（原）Non-local Neural Networks

转载请注明出处：

https://www.cnblogs.com/darkknightzh/p/12592351.html

论文：

https://arxiv.org/abs/1711.07971

第三方pytorch代码：

https://github.com/AlexHex7/Non-local_pytorch

1. non local操作

该论文定义了通用了non local操作：

${{\mathbf{y}}_{i}}=\frac{1}{C(\mathbf{x})}\sum\limits_{\forall j}{f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})g({{\mathbf{x}}_{j}})}$

其中i为需要计算响应的输出位置的索引，j为所有的位置。x为输入信号（图像，序列，视频等，通常为这些信号的特征），y为个x相同尺寸的输出信号。f为pairwise的函数，f计算当前i和所有j之间的关系，并得到一个标量。一元函数g计算输入信号在位置j的表征。（这段翻译起来怪怪的）。C(x)为归一化系数，用于归一化f和g的结果。

2. non local和其他操作的区别

① non local考虑到了所有的位置j。卷积操作仅考虑了当前位置的一个邻域（如核为3的一维卷积仅考虑了i-1<=j<=i+1）；循环操作通常只考虑当前和上一个时间，j=i或j=i-1.

② non local根据不同位置的关系计算响应，fc使用学习到的权重。换言之，fc中，${{\mathbf{x}}_{i}}$和${{\mathbf{x}}_{j}}$之间不是函数关系，而non local中则是函数关系。

③ non local支持输入不同尺寸，并且保持输出和输入相同的尺寸；fc则需要输入和输出均为固定的尺寸，并且丢失了位置关系。

④ non local可以用在网络的早期部分，fc通常用在网络最后。

 

3. f和g的形式

3.1 g的形式

为简单起见，只考虑g为线性形式，$g({{\mathbf{x}}_{j}})\text{=}{{W}_{g}}{{\mathbf{x}}_{j}}$，${{W}_{g}}$为需要学习的权重向量，在空域可以使用1*1conv实现，在空间时间域（如时间序列的图像）可以通过1*1*1的卷积实现。

3.2 f为gaussian

$f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})\text{=}{{e}^{\mathbf{x}_{i}^{T}{{\mathbf{x}}_{j}}}}$

其中$\mathbf{x}_{i}^{T}{{\mathbf{x}}_{j}}$为点乘，因为点乘在深度学习平台中更易实现（欧式距离也可以）。此时归一化系数$C(\mathbf{x})=\sum\nolimits_{\forall j}{f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})}$

3.3 f为embedded Gaussian

$f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})\text{=}{{e}^{\theta {{({{\mathbf{x}}_{i}})}^{T}}\phi ({{\mathbf{x}}_{j}})}}$

其中$\theta ({{\mathbf{x}}_{i}})\text{=}{{W}_{\theta }}{{\mathbf{x}}_{i}}$，$\phi ({{\mathbf{x}}_{j}})\text{=}{{W}_{\phi }}{{\mathbf{x}}_{j}}$，此时$C(\mathbf{x})=\sum\nolimits_{\forall j}{f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})}$

self attention模块和non local的关系：可以认为self attention为embedded Gaussian的特殊形式，如给定i，$\frac{1}{C(\mathbf{x})}f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})$沿着j维度变成了计算softmax。此时$\mathbf{y}=softmax({{\mathbf{x}}^{T}}W_{\theta }^{T}{{W}_{\phi }}\mathbf{x})g(\mathbf{x})$，即为self attention的形式。

3.4 点乘

f可以定义为点乘的相似度（此处使用embedded的形式）：

$f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})\text{=}\theta {{({{\mathbf{x}}_{i}})}^{T}}\phi ({{\mathbf{x}}_{j}})$

此时，归一化系数$C(\mathbf{x})=N$，N为x中所有位置的数量，而不是f的sum，这样可以简化梯度的计算。

点乘和embedded Gaussian的区别是是否使用了作为激活函数的softmax。

3.5 Concatenation

$f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})\text{=ReLU(w}_{f}^{T}[\theta ({{\mathbf{x}}_{i}}),\phi ({{\mathbf{x}}_{j}})]\text{)}$

其中$[\cdot \cdot ]$代表concatenation，即拼接。${{w}_{f}}$为权重向量，用于将拼接后的向量映射到一个标量。$C(\mathbf{x})=N$

