【TensorFlow】tf.nn.conv2d实现卷积

实验环境：tensorflow版本1.2.0，python2.7

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介绍

惯例先展示函数：

tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, name=None)
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除去name参数用以指定该操作的name，与方法有关的一共五个参数：

• input： 
  指需要做卷积的输入图像，它要求是一个Tensor，具有[batch, in_height, in_width, in_channels]这样的shape，具体含义是[训练时一个batch的图片数量, 图片高度, 图片宽度, 图像通道数]，注意这是一个4维的Tensor，要求类型为float32和float64其中之一

• filter： 
  相当于CNN中的卷积核，它要求是一个Tensor，具有[filter_height, filter_width, in_channels, out_channels]这样的shape，具体含义是[卷积核的高度，卷积核的宽度，图像通道数，卷积核个数]，要求类型与参数input相同，有一个地方需要注意，第三维in_channels，就是参数input的第四维

• strides：卷积时在图像每一维的步长，这是一个一维的向量，长度4

• padding： 
  string类型的量，只能是”SAME”,”VALID”其中之一，这个值决定了不同的卷积方式（后面会介绍）

• use_cudnn_on_gpu： 
  bool类型，是否使用cudnn加速，默认为true

结果返回一个Tensor，这个输出，就是我们常说的feature map

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实验

那么TensorFlow的卷积具体是怎样实现的呢，用一些例子去解释它：

1.考虑一种最简单的情况，现在有一张3×3单通道的图像（对应的shape：[1，3，3，1]），用一个1×1的卷积核（对应的shape：[1，1，1，1]）去做卷积，最后会得到一张3×3的feature map

2.增加图片的通道数，使用一张3×3五通道的图像（对应的shape：[1，3，3，5]），用一个1×1的卷积核（对应的shape：[1，1，1，1]）去做卷积，仍然是一张3×3的feature map，这就相当于每一个像素点，卷积核都与该像素点的每一个通道做点积

input = tf.Variable(tf.random_normal([1,3,3,5]))filter = tf.Variable(tf.random_normal([1,1,5,1]))op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')
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3.把卷积核扩大，现在用3×3的卷积核做卷积，最后的输出是一个值，相当于情况2的feature map所有像素点的值求和

input = tf.Variable(tf.random_normal([1,3,3,5]))filter = tf.Variable(tf.random_normal([3,3,5,1]))op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')
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4.使用更大的图片将情况2的图片扩大到5×5，仍然是3×3的卷积核，令步长为1，输出3×3的feature map

......xxx..xxx..xxx......
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5.上面我们一直令参数padding的值为‘VALID’，当其为‘SAME’时，表示卷积核可以停留在图像边缘，如下，输出5×5的feature map

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')
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xxxxxxxxxxxxxxxxxxxxxxxxx
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6.如果卷积核有多个

input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')
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此时输出7张5×5的feature map

7.步长不为1的情况，文档里说了对于图片，因为只有两维，通常strides取[1，stride，stride，1]

input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')
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此时，输出7张3×3的feature map

x.x.x.....x.x.x.....x.x.x
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8.如果batch值不为1，同时输入10张图

input = tf.Variable(tf.random_normal([10,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')
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每张图，都有7张3×3的feature map，输出的shape就是[10，3，3，7]

---

代码清单

最后，把程序总结一下：

import tensorflow as tf#case 2input = tf.Variable(tf.random_normal([1,3,3,5]))filter = tf.Variable(tf.random_normal([1,1,5,1]))op2 = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')#case 3input = tf.Variable(tf.random_normal([1,3,3,5]))filter = tf.Variable(tf.random_normal([3,3,5,1]))op3 = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')#case 4input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,1]))op4 = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')#case 5input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,1]))op5 = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')#case 6input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op6 = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')#case 7input = tf.Variable(tf.random_normal([1,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op7 = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')#case 8input = tf.Variable(tf.random_normal([10,5,5,5]))filter = tf.Variable(tf.random_normal([3,3,5,7]))op8 = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')init = tf.initialize_all_variables()with tf.Session() as sess:    sess.run(init)    print("case 2")    print(sess.run(op2))    print("case 3")    print(sess.run(op3))    print("case 4")    print(sess.run(op4))    print("case 5")    print(sess.run(op5))    print("case 6")    print(sess.run(op6))    print("case 7")    print(sess.run(op7))    print("case 8")    print(sess.run(op8))
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因为是随机初始化，我的结果是这样的：

