神經網路中的降維和升維方法 (tensorflow & pytorch)
大名鼎鼎的UNet和我們經常看到的編解碼器模型，他們的模型都是先將資料下采樣，也稱為特徵提取，然後再將下采樣後的特徵恢復回原來的維度。這個特徵提取的過程我們稱為“下采樣”，這個恢復的過程我們稱為“上取樣”，本文就專注於神經網路中的下采樣和上取樣來進行一次總結。寫的不好勿怪哈。
神經網路中的降維方法
池化層
池化層（平均池化層、最大池化層），卷積
平均池化層
- pytorch
nn.AvgPool1dnn.AvgPool2d
- tensorflow
- tf.layers.AveragePooling1D
- tf.layers.AveragePooling2D
最大池化層
- pytorch
- nn.MaxPool1d
- nn.MaxPool2d
- tensorflow
- tf.layers.MaxPooling1D
- tf.layers.MaxPooling2D
還有另外一些pool層：nn.LPPool、nn.AdaptiveMaxPool、nn.AdaptiveAvgPool、nn.FractionalMaxPool2d
卷積
普通卷積
- pytorch
nn.Conv1dnn.Conv2d
- tensorflow
- tf.layers.Conv1D
- tf.layers.Conv2D
還有一些獨特的卷積，感興趣的可以自己去了解
- 擴張卷積 (又稱空洞卷積)： tf.nn.atrous_conv2d
- depthwise卷積： tf.nn.depthwise_conv2d
- 分離卷積： tf.nn.separable_conv2d
- 量化卷積： tf.nn.quantized_conv2d
- ...
升維方法
插值方法
插值方法有很多種有：階梯插值、線性插值、三次樣條插值等等
numpy的實現方法我在另外一篇文章中已經介紹過了，為了避免重複，想要了解的同學請移步【插值方法及python實現】
pytorch實現方法
torch.nn.Upsample(size=None, scale_factor=None, mode='nearest', align_corners=None)
對給定多通道的1維（時間）、2維（空間）、3維（體積）資料進行上取樣。
- 1維(向量資料)，輸入資料Tensor格式為3維：(batch_size, channels, width)
- 2維(影象資料)，輸入資料Tensor格式為4維：(batch_size, channels, height, width)
- 3維(點雲資料)，輸入資料Tensor格式為5維：(batch_size, channels, depth, height, width)
引數
- size：輸入資料（一維 or 二維 or 三維）
- scale_factor：縮放大小
- mode：上取樣演算法（nearest（最近鄰插值）、linear（線性插值）、bilinear（雙線性插值）、bicubic（雙三次插值）、trilinear（三次線性插值））
- align_corners：如果為True，則輸入和輸出張量的角畫素對齊，從而保留這些畫素處的值。 僅在模式為“線性”，“雙線性”或“三線性”時有效。 預設值：False
返回：
-
Input：$(N, C, W_{in}), (N, C, H_{in}, W_{in}) 或(N, C, D_{in}, H_{in}, W_{in})$
-
Output: $(N, C, W_{out}), (N, C, H_{out}, W_{out}) 或(N, C, D_{out}, H_{out}, W_{out})$
$D_{out}=[D_{in}× \text{scale_factor}]$
$H_{out} = [H_{in} \times \text{scale_factor}]$
$W_{out} = [W_{in} \times \text{scale_factor}]$
unpooling
Unpooling是在CNN中常用的來表示max pooling的逆操作。這是從2013年紐約大學Matthew D. Zeiler和Rob Fergus發表的《Visualizing and Understanding Convolutional Networks》中產生的idea：鑑於max pooling不可逆，因此使用近似的方式來反轉得到max pooling操作之前的原始情況
簡單來說，記住做max pooling的時候的最大item的位置，比如一個3x3的矩陣，max pooling的size為2x2，stride為1，反捲積記住其位置，其餘位置至為0就行：
$$\left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]->(\text { maxpooling })\left[\begin{array}{ll}
5 & 6 \\
8 & 9
\end{array}\right]->(\text { unpooling })\left[\begin{array}{lll}
0 & 0 & 0 \\
0 & 5 & 6 \\
0 & 8 & 9
\end{array}\right]$$
方法一
def unpool_with_with_argmax(pooled, ind, ksize=[1, 2, 2, 1]):
"""https://github.com/sangeet259/tensorflow_unpooling
To unpool the tensor after max_pool_with_argmax.
