TensorFlow使用记录 (二）： 理解tf.nn.conv2d方法

方法定义

tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=True, data_format="NHWC", dilations=[1,1,1,1], name=None)

参数：

• input:  输入的要做卷积的数据体，要求是一个`Tensor`
• filter: 卷积核，要求也是一个`Tensor`, shape= [filter_height, filter_width, in_channels, out_channels], 其中 filter_height 为卷积核高度，filter_weight 为卷积核宽度，in_channel 是要做卷积的数据体的通道数 ，out_channel 是卷积核数量。
• strides: 卷积步长（1-D tensor of length 4）， shape=[1, strides, strides, 1]，第一位和最后一位固定是1
• padding: A `string` from: `"SAME", "VALID"`. "SAME" 表示使用0去填充边界， "VALID"则不填充

• data_format: An optional `string` from: `"NHWC", "NCHW"`. Defaults to `"NHWC"`.
  Specify the data format of the input and output data.
  With the default format "NHWC", the data is stored in the order of:  [batch, height, width, channels].

• name: A name for the operation (optional).

具体实现

input shape: [batch, in_height, in_width, in_channels]

filter shape: [filter_height, filter_width, in_channels, out_channels]

计算过程：

1. 将filter展开成2-D matrix, shape: [filter_height*filter_width*in_channels, output_channels]

2. 从input tensor中提取patches构成一个virtual tensor, shape: [batch, out_height, out_width, filter_height*filter_width*in_channels]

3. 对于每一个patch,右乘上1中的filter matrix。即 [batch, out_height, out_width, filter_height*filter_width*in_channels] x [filter_height * filter_width * in_channels, output_channels], 那么输出的shape: [batch, out_height, out_width, output_channels]

【注：必须有 strides[0] = strides[3] = 1】。绝大多数情况下，水平的stride和竖直的stride一样，即strides = [1, stride, stride, 1]。

输出结果的shape计算:

在caffe中是这样的：

out_height =floor(in_height+2*pad-filter_height)/stride+1; floor向下取整

out_width=floor(in_width+2*pad-filter_width)/stride+1

在TensorFlow中是这样的：

"SAME" 类型的padding:

out_height = ceil(in_height / strides[1]); ceil向上取整

out_width = ceil(in_width / strides[2])

"VALID"类型的padding:

out_height = ceil((in_height - filter_height + 1) / striders[1])

out_width = ceil((in_width - filter_width + 1) / striders[2]

验证代码

# -*- coding:utf-8 -*-

from __future__ import division
import tensorflow as tf
import numpy as np
import math
import pandas as pd

input_arr = np.zeros((12, 15), dtype=np.float32)
number = 0
for row_idx in range(input_arr.shape[0]):
    for col_idx in range(input_arr.shape[1]):
        input_arr[row_idx][col_idx] = number
        number +=1

number = 6
w_arr = np.zeros((2, 3), dtype=np.float32)
for row_idx in range(w_arr.shape[0]):
    for col_idx in range(w_arr.shape[1]):
        w_arr[row_idx][col_idx] = number
        number += 1

stride = [1, 1, 1, 1]

# 从卷积的定义【实际上不是卷积，而是cross-correlation】进行计算验证---对VALID类型卷积进行
res_shape_h = int(math.ceil((input_arr.shape[0] - w_arr.shape[0] + 1) / stride[1]))
res_shape_w = int(math.ceil(input_arr.shape[1] - w_arr.shape[1] + 1) / stride[2])
validation_res = np.zeros(shape=(res_shape_h, res_shape_w), dtype=np.float32)

for row_idx in range(validation_res.shape[0]):
    for col_idx in range(validation_res.shape[1]):
        patch = input_arr[row_idx : row_idx+w_arr.shape[0], col_idx : col_idx+w_arr.shape[1]]
        # 这里的 * 实际上代表的是点积，即对应元素位置相乘
        res = np.sum(patch * w_arr)
        validation_res[row_idx][col_idx] = res

print('result of convolution from its definition: validation_res')
print(validation_res)
pd.DataFrame(validation_res).to_csv('validation_res.csv', index = False, header=False)

# 从TensorFlow实现出发
input_arr = np.reshape(input_arr, [1, input_arr.shape[0], input_arr.shape[1], 1])
w_arr = np.reshape(w_arr, [w_arr.shape[0], w_arr.shape[1], 1, 1])

# 输入Tensor, shape: [1, 12, 15, 1]
net_in = tf.constant(value=input_arr, dtype=tf.float32)

# filter, shape: [2, 3, 1, 1]
W = tf.constant(value=w_arr, dtype=tf.float32)

# TensorFlow卷积的计算结果
# valid卷积结果, shape: [1, 11, 13, 1]
result_conv_valid = tf.nn.conv2d(net_in, W, stride, 'VALID')
# same卷积结果, shape: [1, 12, 15, 1]
result_conv_smae = tf.nn.conv2d(net_in, W, stride, 'SAME')

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    valid_conv_res, same_conv_res = sess.run([result_conv_valid, result_conv_smae])

print(valid_conv_res.shape)
valid_conv_res = np.reshape(valid_conv_res, [valid_conv_res.shape[1], valid_conv_res.shape[2]])
same_conv_res = np.reshape(same_conv_res, [same_conv_res.shape[1], same_conv_res.shape[2]])
print('TensorFlow con res: valid_conv_res')
print(valid_conv_res)
pd.DataFrame(valid_conv_res).to_csv('conv_res.csv', index=False, header=False)
pd.DataFrame(same_conv_res).to_csv('same_res.csv', index=False, header=False)