case 2[[[[-0.64064658]   [-1.82183945]   [-2.63191342]]  [[ 8.05008984]   [ 1.66023612]   [ 2.53465152]]  [[-3.51703644]   [-5.92647743]   [ 0.55595356]]]]case 3[[[[ 10.53139973]]]]case 4[[[[ 10.45460224]   [  6.23760509]   [  4.97157574]]  [[  3.05653667]   [-11.43907833]   [ -2.05077457]]  [[ -7.48340607]   [ -0.90697062]   [  3.27171206]]]]case 5[[[[  5.30279875]   [ -2.75329947]   [  5.62432575]   [-10.24609661]   [  0.12603235]]  [[  0.2113893 ]   [  1.73748684]   [ -3.04372549]   [ -7.2625494 ]   [-12.76445198]]  [[ -1.57414591]   [ -3.39802694]   [ -6.01582575]   [ -1.73042905]   [ -3.07183361]]  [[  1.41795194]   [ -2.02815866]   [-17.08983231]   [ 11.98958111]   [  2.44879103]]  [[  0.29902667]   [ -3.19712877]   [ -2.84978414]   [ -2.71143317]   [  5.99366283]]]]case 6[[[[ 12.02504349   4.35077286   2.67207813   5.77893162   6.98221684     -0.96858567  -8.1147871 ]   [ -0.02988982  -2.52141953  15.24755192   6.39476395  -4.36355495     -2.34515095   5.55743504]   [ -2.74448752  -1.62703776  -6.84849405  10.12248802   3.7408421      4.71439075   6.13722801]   [  0.82365227  -1.00546622  -3.29460764   5.12690163  -0.75699937     -2.60097408  -8.33882809]   [  0.76171923  -0.86230004  -6.30558443  -5.58426857   2.70478535      8.98232937  -2.45504045]]  [[  3.13419819 -13.96483231   0.42031103   2.97559547   6.86646557     -3.44916964  -0.10199898]   [ 11.65359879  -5.2145977    4.28352737   2.68335319   3.21993709     -6.77338028   8.08918095]   [  0.91533852  -0.31835344  -1.06122255  -9.11237717   5.05267143      5.6913228   -5.23855162]   [ -0.58775592  -5.03531456  14.70254898   9.78966522 -11.00562763     -4.08925819  -3.29650426]   [ -2.23447251  -0.18028721  -4.80610704  11.2093544   -6.72472     -2.67547607   1.68422937]]  [[ -3.40548897  -9.70355129  -1.05640507  -2.55293012  -2.78455877    -15.05377483  -4.16571808]   [ 13.66925812   2.87588191   8.29056358   6.71941566   2.56558466     10.10329056   2.88392687]   [ -6.30473804  -3.3073864   12.43273926  -0.66088223   2.94875336      0.06056046  -2.78857946]   [ -7.14735603  -1.44281793   3.3629775   -7.87305021   2.00383091     -2.50426936  -6.93097973]   [ -3.15817571   1.85821593   0.60049552  -0.43315536  -4.43284273      0.54264796   1.54882073]]  [[  2.19440389  -0.21308756  -4.35629082  -3.62100363  -0.08513772     -0.80940366   7.57606506]   [ -2.65713739   0.45524287 -16.04298019  -5.19629049  -0.63200498      1.13256514  -6.70045137]   [  8.00792599   4.09538221  -6.16250181   8.35843849  -4.25959206     -1.5945878   -7.60996151]   [  8.56787586   5.85663748  -4.38656425   0.12728286  -6.53928804      2.3200655    9.47253895]   [ -6.62967777   2.88872099  -2.76913023  -0.86287498  -1.4262073     -6.59967232   5.97229099]]  [[ -3.59423327   4.60458899  -5.08300591   1.32078576   3.27156973      0.5302844   -5.27635145]   [ -0.87793881   1.79624665   1.66793108  -4.70763969  -2.87593603     -1.26820421  -7.72825718]   [ -1.49699068  -3.40959787  -1.21225107  -1.11641395  -8.50123024     -0.59399474   3.18010235]   [ -4.4249506   -0.73349547  -1.49064219  -6.09967899   5.18624878     -3.80284953  -0.55285597]   [ -1.42934585   2.76053572  -5.19795799   0.83952439  -0.15203482      0.28564462   2.66513705]]]]case 7[[[[  2.66223097   2.64498258  -2.93302107   3.50935125   4.62247562      