TensorFlow conv2d原理及实践

时间:2023-03-08 16:54:43

tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, data_format=None, name=None)

官方教程说明:

给定四维的inputfilter tensor,计算一个二维卷积

Args:
  • input: A Tensor. type必须是以下几种类型之一: halffloat32float64.
  • filter: A Tensor. type和input必须相同
  • strides: A list of ints.一维,长度4, 在input上切片采样时,每个方向上的滑窗步长,必须和format指定的维度同阶
  • padding: A string from: "SAME", "VALID". padding 算法的类型
  • use_cudnn_on_gpu: An optional bool. Defaults to True.
  • data_format: An optional string from: "NHWC", "NCHW", 默认为"NHWC"
    指定输入输出数据格式,默认格式为"NHWC", 数据按这样的顺序存储:
    [batch, in_height, in_width, in_channels]
    也可以用这种方式:"NCHW", 数据按这样的顺序存储:
    [batch, in_channels, in_height, in_width]
  • name: 操作名,可选.
Returns:

Tensor. type与input相同

Given an input tensor of shape [batch, in_height, in_width, in_channels]
and a filter / kernel tensor of shape
[filter_height, filter_width, in_channels, out_channels]

conv2d实际上执行了以下操作:

  1. 将filter转为二维矩阵,shape为
    [filter_height * filter_width * in_channels, output_channels].
  2. 从input tensor中提取image patches,每个patch是一个virtual tensor,shape[batch, out_height, out_width, filter_height * filter_width * in_channels].
  3. 将每个filter矩阵和image patch向量相乘

具体来讲,当data_format为NHWC时:

output[b, i, j, k] =
sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
filter[di, dj, q, k]

input 中的每个patch都作用于filter,每个patch都能获得其他patch对filter的训练
需要满足strides[0] = strides[3] = 1. 大多数水平步长和垂直步长相同的情况下:strides = [1, stride, stride, 1].

下面举例来进行说明

在最基本的例子中,没有padding和stride = 1。让我们假设你的inputkernel有:

TensorFlow conv2d原理及实践

当您的内核您将收到以下输出:TensorFlow conv2d原理及实践,它按以下方式计算:

  • 14 = 4 * 1 + 3 * 0 + 1 * 1 + 2 * 2 + 1 * 1 + 0 * 0 + 1 * 0 + 2 * 0 + 4 * 1
  • 6 = 3 * 1 + 1 * 0 + 0 * 1 + 1 * 2 + 0 * 1 + 1 * 0 + 2 * 0 + 4 * 0 + 1 * 1
  • 6 = 2 * 1 + 1 * 0 + 0 * 1 + 1 * 2 + 2 * 1 + 4 * 0 + 3 * 0 + 1 * 0 + 0 * 1
  • 12 = 1 * 1 + 0 * 0 + 1 * 1 + 2 * 2 + 4 * 1 + 1 * 0 + 1 * 0 + 0 * 0 + 2 * 1

TF的conv2d函数批量计算卷积,并使用稍微不同的格式。对于一个输入,它是[batch, in_height, in_width, in_channels]内核的[filter_height, filter_width, in_channels, out_channels]。所以我们需要以正确的格式提供数据:

import tensorflow as tf
k = tf.constant([
[1, 0, 1],
[2, 1, 0],
[0, 0, 1]
], dtype=tf.float32, name='k')
i = tf.constant([
[4, 3, 1, 0],
[2, 1, 0, 1],
[1, 2, 4, 1],
[3, 1, 0, 2]
], dtype=tf.float32, name='i')
kernel = tf.reshape(k, [3, 3, 1, 1], name='kernel')
image = tf.reshape(i, [1, 4, 4, 1], name='image')

之后,卷积用下式计算:

res = tf.squeeze(tf.nn.conv2d(image, kernel, [1, 1, 1, 1], "VALID"))
# VALID means no padding
with tf.Session() as sess:
print sess.run(res)

并将相当于我们手工计算的,输出结果:

[[ 14. 6.]
[ 6. 12.]]

附上一张图:

TensorFlow conv2d原理及实践

区别SAME和VALID

VALID

input = tf.Variable(tf.random_normal([1,5,5,5]))  

filter = tf.Variable(tf.random_normal([3,3,5,1]))  

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')  

输出图形:

.....
.xxx.
.xxx.
.xxx.
.....

SAME

input = tf.Variable(tf.random_normal([1,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,1])) op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')

输出图形:

xxxxx
xxxxx
xxxxx
xxxxx
xxxxx

参考链接