4. Non local block

将之前公式的non local操作扩展成non local block，可以嵌入到目前的网络结构中，如下：

${{\mathbf{z}}_{i}}={{W}_{z}}{{\mathbf{y}}_{i}}+{{\mathbf{x}}_{i}}$

其中${{\mathbf{y}}_{i}}=\frac{1}{C(\mathbf{x})}\sum\limits_{\forall j}{f({{\mathbf{x}}_{i}},{{\mathbf{x}}_{j}})g({{\mathbf{x}}_{j}})}$，$+{{\mathbf{x}}_{i}}$代表残差连接。残差连接方便将non local block嵌入到之前与训练的模型中，避免打乱其初始行为（如将${{W}_{z}}$初始化为0）。

non local block如下图所示。3.2,3.3,3.4中的pairwise计算对应于下图中的矩阵乘法。在网络后面的特征图上，pairwise计算量比较小。

说明：

1. 若为图像，则使用1*1conv，且图中无T；若为视频，则使用1*1*1conv，且图中有T。

2. 图中softmax指对该矩阵每行计算softmax。

5. 降低计算量

5.1 降低x的通道数量

将${{W}_{g}}$，${{W}_{\theta }}$，${{W}_{\phi }}$降低为x的通道数量的一半，可以降低计算量。

5.2 对x下采样。

对x下采样，可以进一步降低计算量。

此时，1中的共识修改为${{\mathbf{y}}_{i}}=\frac{1}{C(\mathbf{\hat{x}})}\sum\limits_{\forall j}{f({{\mathbf{x}}_{i}},{{{\mathbf{\hat{x}}}}_{j}})g({{{\mathbf{\hat{x}}}}_{j}})}$，其中$\mathbf{\hat{x}}$为对x进行下采样后的输入（如pooling）。这种方式可以降低pariwsie计算到原来的1/4，一方面不影响non local的行为，另一方面，使得计算更加稀疏。可以通过在上图中$\phi $和$g$后面加一个max pooling来实现。

6. 代码：

6.1 embedded_gaussian

class _NonLocalBlockND(nn.Module):
    def __init__(self, in_channels, inter_channels=None, dimension=3, sub_sample=True, bn_layer=True):
        """
        :param in_channels:
        :param inter_channels:
        :param dimension:
        :param sub_sample:
        :param bn_layer:
        """

        super(_NonLocalBlockND, self).__init__()

        assert dimension in [1, 2, 3]

        self.dimension = dimension
        self.sub_sample = sub_sample

        self.in_channels = in_channels
        self.inter_channels = inter_channels

        if self.inter_channels is None:
            self.inter_channels = in_channels // 2
            if self.inter_channels == 0:
                self.inter_channels = 1

        if dimension == 3:
            conv_nd = nn.Conv3d
            max_pool_layer = nn.MaxPool3d(kernel_size=(1, 2, 2))
            bn = nn.BatchNorm3d
        elif dimension == 2:
            conv_nd = nn.Conv2d
            max_pool_layer = nn.MaxPool2d(kernel_size=(2, 2))
            bn = nn.BatchNorm2d
        else:
            conv_nd = nn.Conv1d
            max_pool_layer = nn.MaxPool1d(kernel_size=(2))
            bn = nn.BatchNorm1d

        self.g = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                         kernel_size=1, stride=1, padding=0)    # g函数，1*1conv，用于降维

        if bn_layer:
            self.W = nn.Sequential(    # 1*1conv，用于图2中变换到原始维度
                conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                        kernel_size=1, stride=1, padding=0),
                bn(self.in_channels)
            )
            nn.init.constant_(self.W[1].weight, 0)
            nn.init.constant_(self.W[1].bias, 0)
        else:
            self.W = conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                             kernel_size=1, stride=1, padding=0)   # 1*1conv，用于图2中变换到原始维度
            nn.init.constant_(self.W.weight, 0)
            nn.init.constant_(self.W.bias, 0)

        self.theta = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                             kernel_size=1, stride=1, padding=0)   # θ函数，1*1conv，用于降维
        self.phi = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                           kernel_size=1, stride=1, padding=0)    # φ函数，1*1conv，用于降维

        if sub_sample:
            self.g = nn.Sequential(self.g, max_pool_layer)
            self.phi = nn.Sequential(self.phi, max_pool_layer)

    def forward(self, x, return_nl_map=False): 
        """
        :param x: (b, c, t, h, w)
        :param return_nl_map: if True return z, nl_map, else only return z.
        :return:
        """
        # 令x维度B*C*(K):一维时，x为B*C*(K1)；二维时，x为B*C*(K1*K2)；三维时，x为B*C*(K1*K2*K3)
        batch_size = x.size(0)   # batchsize

