對(duì)于fcn，經(jīng)常要使用到Deconvolution進(jìn)行上采樣。對(duì)于caffe使用者，使用Deconvolution上采樣，其參數(shù)往往直接給定，不需要通過(guò)學(xué)習(xí)獲得。

給定參數(shù)的方式很有意思，可以通過(guò)兩種方式實(shí)現(xiàn)，但是這兩種方式并非完全等價(jià)，各有各的價(jià)值。

第一種方式： 通過(guò)net_surgery給定，

這種方式最開(kāi)始出現(xiàn)在FCN中。https://github.com/shelhamer/fcn.berkeleyvision.org/blob/master/voc-fcn32s/solve.py
代碼如下：

import caffe import surgery, scoreimport numpy as np import os import systry:import setproctitlesetproctitle.setproctitle(os.path.basename(os.getcwd())) except:passweights = '../ilsvrc-nets/vgg16-fcn.caffemodel'# init caffe.set_device(int(sys.argv[1])) caffe.set_mode_gpu()solver = caffe.SGDSolver('solver.prototxt') solver.net.copy_from(weights)# surgeries （這里就是對(duì)于反卷積層的參數(shù)進(jìn)行初始化） interp_layers = [k for k in solver.net.params.keys() if 'up' in k] surgery.interp(solver.net, interp_layers)# scoring val = np.loadtxt('../data/segvalid11.txt', dtype=str)for _ in range(25):solver.step(4000)score.seg_tests(solver, False, val, layer='score')

上采樣的函數(shù)：

# make a bilinear interpolation kerneldef upsample_filt(self,size):factor = (size + 1) // 2if size % 2 == 1:center = factor - 1else:center = factor - 0.5og = np.ogrid[:size, :size]return (1 - abs(og[0] - center) / factor) * \(1 - abs(og[1] - center) / factor)# set parameters s.t. deconvolutional layers compute bilinear interpolation# N.B. this is for deconvolution without groupsdef interp_surgery(self,net, layers):for l in layers:print lm, k, h, w = net.params[l][0].data.shape #僅僅修改w，不需要修改bias，其為0print("deconv shape:\n")print m, k, h, w if m != k and k != 1:print 'input + output channels need to be the same or |output| == 1'raiseif h != w:print 'filters need to be square'raisefilt = self.upsample_filt(h)print(filt)net.params[l][0].data[range(m), range(k), :, :] = filt

第二種方式：直接在Deconvolution中給定參數(shù)weight_filler，即：

代碼如下:

layer {name: "fc8_upsample"type: "Deconvolution"bottom: "fc8"top: "fc8_upsample"param {lr_mult: 0decay_mult: 0}param {lr_mult: 0decay_mult: 0}convolution_param {num_output: 1kernel_size: 16stride: 8pad: 3weight_filler { # 這里相當(dāng)于上面的直接賦值type: "bilinear"}} }

weight_filler初始化成雙線性就等價(jià)于直接按照上面的方式賦值。

看起來(lái)好像以上兩種方法一樣，但是實(shí)際上有不同。主要區(qū)別在對(duì)于num_output>1的情形。

比如對(duì)于一個(gè)輸入是2個(gè)通道的map，希望對(duì)其進(jìn)行上采樣，自然我們希望分別對(duì)于map放大即可。如果使用Deconvolution，則shape大小為2,2,16,16（設(shè)其大小為16*16）.不考慮bias項(xiàng)。

假設(shè)按照上面的方式初始化，則對(duì)于第一種方法，得到結(jié)果：
[0,0,:,:]:

