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這篇文章主要介紹TensorFlow tf.nn.conv2d如何實現卷積的方式，文中介紹的非常詳細，具有一定的參考價值，感興趣的小伙伴們一定要看完！
介紹
慣例先展示函數：
tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, name=None)
除去name參數用以指定該操作的name，與方法有關的一共五個參數：
input：
指需要做卷積的輸入圖像，它要求是一個Tensor，具有[batch, in_height, in_width, in_channels]這樣的shape，具體含義是[訓練時一個batch的圖片數量, 圖片高度, 圖片寬度, 圖像通道數]，注意這是一個4維的Tensor，要求類型為float32和float64其中之一
filter：
相當于CNN中的卷積核，它要求是一個Tensor，具有[filter_height, filter_width, in_channels, out_channels]這樣的shape，具體含義是[卷積核的高度，卷積核的寬度，圖像通道數，卷積核個數]，要求類型與參數input相同，有一個地方需要注意，第三維in_channels，就是參數input的第四維
strides：卷積時在圖像每一維的步長，這是一個一維的向量，長度4
padding：
string類型的量，只能是”SAME”,”VALID”其中之一，這個值決定了不同的卷積方式（后面會介紹）
use_cudnn_on_gpu：
bool類型，是否使用cudnn加速，默認為true
結果返回一個Tensor，這個輸出，就是我們常說的feature map
實驗
那么TensorFlow的卷積具體是怎樣實現的呢，用一些例子去解釋它：
1.考慮一種最簡單的情況，現在有一張3×3單通道的圖像（對應的shape：[1，3，3，1]），用一個1×1的卷積核（對應的shape：[1，1，1，1]）去做卷積，最后會得到一張3×3的feature map
2.增加圖片的通道數，使用一張3×3五通道的圖像（對應的shape：[1，3，3，5]），用一個1×1的卷積核（對應的shape：[1，1，1，1]）去做卷積，仍然是一張3×3的feature map，這就相當于每一個像素點，卷積核都與該像素點的每一個通道做點積
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')
3.把卷積核擴大，現在用3×3的卷積核做卷積，最后的輸出是一個值，相當于情況2的feature map所有像素點的值求和
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')
4.使用更大的圖片將情況2的圖片擴大到5×5，仍然是3×3的卷積核，令步長為1，輸出3×3的feature map
..... .xxx. .xxx. .xxx. .....
5.上面我們一直令參數padding的值為‘VALID'，當其為‘SAME'時，表示卷積核可以停留在圖像邊緣，如下，輸出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')
xxxxx xxxxx xxxxx xxxxx xxxxx
6.如果卷積核有多個
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')
此時輸出7張5×5的feature map
7.步長不為1的情況，文檔里說了對于圖片，因為只有兩維，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')
此時，輸出7張3×3的feature map
x.x.x ..... x.x.x ..... x.x.x
8.如果batch值不為1，同時輸入10張圖
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')
每張圖，都有7張3×3的feature map，輸出的shape就是[10，3，3，7]
代碼清單
最后，把程序總結一下：
import tensorflow as tf
#case 2
input = 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 3
input = 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 4
input = 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 5
input = 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 6
input = 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 7
input = 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 8
input = 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))因為是隨機初始化，我的結果是這樣的：
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 1.02003086e+00 5.31300211e+00] [ -8.97491455e-01 6.52438164e+00 -4.43710327e+00 7.10509634e+00 8.84234428e+00 3.08552694e+00 2.78152227e+00] [ -9.40537453e-02 2.34666920e+00 -5.57496691e+00 -8.62346458e+00 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