Argumnets:
pooled: the max pooled output tensor
ind: argmax indices , the second output of max_pool_with_argmax
ksize: ksize should be the same as what you have used to pool
Returns:
unpooled: the tensor after unpooling
Some points to keep in mind ::
1. In tensorflow the indices in argmax are flattened, so that a maximum value at position [b, y, x, c] becomes flattened index ((b * height + y) * width + x) * channels + c
2. Due to point 1, use broadcasting to appropriately place the values at their right locations !
"""
# Get the the shape of the tensor in th form of a list
input_shape = pooled.get_shape().as_list()
# Determine the output shape
output_shape = (input_shape[0], input_shape[1] * ksize[1], input_shape[2] * ksize[2], input_shape[3])
# Ceshape into one giant tensor for better workability
pooled_ = tf.reshape(pooled, [input_shape[0] * input_shape[1] * input_shape[2] * input_shape[3]])
# The indices in argmax are flattened, so that a maximum value at position [b, y, x, c] becomes flattened index ((b * height + y) * width + x) * channels + c
# Create a single unit extended cuboid of length bath_size populating it with continous natural number from zero to batch_size
batch_range = tf.reshape(tf.range(output_shape[0], dtype=ind.dtype), shape=[input_shape[0], 1, 1, 1])
b = tf.ones_like(ind) * batch_range
b_ = tf.reshape(b, [input_shape[0] * input_shape[1] * input_shape[2] * input_shape[3], 1])
ind_ = tf.reshape(ind, [input_shape[0] * input_shape[1] * input_shape[2] * input_shape[3], 1])
ind_ = tf.concat([b_, ind_], 1)
ref = tf.Variable(tf.zeros([output_shape[0], output_shape[1] * output_shape[2] * output_shape[3]]))
# Update the sparse matrix with the pooled values , it is a batch wise operation
unpooled_ = tf.scatter_nd_update(ref, ind_, pooled_)
# Reshape the vector to get the final result
unpooled = tf.reshape(unpooled_, [output_shape[0], output_shape[1], output_shape[2], output_shape[3]])
return unpooled
original_tensor = tf.random_uniform([1, 4, 4, 3], maxval=100, dtype='float32', seed=2)
pooled_tensor, max_indices = tf.nn.max_pool_with_argmax(original_tensor, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1],
padding='SAME')
print(pooled_tensor.shape) # (1, 2, 2, 3)
unpooled_tensor = unpool_with_with_argmax(pooled_tensor, max_indices)
print(unpooled_tensor.shape) # (1, 4, 4, 3)
View Code
方法二
from tensorflow.python.ops import gen_nn_ops
inputs = tf.get_variable(name="a", shape=[64, 32, 32, 4], dtype=tf.float32,
initializer=tf.random_normal_initializer(mean=0, stddev=1))
# 最大池化
pool1 = tf.nn.max_pool(inputs,
ksize=[1, 2, 2, 1],
strides=[1, 2, 2, 1],
padding='SAME')
print(pool1.shape) # (64, 16, 16, 4)
# 最大反池化
grad = gen_nn_ops.max_pool_grad(inputs, # 池化前的tensor，即max pool的輸入
pool1, # 池化後的tensor，即max pool 的輸出
pool1, # 需要進行反池化操作的tensor，可以是任意shape和pool1一樣的tensor
ksize=[1, 2, 2, 1],
strides=[1, 2, 2, 1],
padding='SAME')
print(grad.shape) # (64, 32, 32, 4)
View Code
在tensorflow 2.4版本中官方已經幫我們實現好了
tf.keras.layers.UpSampling2D(size=(2, 2), data_format=None, interpolation='nearest')
pytorch版本
nn.MaxUnpool1dnn.MaxUnpool2d
轉置卷積
轉置卷積 (transpose convolution) 也會被稱為 反捲積（Deconvolution），與Unpooling不同，使用反捲積來對影象進行上取樣是可以習得的。通常用來對卷積層的結果進行上取樣，使其回到原始圖片的解析度。
- pytorch
nn.ConvTranspose1d(in_channels=N, out_channels=2N, kernel_size=2*S, stride=S, padding=S//2 + S%2, otuput_padding=S%2)nn.ConvTranspose2d
- tensorflow
- tf.nn.conv2d_transpose
- tf.nn.conv1d_transpose
PixelShuffle
pixelshuffle演算法的實現流程如上圖，其實現的功能是：將一個[H, W]的低解析度輸入影象（Low Resolution），通過Sub-pixel操作將其變為[r*H, e*W]的高解析度影象（High Resolution）。
但是其實現過程不是直接通過插值等方式產生這個高解析度影象，而是通過卷積先得到$r^2$個通道的特徵圖（特徵圖大小和輸入低解析度影象一致），然後通過週期篩選（periodic shuffing）的方法得到這個高解析度的影象，其中$r$為上取樣因子（upscaling factor），也就是影象的擴大倍率。
二維SubPixel上取樣
