【TensorFlow】tf.nn.conv2d是怎样实现卷积的？

int height_col= (height + 2 * pad_h - kernel_h) / stride_h + 1;int width_col = (width + 2 * pad_w - kernel_w) / stride_w + 1;tf.nn.conv2d是TensorFlow里面实现卷积的函数，参考文档对它的介绍并不是很详细，实际上这是搭建卷积神经网络比较核心的一个方法，非常重要

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

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

：

第一个参数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
第二个参数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][code]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

第三个参数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

[/code]

第四个参数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）

第五个参数：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

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[code]

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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

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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[python] view
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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')

注意我们可以把这种情况看成情况2和情况3的中间状态，卷积核以步长1滑动遍历全图，以下x表示的位置，表示卷积核停留的位置，每停留一个，输出feature map的一个像素

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......xxx..xxx..xxx......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[python] view
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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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xxxxxxxxxxxxxxxxxxxxxxxxx6.如果卷积核有多个[python] view
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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]

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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')此时，输出7张3×3的feature map

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x.x.x.....x.x.x.....x.x.x8.如果batch值不为1，同时输入10张图

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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')每张图，都有7张3×3的feature map，输出的shape就是[10，3，3，7]

最后，把程序总结一下：

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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))因为是随机初始化，我的结果是这样的：

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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 3.74084214.71439075 6.13722801][ 0.82365227 -1.00546622 -3.29460764 5.12690163 -0.75699937-2.60097408 -8.33882809][ 0.76171923 -0.86230004 -6.30558443 -5.58426857 2.704785358.98232937 -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 5.052671435.6913228 -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 2.5655846610.10329056 2.88392687][ -6.30473804 -3.3073864 12.43273926 -0.66088223 2.948753360.06056046 -2.78857946][ -7.14735603 -1.44281793 3.3629775 -7.87305021 2.00383091-2.50426936 -6.93097973][ -3.15817571 1.85821593 0.60049552 -0.43315536 -4.432842730.54264796 1.54882073]][[ 2.19440389 -0.21308756 -4.35629082 -3.62100363 -0.08513772-0.80940366 7.57606506][ -2.65713739 0.45524287 -16.04298019 -5.19629049 -0.632004981.13256514 -6.70045137][ 8.00792599 4.09538221 -6.16250181 8.35843849 -4.25959206-1.5945878 -7.60996151][ 8.56787586 5.85663748 -4.38656425 0.12728286 -6.539288042.3200655 9.47253895][ -6.62967777 2.88872099 -2.76913023 -0.86287498 -1.4262073-6.59967232 5.97229099]][[ -3.59423327 4.60458899 -5.08300591 1.32078576 3.271569730.5302844 -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 -0.152034820.28564462 2.66513705]]]]case 7[[[[ 2.66223097 2.64498258 -2.93302107 3.50935125 4.622475622.04241085 -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 3.810350422.45559502 -2.35436153][ 3.93275881 5.11939669 -4.7114296 -11.96386623 2.118666890.57433248 -7.19815397]][[ 0.25111672 1.40801668 1.28818977 -2.64093828 0.981823923.69512987 4.78833389][ 0.30391204 -10.26406097 6.05877018 -6.04775047 8.959220890.80235004 -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+008.22002888e+00 -4.94586229e-02 4.19012117e+00][ 6.79884481e+00 1.21652853e+00 -5.69557810e+00 -1.33555794e+003.24849486e-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+001.96754158e+00 -4.54203081e+00 -1.37485743e+00][ -1.76783955e+00 2.35163045e+00 -2.21175838e+00 3.83091879e+003.16964531e+00 -7.58307219e+00 4.71943617e+00][ 1.20776439e+00 4.86006308e+00 1.04233503e+01 -7.82327271e+005.39195156e+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+002.32186103e+00 1.65402293e-01 -5.32707453e+00][ 3.91779566e+00 6.27949667e+00 2.32975650e+00 -1.06336937e+014.44044876e+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+003.89780998e+00 -6.36872959e+00 7.12107182e+00][ -8.85006547e-01 1.92706418e+00 3.26668215e+00 2.03566647e+001.44209075e+00 -6.48463774e+00 -8.33671093e-02]]][[[ -2.64583921e+00 3.86011934e+00 4.18198538e+00 3.50338411e+006.35944796e+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+005.06610107e+00 1.24989772e+00 -3.06433105e+00][ 2.49973416e+00 2.14041996e+00 -4.71008825e+00 7.39326143e+003.94770741e+00 8.23049164e+00 -1.67046225e+00][ -2.94665837e+00 -4.58543825e+00 7.21219683e+00 1.09780006e+015.17258358e+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+009.20719814e+00 -2.55552864e+00 -2.16087699e-02][ -3.02986956e+00 -1.29726543e+01 1.53023469e+00 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