2.04241085  -2.65325522]   [ -0.03272867  -1.00103927  -4.3691597    2.16724801   7.75251007     -4.6788125   -0.89318085]   [  4.74175072  -0.80443329  -1.02710629  -6.68772554   4.57605314     -3.72993755   4.79951382]]  [[  5.249547     8.92288399   7.10703182  -9.10498428  -7.43814278     -8.69616318   1.78862095]   [  7.53669024 -14.52316284  -2.55870199  -1.11976743   3.81035042      2.45559502  -2.35436153]   [  3.93275881   5.11939669  -4.7114296  -11.96386623   2.11866689      0.57433248  -7.19815397]]  [[  0.25111672   1.40801668   1.28818977  -2.64093828   0.98182392      3.69512987   4.78833389]   [  0.30391204 -10.26406097   6.05877018  -6.04775047   8.95922089      0.80235004  -5.4520669 ]   [ -7.24697018  -2.33498096 -10.20039558  -1.24307609   3.99351597     -8.1029129    2.44411373]]]]case 8[[[[ -6.84037447e+00   1.33321762e-01  -5.09891272e+00   5.55682087e+00      8.22002888e+00  -4.94586229e-02   4.19012117e+00]   [  6.79884481e+00   1.21652853e+00  -5.69557810e+00  -1.33555794e+00      3.24849486e-01   4.88868570e+00  -3.90220714e+00]   [ -3.53190374e+00  -4.11765718e+00   4.54340839e+00   1.85549557e+00     -3.38682461e+00   2.62719369e+00  -4.98658371e+00]]  [[ -9.86354351e+00  -6.76713943e+00   3.62617874e+00  -6.16720629e+00      1.96754158e+00  -4.54203081e+00  -1.37485743e+00]   [ -1.76783955e+00   2.35163045e+00  -2.21175838e+00   3.83091879e+00      3.16964531e+00  -7.58307219e+00   4.71943617e+00]   [  1.20776439e+00   4.86006308e+00   1.04233503e+01  -7.82327271e+00      5.39195156e+00  -6.31672382e+00   1.35577369e+00]]  [[ -3.65947580e+00  -1.98961139e+00   7.53771305e+00   2.79224634e-01     -2.90050888e+00  -3.57466817e+00  -6.33232594e-01]   [  5.89931488e-01   2.83219159e-01  -1.65850735e+00  -6.45545387e+00     -1.17044592e+00   1.40343285e+00   5.74970901e-01]   [ -8.58810043e+00  -1.25172977e+01   6.84177876e-01   3.80004168e+00     -1.54420209e+00  -3.32161427e+00  -1.05423713e+00]]] [[[ -4.82677078e+00   3.11167526e+00  -4.32694483e+00  -4.77198696e+00      2.32186103e+00   1.65402293e-01  -5.32707453e+00]   [  3.91779566e+00   6.27949667e+00   2.32975650e+00  -1.06336937e+01      4.44044876e+00   8.08288479e+00  -5.83346319e+00]   [ -2.82141399e+00  -9.16103745e+00   6.98908520e+00  -5.66505909e+00     -2.11039782e+00   2.27499461e+00  -5.74120235e+00]]  [[  6.71680808e-01  -4.01104212e+00  -4.61760712e+00   1.02667952e+01     -8.21200657e+00  -8.57054043e+00   1.71461976e+00]   [  2.40794683e+00  -2.63071585e+00   9.68963623e+00  -4.51778412e+00     -3.91073084e+00  -5.91874409e+00   9.96273613e+00]   [  2.67705870e+00   2.85607010e-01   2.45853162e+00   4.44810390e+00     -2.11300468e+00  -5.77583075e+00   2.83322239e+00]]  [[ -8.21949577e+00  -7.57754421e+00   3.93484974e+00   2.26189137e+00     -3.49395227e+00  -6.40283823e+00  -6.00450039e-01]   [  2.95964479e-02  -1.19976890e+00   5.38537979e+00   4.62369967e+00      3.89780998e+00  -6.36872959e+00   7.12107182e+00]   [ -8.85006547e-01   1.92706418e+00   3.26668215e+00   2.03566647e+00      1.44209075e+00  -6.48463774e+00  -8.33671093e-02]]] [[[ -2.64583921e+00   3.86011934e+00   4.18198538e+00   3.50338411e+00      6.35944796e+00  -4.28423309e+00   4.87355423e+00]   [  4.42271233e+00   3.92883778e+00  -5.59371090e+00   4.98251200e+00     -3.45068884e+00   2.91921115e+00   