[batch, height, width, channels * r * r] --> [batch, height * r, width * r, channels]
tensorflow方法實現
import tensorflow as tf
def _phase_shift(I, r):
# 相位偏移操作
bsize, a, b, c = I.get_shape().as_list()
bsize = tf.shape(I)[0] # Handling Dimension(None) type for undefined batch dim
X = tf.reshape(I, (bsize, a, b, r, r))
X = tf.transpose(X, (0, 1, 2, 4, 3)) # bsize, a, b, 1, 1
X = tf.split(X, a, 1) # a, [bsize, b, r, r]
X = tf.concat([tf.squeeze(x, axis=1) for x in X], axis=2) # bsize, b, a*r, r
X = tf.split(X, b, 1) # b, [bsize, a*r, r]
X = tf.concat([tf.squeeze(x, axis=1) for x in X], axis=2) # bsize, a*r, b*r
return tf.reshape(X, (bsize, a * r, b * r, 1))
def PixelShuffle(X, r, color=False):
if color:
Xc = tf.split(X, 3, 3)
X = tf.concat([_phase_shift(x, r) for x in Xc], axis=3)
else:
X = _phase_shift(X, r)
return X
if __name__ == "__main__":
X1 = tf.get_variable(name='X1',
shape=[2, 8, 8, 4],
initializer=tf.random_normal_initializer(stddev=1.0),
dtype=tf.float32)
Y = PixelShuffle(X1, 2)
print(Y.shape) # (2, 16, 16, 1)
X2 = tf.get_variable(name='X2',
shape=[2, 8, 8, 4 * 3],
initializer=tf.random_normal_initializer(stddev=1.0),
dtype=tf.float32)
Y2 = PixelShuffle(X2, 2, color=True)
print(Y2.shape) # (2, 16, 16, 3)
View Code
pytorch方法實現
import torch import torch.nn as nn input = torch.randn(size=(1, 9, 4, 4)) ps = nn.PixelShuffle(3) output = ps(input) print(output.size()) # torch.Size([1, 1, 12, 12])View Code
numpy方法實現
def PS(I, r):
assert len(I.shape) == 3
assert r>0
r = int(r)
O = np.zeros((I.shape[0]*r, I.shape[1]*r, I.shape[2]/(r*2)))
for x in range(O.shape[0]):
for y in range(O.shape[1]):
for c in range(O.shape[2]):
c += 1
a = np.floor(x/r).astype("int")
b = np.floor(y/r).astype("int")
d = c*r*(y%r) + c*(x%r)
print a, b, d
O[x, y, c-1] = I[a, b, d]
return O
View Code
一維SubPixel上取樣
(batch_size, width, channels * r)-->(batch_size, width * r, channels)
tensorflow實現
import tensorflow as tf
def SubPixel1D(I, r):
"""一維subpixel upsampling layer，
輸入維度(batch, width, r).
"""
with tf.name_scope('subpixel'):
X = tf.transpose(I, [2, 1, 0]) # (r, w, b)
X = tf.batch_to_space_nd(X, [r], [[0, 0]]) # (1, r*w, b)
X = tf.transpose(X, [2, 1, 0])
return X
# 示例
# ---------------------------------------------------
if __name__ == "__main__":
inputs = tf.get_variable(name='input',
shape=[64, 8192, 32],
initializer=tf.random_normal_initializer(stddev=1.0),
dtype=tf.float32)
upsample_SubPixel1D = SubPixel1D(I=inputs, r=2)
print(upsample_SubPixel1D.shape) # (64, 16384, 16)
View Code
pytorch方法實現
class PixelShuffle1D(nn.Module):
"""
1D pixel shuffler. https://arxiv.org/pdf/1609.05158.pdf
Upscales sample length, downscales channel length
"short" is input, "long" is output
"""
def __init__(self, upscale_factor):
super(PixelShuffle1D, self).__init__()
self.upscale_factor = upscale_factor
def forward(self, x):
batch_size, channels, in_width = x.size()
channels //= self.upscale_factor
out_width = self.upscale_factor * in_width
x = x.contiguous().view([batch_size, channels, self.upscale_factor, in_width])
x = x.permute(0, 1, 3, 2).contiguous()
x = x.view(batch_size, channels, out_width)
return x
View Code
sub-pixel or fractional convolution可以看成是transposed convolution的一個特例
Meta upscale module
可以任意上取樣尺寸，還不是很出名，等於後出名了再來補全
參考
這裡很多API我還是分享的tensorflow 1.*的，主要原因是因為我最開始學深度學習的時候用的是 tensoflow 1，現在我已經轉學pytorch了，今天看了看tensorflow，2版本已經發布一年多了，1版本相當於是爛尾了，2版本雖然解決了原來的問題，可是人是向前看的，我已經使用pytorch起來，再讓我回頭學tensorflow 2似乎是一件很不情願的事情。而且tensorflow 2 已經在走向沒落了，使用tensorflow 2的開原始碼，除了google自家公司外，真的也越來越少。tensorflow加油吧，我內心深處還是喜歡你的，只不過pytorch太方便了，開源社群也很強大了。
【文件】tensorflow官方文件
【文件】pytorch官方文件
【程式碼】2D_subpixel
【程式碼】1D_pytorch-pixelshuffle1d
【程式碼】1D_pytorch_pixelshuffle
【論文】《Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network》
【動圖】卷積的