[[ 0.00390625 0.01171875 0.01953125 0.02734375 0.03515625 0.04296875
0.05078125 0.05859375 0.05859375 0.05078125 0.04296875 0.03515625
0.02734375 0.01953125 0.01171875 0.00390625]
[ 0.01171875 0.03515625 0.05859375 0.08203125 0.10546875 0.12890625
0.15234375 0.17578125 0.17578125 0.15234375 0.12890625 0.10546875
0.08203125 0.05859375 0.03515625 0.01171875]
[ 0.01953125 0.05859375 0.09765625 0.13671875 0.17578125 0.21484375
0.25390625 0.29296875 0.29296875 0.25390625 0.21484375 0.17578125
0.13671875 0.09765625 0.05859375 0.01953125]
[ 0.02734375 0.08203125 0.13671875 0.19140625 0.24609375 0.30078125
0.35546875 0.41015625 0.41015625 0.35546875 0.30078125 0.24609375
0.19140625 0.13671875 0.08203125 0.02734375]
[ 0.03515625 0.10546875 0.17578125 0.24609375 0.31640625 0.38671875
0.45703125 0.52734375 0.52734375 0.45703125 0.38671875 0.31640625
0.24609375 0.17578125 0.10546875 0.03515625]
[ 0.04296875 0.12890625 0.21484375 0.30078125 0.38671875 0.47265625
0.55859375 0.64453125 0.64453125 0.55859375 0.47265625 0.38671875
0.30078125 0.21484375 0.12890625 0.04296875]
[ 0.05078125 0.15234375 0.25390625 0.35546875 0.45703125 0.55859375
0.66015625 0.76171875 0.76171875 0.66015625 0.55859375 0.45703125
0.35546875 0.25390625 0.15234375 0.05078125]
[ 0.05859375 0.17578125 0.29296875 0.41015625 0.52734375 0.64453125
0.76171875 0.87890625 0.87890625 0.76171875 0.64453125 0.52734375
0.41015625 0.29296875 0.17578125 0.05859375]
[ 0.05859375 0.17578125 0.29296875 0.41015625 0.52734375 0.64453125
0.76171875 0.87890625 0.87890625 0.76171875 0.64453125 0.52734375
0.41015625 0.29296875 0.17578125 0.05859375]
[ 0.05078125 0.15234375 0.25390625 0.35546875 0.45703125 0.55859375
0.66015625 0.76171875 0.76171875 0.66015625 0.55859375 0.45703125
0.35546875 0.25390625 0.15234375 0.05078125]
[ 0.04296875 0.12890625 0.21484375 0.30078125 0.38671875 0.47265625
0.55859375 0.64453125 0.64453125 0.55859375 0.47265625 0.38671875
0.30078125 0.21484375 0.12890625 0.04296875]
[ 0.03515625 0.10546875 0.17578125 0.24609375 0.31640625 0.38671875
0.45703125 0.52734375 0.52734375 0.45703125 0.38671875 0.31640625
0.24609375 0.17578125 0.10546875 0.03515625]
[ 0.02734375 0.08203125 0.13671875 0.19140625 0.24609375 0.30078125
0.35546875 0.41015625 0.41015625 0.35546875 0.30078125 0.24609375
0.19140625 0.13671875 0.08203125 0.02734375]
[ 0.01953125 0.05859375 0.09765625 0.13671875 0.17578125 0.21484375
0.25390625 0.29296875 0.29296875 0.25390625 0.21484375 0.17578125
0.13671875 0.09765625 0.05859375 0.01953125]
[ 0.01171875 0.03515625 0.05859375 0.08203125 0.10546875 0.12890625
0.15234375 0.17578125 0.17578125 0.15234375 0.12890625 0.10546875
0.08203125 0.05859375 0.03515625 0.01171875]
[ 0.00390625 0.01171875 0.01953125 0.02734375 0.03515625 0.04296875
0.05078125 0.05859375 0.05859375 0.05078125 0.04296875 0.03515625
0.02734375 0.01953125 0.01171875 0.00390625]]
[0,1,:,:]:

[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
[1,0,:,:]：

[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
[1,1,:,:]:

