如何理解卷积层 output 形状

Question

I am a bit confused about the output shape of the convolutional layer. For example, as the image showed, 2 filters for 6 6 3 images, finally output will be 4 4 2, which the three color channel will fuse to 1 layer, but in some network after the convolution layer, the color channel still keep, for example here model.add(Conv2D(32, kernel_size=5,strides=1, activation=None, input_shape=(128,128,3))), the output shape of this is conv2d_5 (5, 5, 3, 32), and the question is I didn't see any specific code to say color channel keep or not. enter image description here

Answer 1

In the example image posted by OP for input of size 6 x 6 x 3 ( input_dim=6, channel_in=3 ) with 2 filters of size 3 x 3 ( filter_size=3 ) the spatial dimension can be computed as (input_dim - filter_size + 2 * padding) / stride + 1 = (6 - 3 + 2 * 0)/1 + 1 = 4 (where padding=0 and stride=1 )

Thus the 4 x 4 feature map. The operation used in standard CNN layer for computing the element in this feature map is that of fully-connected layer. Consider an example filter and image patch below (from CS231n ):

then the output element is computed as:

import numpy as np

# filter weights of size 3 x 3 x 3
w0 = np.array([
    [[0., -1., 0.],
     [1., -1., 0.],
     [0., -1., 0.]],
    [[0., 1., -1.],
     [-1., 1., 0.],
     [1., -1., 0.]],
    [[-1., 0., 0.],
     [0., -1., -1.],
     [1., -1., 0.]]
])
# bias value for the filter
b0 = 1

# an input image patch 3 x 3 x 3
x_patch = np.array([
    [[0., 0., 0.],
     [0., 2., 1.],
     [0., 1., 1.]],
    [[0., 0., 0.],
     [0., 0., 1.],
     [0., 0., 1.]],
    [[0., 0., 0.],
     [0., 0., 0.],
     [0., 0., 2.]]
])

# define the operation for each channel
>>> op = lambda xs, ws: np.sum(xs*ws)
>>> op(x_patch[:, :, 0], w0[:, :, 0]) # channel 1
0.0
>>> op(x_patch[:, :, 1], w0[:, :, 1]) # channel 2
-3.0
>>> op(x_patch[:, :, 2], w0[:, :, 2]) # channel 3
0.0

# add the values for each channel (this is where 
# channel dimension is summed over) plus the bias
>>> 0.0 + (-3.0) + 0.0 + b0
-2.0

# or simply
>>> np.sum(x_patch * w0) + b0
-2.0

This is generally the case for CNN, which can alterantively be visualized as

compared to Depth-wise convolution where the channel dimension is kept as is:

TensorFlow provides separate implementations for each in tf.keras.layers.Conv2D ( here ) and tf.keras.layers.DepthwiseConv2D ( here ) so you can use according to your application.

I cannot reproduce the output dimension of 5 x 5 x 3 x 32 for your second example (using tf v2.9.0):

import tensorflow as tf

# The inputs are 128 x 128 RGB images with 
# `data_format=channels_last` (by default) and 
# the batch size is 4.
>>> input_shape = (4, 128, 128, 3)
>>> x = tf.random.normal(input_shape)
>>> y = tf.keras.layers.Conv2D(
 32, 
 kernel_size=5, 
 strides=1, 
 activation=None, 
 input_shape=(128, 128, 3)
)(x)
>>> print(y.shape)
(4, 124, 124, 32)

The example code is slightly adjusted from the official documentation example .

Answer 2

model = Sequential()

model.add(Conv2D(32, kernel_size=5,strides=1, activation=None, input_shape=(128,128,3)))
model.add(BatchNormalization())
model.add(Activation('relu'))
model.add(MaxPool2D(2,2))
model.add(Dropout(0.2))

model.add(Flatten())
model.add(Dense(64,activation='relu'))
model.add(Dropout(0.5))

model.add(Dense(units=1))
model.add(Activation('sigmoid'))


for layer in model.layers:
    # check for convolutional layer
    if 'conv' not in layer.name:
        continue
    # get filter weights
    filters, biases = layer.get_weights()
    print(layer.name, filters.shape)

so when I print the conv output layer shape it shows as conv2d_46 (5, 5, 3, 32). when I print the summary the out shape show different, what is None? Layer (type) Output Shape Param #

conv2d_45 (Conv2D) (None, 124, 124, 32) 2432

batch_normalization_38 (Bat (None, 124, 124, 32) 128
chNormalization)

activation_36 (Activation) (None, 124, 124, 32) 0

max_pooling2d_17 (MaxPoolin (None, 62, 62, 32) 0
g2D)

dropout_26 (Dropout) (None, 62, 62, 32) 0

flatten_11 (Flatten) (None, 123008) 0

dense_23 (Dense) (None, 64) 7872576

dropout_27 (Dropout) (None, 64) 0

dense_24 (Dense) (None, 1) 65

activation_37 (Activation) (None, 1) 0