (Activation)  (None, 7, 7, 8)           0         
_________________________________________________________________
conv2d_158 (Conv2D)          (None, 7, 7, 8)           584       
_________________________________________________________________
activation_165 (Activation)  (None, 7, 7, 8)           0         
_________________________________________________________________
up_sampling2d_25 (UpSampling (None, 14, 14, 8)         0         
_________________________________________________________________
conv2d_159 (Conv2D)          (None, 14, 14, 16)        1168      
_________________________________________________________________
activation_166 (Activation)  (None, 14, 14, 16)        0         
_________________________________________________________________
up_sampling2d_26 (UpSampling (None, 28, 28, 16)        0         
_________________________________________________________________
conv2d_160 (Conv2D)          (None, 28, 28, 1)         145       
=================================================================
Total params: 8,001
Trainable params: 8,001
Non-trainable params: 0
_________________________________________________________________

我不知道如何 MaxPooling2D , Conv2D , UpSampling2D计算输出尺寸。我已经阅读了 keras 文档，但我仍然感到困惑。影响输出形状的参数有很多，比如 stride或 padding对于 Conv2D 层，我不知道它究竟如何影响输出形状。

我不明白为什么没有 MaxPooling2D注释行之前的图层。编辑代码以包含 convmodel3.add(MaxPooling2D(pool_size=(2,2)))注释上方的图层，它将最终输出形状变为 (None, 12, 12, 1)

编辑代码以包含 convmodel3.add(MaxPooling2D(pool_size=(2,2)))评论之前的图层，然后是 convmodel3.add(UpSampling2D((2,2)))将最终输出变为 (None, 24, 24, 1)。这不应该是 (None, 28, 28, 1) 吗？
代码和总结:

convmodel3 = Sequential()
convmodel3.add(Conv2D(32, (3,3), input_shape=(28,28,1), padding='same')) 
convmodel3.add(Activation('relu'))
convmodel3.add(MaxPooling2D(pool_size=(2,2)))

convmodel3.add(Conv2D(16, (3,3), padding='same'))
convmodel3.add(Activation('relu'))
convmodel3.add(MaxPooling2D(pool_size=(2,2)))

convmodel3.add(Conv2D(8, (3,3), padding='same'))
convmodel3.add(Activation('relu'))
convmodel3.add(MaxPooling2D(pool_size=(2,2))) # ADDED MAXPOOL

################## HEY WHAT NO MAXPOOLING?

convmodel3.add(UpSampling2D((2,2))) # ADDED UPSAMPLING
convmodel3.add(Conv2D(16, (3,3), padding='same'))
convmodel3.add(Activation('relu'))
convmodel3.add(UpSampling2D((2,2)))

convmodel3.add(Conv2D(32, (3,3), padding='same'))
convmodel3.add(Activation('relu'))
convmodel3.add(UpSampling2D((2,2)))

convmodel3.add(Conv2D(1, (3,3), padding='same'))

convmodel3.compile(optimizer='adam', loss='mean_squared_error', metrics=['accuracy'])
convmodel3.summary()

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_247 (Conv2D)          (None, 28, 28, 32)        320       
_________________________________________________________________
activation_238 (Activation)  (None, 28, 28, 32)        0         
_________________________________________________________________
max_pooling2d_141 (MaxPoolin (None, 14, 14, 32)        0         
_________________________________________________________________
conv2d_248 (Conv2D)          (None, 14, 14, 16)        4624      
_________________________________________________________________
activation_239 (Activation)  (None, 14, 14, 16)        0         
_________________________________________________________________
max_pooling2d_142 (MaxPoolin (None, 7, 7, 16)          0         
_________________________________________________________________
conv2d_249 (Conv2D)          (None, 7, 7, 8)           1160      
_________________________________________________________________
activation_240 (Activation)  (None, 7, 7, 8)           0         
_________________________________________________________________
max_pooling2d_143 (MaxPoolin (None, 3, 3, 8)           0         
_________________________________________________________________
up_sampling2d_60 (UpSampling (None, 6, 6, 8)           0         
_________________________________________________________________
conv2d_250 (Conv2D)          (None, 6, 6, 16)          1168      
_________________________________________________________________
activation_241 (Activation)  (None, 6, 6, 16)          0         
_________________________________________________________________
up_sampling2d_61 (UpSampling (None, 12, 12, 16)        0         
_________________________________________________________________
conv2d_251 (Conv2D)          (None, 12, 12, 32)        4640      
_________________________________________________________________
activation_242 (Activation)  (None, 12, 12, 32)        0         
_________________________________________________________________
up_sampling2d_62 (UpSampling (None, 24, 24, 32)        0         
_________________________________________________________________
conv2d_252 (Conv2D)          (None, 24, 24, 1)         289       
=================================================================
Total params: 12,201
Trainable params: 12,201
Non-trainable params: 0
_________________________________________________________________

None有什么意义在输出形状？

另外，编辑 Conv2D层不包括填充，会引发错误:
ValueError: Negative dimension size caused by subtracting 3 from 2 for 'conv2d_240/convolution' (op: 'Conv2D') with input shapes: [?,2,2,16], [3,3,16,32].
为什么？

Answer 1

对于卷积(此处为 2D)层，要考虑的重点是图像的体积(宽度 x 高度 x 深度)以及您为其提供的四个参数。这些参数是

过滤器数量 K

过滤器尺寸(空间) F

过滤器在 S 处移动的步幅

零填充 P

输出形状的公式为

Wnew = (W - F + 2*P)/S + 1

Hnew = (H - F + 2*P)/S + 1

Dnew = K

这是取自此线程 what is the effect of tf.nn.conv2d() on an input tensor shape? ，以及有关零填充等的更多信息可以在那里找到。

对于 maxpooling 和 upsampling，大小仅受池大小和步幅的影响。在您的示例中，您的池大小为 (2,2) 且未定义步幅(因此默认为池大小，请参见此处 https://keras.io/layers/pooling/ )。上采样的工作原理相同。池大小只需要一个 2x2 像素的池，找到它们的总和并将它们放入一个像素中。因此将 2x2 像素转换为 1x1 像素，对其进行编码。上采样是同一件事，但不是对像素值求和，而是在池中重复这些值。

您没有 maxpooling 层以及图像尺寸在您的情况下困惑的原因是由于该阶段的图像大小。查看网络，图像尺寸已经是[7,7,8]。池大小和步长分别为 (2,2) 和 2，这会将图像的分辨率降低到 [3,3,8]。在上采样层之后，维度将从 3 -> 6 -> 12 -> 24 开始，每行和每列都丢失了 4 个像素。

None 的重要性(如果我错了，请纠正我，我不是 100% 确定)是由于网络通常在卷积层期望多个图像。通常预期的维度为

[Number of images, Width, Height, Depth]

因此，第一个元素被指定为 none 的原因是您的网络一次只期望一个图像，因此它被指定为 None (同样，我对这一点非常不确定)。