        g_x = self.g(x).view(batch_size, self.inter_channels, -1)   # 通过g函数，并reshape，得到B*inter_channels*(K)矩阵
        g_x = g_x.permute(0, 2, 1)   # 得到B*(K)*inter_channels矩阵，和图2中一致

        theta_x = self.theta(x).view(batch_size, self.inter_channels, -1)   # 通过θ函数，并reshape，得到B*inter_channels*(K)矩阵
        theta_x = theta_x.permute(0, 2, 1)   # 得到B*(K)*inter_channels矩阵，和图2中一致
        phi_x = self.phi(x).view(batch_size, self.inter_channels, -1)   # 通过φ函数，并reshape，得到B*inter_channels*(K)矩阵
        f = torch.matmul(theta_x, phi_x)    # 得到B*(K)*(K)矩阵，和图2中一致
        f_div_C = F.softmax(f, dim=-1)      # 通过softmax，对最后一维归一化，得到归一化的特征，即概率,B*(K)*(K)

        y = torch.matmul(f_div_C, g_x)      # 得到B*(K)*inter_channels矩阵，和图2中一致
        y = y.permute(0, 2, 1).contiguous() # 得到B*inter_channels*(K)矩阵，和图2中一致
        y = y.view(batch_size, self.inter_channels, *x.size()[2:])  # 得到B*inter_channels*(K1或K1*K2或K1*K2*K3)矩阵，和图2中一致
        W_y = self.W(y)  # 得到B*C*(K)矩阵，和图2中一致
        z = W_y + x   # 特征图和non local的图相加，得到新的特征图，B*C*(K)

        if return_nl_map:  
            return z, f_div_C   # 返回结果及归一化的特征
        return z


class NONLocalBlock1D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock1D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=1, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


class NONLocalBlock2D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock2D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=2, sub_sample=sub_sample,
                                              bn_layer=bn_layer,)


class NONLocalBlock3D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock3D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=3, sub_sample=sub_sample,
                                              bn_layer=bn_layer,)


if __name__ == '__main__':
    import torch

    for (sub_sample_, bn_layer_) in [(True, True), (False, False), (True, False), (False, True)]:
        img = torch.zeros(2, 3, 20)
        net = NONLocalBlock1D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

        img = torch.zeros(2, 3, 20, 20)
        net = NONLocalBlock2D(3, sub_sample=sub_sample_, bn_layer=bn_layer_, store_last_batch_nl_map=True)
        out = net(img)
        print(out.size())

        img = torch.randn(2, 3, 8, 20, 20)
        net = NONLocalBlock3D(3, sub_sample=sub_sample_, bn_layer=bn_layer_, store_last_batch_nl_map=True)
        out = net(img)
        print(out.size())

6.2 embedded Gaussian和点乘的区别

点乘代码：

class _NonLocalBlockND(nn.Module):
    def __init__(self, in_channels, inter_channels=None, dimension=3, sub_sample=True, bn_layer=True):
        super(_NonLocalBlockND, self).__init__()

        assert dimension in [1, 2, 3]

        self.dimension = dimension
        self.sub_sample = sub_sample

        self.in_channels = in_channels
        self.inter_channels = inter_channels

        if self.inter_channels is None:
            self.inter_channels = in_channels // 2
            if self.inter_channels == 0:
                self.inter_channels = 1

        if dimension == 3:
            conv_nd = nn.Conv3d
            max_pool_layer = nn.MaxPool3d(kernel_size=(1, 2, 2))
            bn = nn.BatchNorm3d
        elif dimension == 2:
            conv_nd = nn.Conv2d
            max_pool_layer = nn.MaxPool2d(kernel_size=(2, 2))
            bn = nn.BatchNorm2d
        else:
            conv_nd = nn.Conv1d
            max_pool_layer = nn.MaxPool1d(kernel_size=(2))
            bn = nn.BatchNorm1d

        self.g = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                         kernel_size=1, stride=1, padding=0)

        if bn_layer:
            self.W = nn.Sequential(
                conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                        kernel_size=1, stride=1, padding=0),
                bn(self.in_channels)
            )
            nn.init.constant_(self.W[1].weight, 0)
            nn.init.constant_(self.W[1].bias, 0)
        else:
            self.W = conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                             kernel_size=1, stride=1, padding=0)
            nn.init.constant_(self.W.weight, 0)
            nn.init.constant_(self.W.bias, 0)