1.03779554e+00]   [  1.36162388e+00  -1.06808968e+01  -3.92534947e+00   1.85111761e-01     -4.87255526e+00   1.66666222e+01  -1.04918976e+01]]  [[ -4.34632540e+00   1.74614882e+00  -2.89012527e+00  -8.74067783e+00      5.06610107e+00   1.24989772e+00  -3.06433105e+00]   [  2.49973416e+00   2.14041996e+00  -4.71008825e+00   7.39326143e+00      3.94770741e+00   8.23049164e+00  -1.67046225e+00]   [ -2.94665837e+00  -4.58543825e+00   7.21219683e+00   1.09780006e+01      5.17258358e+00   7.90257788e+00  -2.13929534e+00]]  [[  4.20402241e+00  -2.98926830e+00  -3.89006615e-01  -8.16001511e+00     -2.38355541e+00   1.42584383e+00  -5.46632290e+00]   [  5.52395058e+00   5.09255171e+00  -1.08742390e+01  -4.96262169e+00     -1.35298109e+00   3.65663052e-01  -3.40589857e+00]   [ -6.95647061e-01  -4.12855625e+00   2.66609401e-01  -9.39565372e+00     -3.85058141e+00   2.51248240e-01  -5.77149725e+00]]] [[[  1.22103825e+01   5.72040796e+00  -3.56989503e+00  -1.02248180e+00     -5.20942688e-01   7.15008640e+00   3.43482435e-01]   [  6.01409674e+00  -1.59511256e+00  -6.48080063e+00  -1.82889538e+01     -1.03537569e+01  -1.48270035e+01  -5.26662111e+00]   [  5.51758146e+00  -2.91831636e+00   3.75461340e-01  -9.23893452e-02     -9.22101116e+00   7.16952372e+00  -6.86479330e-01]]  [[ -3.03645611e+00   6.68620300e+00  -3.31973934e+00  -4.91346550e+00      9.20719814e+00  -2.55552864e+00  -2.16087699e-02]   [ -3.02986956e+00  -1.29726543e+01   1.53023469e+00  -8.19733238e+00      5.68085670e+00  -1.72856820e+00  -4.69369221e+00]   [ -6.67176056e+00   8.76355553e+00   2.18996063e-01  -4.38777208e+00     -6.35764122e-01  -1.37812555e+00  -4.41474581e+00]]  [[  2.25345469e+00   1.02142305e+01  -1.71714854e+00  -5.29060185e-01      2.27982092e+00  -8.75302982e+00   7.13998675e-02]   [ -6.67547846e+00   3.67722750e+00  -3.44172812e+00   5.69674826e+00     -2.28723526e+00   5.92991543e+00   5.53608060e-01]   [ -1.01174891e-01  -2.73731589e+00  -4.06187654e-01   6.54158068e+00      2.59603882e+00   2.99202776e+00  -2.22350287e+00]]] [[[ -1.81271315e+00   2.47674489e+00  -2.90284491e+00   1.34291325e+01      7.69864845e+00  -1.27134466e+00   3.02233839e+00]   [ -2.08135307e-01   1.03206539e+00   1.90775347e+00   9.01517391e+00     -3.52140331e+00   9.05393791e+00  -9.12732124e-01]   [  1.12128162e+00   5.98179293e+00  -2.27206993e+00  -5.21281779e-01      6.20835352e+00   3.73474598e+00   1.18961644e+00]]  [[  3.17242837e+00  -6.00571585e+00   2.37661076e+00  -5.64483738e+00     -6.45412731e+00   8.75251675e+00   7.33790398e-02]   [  3.08957529e+00  -1.06855690e-01  -5.16810894e-01  -9.41085911e+00      8.23878098e+00   6.79738426e+00  -1.23478663e+00]   [ -9.20640087e+00  -6.82801771e+00  -5.96975613e+00   7.61030674e-01     -4.35995817e+00  -3.54818010e+00  -2.56281614e+00]]  [[  4.69872713e-01   8.36402321e+00   5.37103415e-01  -1.68033957e-01     -3.21731424e+00  -7.34270859e+00  -3.14253521e+00]   [  6.69656086e+00  -5.27954197e+00  -8.57314682e+00   4.84328842e+00     -2.96387672e+00   2.47114658e+00   2.85376692e+00]   [ -7.86032295e+00  -7.18845367e+00  -3.27161223e-01   9.27330971e+00     -6.14093494e+00  -4.49041557e+00   3.47160912e+00]]] [[[ -1.89188433e+00   5.43082857e+00   6.04252160e-01   6.92894220e+00      8.59178162e+00   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