[[ 0.00390625 0.01171875 0.01953125 0.02734375 0.03515625 0.04296875
0.05078125 0.05859375 0.05859375 0.05078125 0.04296875 0.03515625
0.02734375 0.01953125 0.01171875 0.00390625]
[ 0.01171875 0.03515625 0.05859375 0.08203125 0.10546875 0.12890625
0.15234375 0.17578125 0.17578125 0.15234375 0.12890625 0.10546875
0.08203125 0.05859375 0.03515625 0.01171875]
[ 0.01953125 0.05859375 0.09765625 0.13671875 0.17578125 0.21484375
0.25390625 0.29296875 0.29296875 0.25390625 0.21484375 0.17578125
0.13671875 0.09765625 0.05859375 0.01953125]
[ 0.02734375 0.08203125 0.13671875 0.19140625 0.24609375 0.30078125
0.35546875 0.41015625 0.41015625 0.35546875 0.30078125 0.24609375
0.19140625 0.13671875 0.08203125 0.02734375]
[ 0.03515625 0.10546875 0.17578125 0.24609375 0.31640625 0.38671875
0.45703125 0.52734375 0.52734375 0.45703125 0.38671875 0.31640625
0.24609375 0.17578125 0.10546875 0.03515625]
[ 0.04296875 0.12890625 0.21484375 0.30078125 0.38671875 0.47265625
0.55859375 0.64453125 0.64453125 0.55859375 0.47265625 0.38671875
0.30078125 0.21484375 0.12890625 0.04296875]
[ 0.05078125 0.15234375 0.25390625 0.35546875 0.45703125 0.55859375
0.66015625 0.76171875 0.76171875 0.66015625 0.55859375 0.45703125
0.35546875 0.25390625 0.15234375 0.05078125]
[ 0.05859375 0.17578125 0.29296875 0.41015625 0.52734375 0.64453125
0.76171875 0.87890625 0.87890625 0.76171875 0.64453125 0.52734375
0.41015625 0.29296875 0.17578125 0.05859375]
[ 0.05859375 0.17578125 0.29296875 0.41015625 0.52734375 0.64453125
0.76171875 0.87890625 0.87890625 0.76171875 0.64453125 0.52734375
0.41015625 0.29296875 0.17578125 0.05859375]
[ 0.05078125 0.15234375 0.25390625 0.35546875 0.45703125 0.55859375
0.66015625 0.76171875 0.76171875 0.66015625 0.55859375 0.45703125
0.35546875 0.25390625 0.15234375 0.05078125]
[ 0.04296875 0.12890625 0.21484375 0.30078125 0.38671875 0.47265625
0.55859375 0.64453125 0.64453125 0.55859375 0.47265625 0.38671875
0.30078125 0.21484375 0.12890625 0.04296875]
[ 0.03515625 0.10546875 0.17578125 0.24609375 0.31640625 0.38671875
0.45703125 0.52734375 0.52734375 0.45703125 0.38671875 0.31640625
0.24609375 0.17578125 0.10546875 0.03515625]
[ 0.02734375 0.08203125 0.13671875 0.19140625 0.24609375 0.30078125
0.35546875 0.41015625 0.41015625 0.35546875 0.30078125 0.24609375
0.19140625 0.13671875 0.08203125 0.02734375]
[ 0.01953125 0.05859375 0.09765625 0.13671875 0.17578125 0.21484375
0.25390625 0.29296875 0.29296875 0.25390625 0.21484375 0.17578125
0.13671875 0.09765625 0.05859375 0.01953125]
[ 0.01171875 0.03515625 0.05859375 0.08203125 0.10546875 0.12890625
0.15234375 0.17578125 0.17578125 0.15234375 0.12890625 0.10546875
0.08203125 0.05859375 0.03515625 0.01171875]
[ 0.00390625 0.01171875 0.01953125 0.02734375 0.03515625 0.04296875
0.05078125 0.05859375 0.05859375 0.05078125 0.04296875 0.03515625
0.02734375 0.01953125 0.01171875 0.00390625]]
而第二種方式全部都是[0,0,:,:]這樣的矩陣。

以上兩種方法應(yīng)該是第一種對(duì)的。因?yàn)镈econvolution 其實(shí)與卷積類(lèi)似，按照第一種結(jié)果才能分別單獨(dú)地對(duì)map上采樣，而采用第二種則將會(huì)得到兩個(gè)相同的map。（因?yàn)榫C合了兩個(gè)輸入map的信息）

因此結(jié)論： 對(duì)于多個(gè)輸入輸出的Deconvolution,采用方法1，對(duì)于單個(gè)輸入的，方法1,2通用。

附上Deconvolution的官方編碼：

說(shuō)明：
以上的稱(chēng)述有點(diǎn)瑕疵，其實(shí)caffe已經(jīng)解決了上述的問(wèn)題，我之前沒(méi)有好好留意。 關(guān)鍵就在group這個(gè)選項(xiàng)。
如果num_output>1,則填上group: c 再加上weight_filler: { type: “bilinear” }，即可完成初始化。

總結(jié)

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