        self.theta = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                             kernel_size=1, stride=1, padding=0)

        self.phi = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                           kernel_size=1, stride=1, padding=0)

        if sub_sample:
            self.g = nn.Sequential(self.g, max_pool_layer)
            self.phi = nn.Sequential(self.phi, max_pool_layer)

    def forward(self, x, return_nl_map=False):
        """
        :param x: (b, c, t, h, w)
        :param return_nl_map: if True return z, nl_map, else only return z.
        :return:
        """
        # 令x维度B*C*(K):一维时，x为B*C*(K1)；二维时，x为B*C*(K1*K2)；三维时，x为B*C*(K1*K2*K3)
        batch_size = x.size(0)

        g_x = self.g(x).view(batch_size, self.inter_channels, -1)    # 通过g函数，并reshape，得到B*inter_channels*(K)矩阵
        g_x = g_x.permute(0, 2, 1)   # 得到B*(K)*inter_channels矩阵，和图2中一致

        theta_x = self.theta(x).view(batch_size, self.inter_channels, -1)   # 通过θ函数，并reshape，得到B*inter_channels*(K)矩阵
        theta_x = theta_x.permute(0, 2, 1)    # 得到B*(K)*inter_channels矩阵，和图2中一致
        phi_x = self.phi(x).view(batch_size, self.inter_channels, -1)    # 通过φ函数，并reshape，得到B*inter_channels*(K)矩阵
        f = torch.matmul(theta_x, phi_x)     # 得到B*(K)*(K)矩阵，和图2中一致
        N = f.size(-1)   # 最后一维的维度
        f_div_C = f / N  # 对最后一维归一化

        y = torch.matmul(f_div_C, g_x)    # 得到B*(K)*inter_channels矩阵，和图2中一致
        y = y.permute(0, 2, 1).contiguous()   # 得到B*inter_channels*(K)矩阵，和图2中一致
        y = y.view(batch_size, self.inter_channels, *x.size()[2:])   # 得到B*inter_channels*(K1或K1*K2或K1*K2*K3)矩阵，和图2中一致
        W_y = self.W(y) # 得到B*C*(K)矩阵，和图2中一致
        z = W_y + x   # 特征图和non local的图相加，得到新的特征图，B*C*(K)

        if return_nl_map:
            return z, f_div_C  # 返回结果及归一化的特征
        return z


class NONLocalBlock1D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock1D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=1, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


class NONLocalBlock2D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock2D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=2, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


class NONLocalBlock3D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock3D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=3, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


if __name__ == '__main__':
    import torch

    for (sub_sample_, bn_layer_) in [(True, True), (False, False), (True, False), (False, True)]:
        img = torch.zeros(2, 3, 20)
        net = NONLocalBlock1D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

        img = torch.zeros(2, 3, 20, 20)
        net = NONLocalBlock2D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

        img = torch.randn(2, 3, 8, 20, 20)
        net = NONLocalBlock3D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

左侧为embedded Gaussian，右侧为点乘

 

6.3 embedded Gaussian和Gaussian的区别

左侧为embedded Gaussian，右侧为Gaussian

初始化：

forward：

6.4 embedded Gaussian和Concatenation的区别

Concatenation代码：

class _NonLocalBlockND(nn.Module):
    def __init__(self, in_channels, inter_channels=None, dimension=3, sub_sample=True, bn_layer=True):
        super(_NonLocalBlockND, self).__init__()

        assert dimension in [1, 2, 3]

        self.dimension = dimension
        self.sub_sample = sub_sample

        self.in_channels = in_channels
        self.inter_channels = inter_channels

        if self.inter_channels is None:
            self.inter_channels = in_channels // 2
            if self.inter_channels == 0:
                self.inter_channels = 1

        if dimension == 3:
            conv_nd = nn.Conv3d
            max_pool_layer = nn.MaxPool3d(kernel_size=(1, 2, 2))
            bn = nn.BatchNorm3d
        elif dimension == 2:
            conv_nd = nn.Conv2d
            max_pool_layer = nn.MaxPool2d(kernel_size=(2, 2))
            bn = nn.BatchNorm2d
        else:
            conv_nd = nn.Conv1d
            max_pool_layer = nn.MaxPool1d(kernel_size=(2))
            bn = nn.BatchNorm1d

        self.g = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                         kernel_size=1, stride=1, padding=0)

        if bn_layer:
            self.W = nn.Sequential(
                conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                        kernel_size=1, stride=1, padding=0),
                bn(self.in_channels)
            )
            nn.init.constant_(self.W[1].weight, 0)
            nn.init.constant_(self.W[1].bias, 0)
        else:
            self.W = conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
                             kernel_size=1, stride=1, padding=0)
            nn.init.constant_(self.W.weight, 0)
            nn.init.constant_(self.W.bias, 0)

        self.theta = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                             kernel_size=1, stride=1, padding=0)

        self.phi = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
                           kernel_size=1, stride=1, padding=0)

        self.concat_project = nn.Sequential(   # 将concat后的特征降维到1维的矩阵
            nn.Conv2d(self.inter_channels * 2, 1, 1, 1, 0, bias=False),
            nn.ReLU()
        )

        if sub_sample:
            self.g = nn.Sequential(self.g, max_pool_layer)
            self.phi = nn.Sequential(self.phi, max_pool_layer)

    def forward(self, x, return_nl_map=False):
        '''
        :param x: (b, c, t, h, w)
        :param return_nl_map: if True return z, nl_map, else only return z.
        :return:
        '''
        # 令x维度B*C*(K):一维时，x为B*C*(K1)；二维时，x为B*C*(K1*K2)；三维时，x为B*C*(K1*K2*K3)
        batch_size = x.size(0)

        g_x = self.g(x).view(batch_size, self.inter_channels, -1)   # 通过g函数，并reshape，得到B*inter_channels*(K)矩阵
        g_x = g_x.permute(0, 2, 1)  # 得到B*(K)*inter_channels矩阵，和图2中一致

        # (b, c, N, 1)
        theta_x = self.theta(x).view(batch_size, self.inter_channels, -1, 1)  # 通过θ函数，并reshape，得到B*inter_channels*(K)*1矩阵
        # (b, c, 1, N)
        phi_x = self.phi(x).view(batch_size, self.inter_channels, 1, -1) # 通过φ函数，并reshape，得到B*inter_channels*1*(K)矩阵

        h = theta_x.size(2)  # (K)
        w = phi_x.size(3)  # (K)
        theta_x = theta_x.repeat(1, 1, 1, w)  # B*inter_channels*(K)*(K)
        phi_x = phi_x.repeat(1, 1, h, 1)     # B*inter_channels*(K)*(K)

        concat_feature = torch.cat([theta_x, phi_x], dim=1)  # B*(2*inter_channels)*(K)*(K)
        f = self.concat_project(concat_feature)    # B*1*(K)*(K)
        b, _, h, w = f.size()  # B,_,(K),(K)
        f = f.view(b, h, w)   # B*(K)*(K)

        N = f.size(-1)  # (K)
        f_div_C = f / N   # 最后一维归一化，B*(K)*(K)

        y = torch.matmul(f_div_C, g_x)    # 得到B*(K)*inter_channels矩阵，和图2中一致
        y = y.permute(0, 2, 1).contiguous()# 得到B*inter_channels*(K)矩阵，和图2中一致
        y = y.view(batch_size, self.inter_channels, *x.size()[2:])  # 得到B*inter_channels*(K1或K1*K2或K1*K2*K3)矩阵，和图2中一致
        W_y = self.W(y)  # 得到B*C*(K)矩阵，和图2中一致
        z = W_y + x   # 特征图和non local的图相加，得到新的特征图，B*C*(K)

        if return_nl_map:
            return z, f_div_C    # 返回结果及归一化的特征
        return z


class NONLocalBlock1D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock1D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=1, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


class NONLocalBlock2D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True):
        super(NONLocalBlock2D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=2, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


class NONLocalBlock3D(_NonLocalBlockND):
    def __init__(self, in_channels, inter_channels=None, sub_sample=True, bn_layer=True,):
        super(NONLocalBlock3D, self).__init__(in_channels,
                                              inter_channels=inter_channels,
                                              dimension=3, sub_sample=sub_sample,
                                              bn_layer=bn_layer)


if __name__ == '__main__':
    import torch

    for (sub_sample_, bn_layer_) in [(True, True), (False, False), (True, False), (False, True)]:
        img = torch.zeros(2, 3, 20)
        net = NONLocalBlock1D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

        img = torch.zeros(2, 3, 20, 20)
        net = NONLocalBlock2D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

        img = torch.randn(2, 3, 8, 20, 20)
        net = NONLocalBlock3D(3, sub_sample=sub_sample_, bn_layer=bn_layer_)
        out = net(img)
        print(out.size())

左侧为embedded Gaussian，右侧为Concatenation

初始化：

forward：