原文地址：https://arxiv.org/pdf/1711.07971.pdf
代码地址：https://github.com/facebookresearch/video-nonlocal-net
PyTorch实现：https://github.com/AlexHex7/Non-local_pytorch

原理

原理有点类似于Transformer的self-attention，如图所示，我们输入的维度为 H W C HWC HWC，通过1*1的卷积我们得到 θ \theta θ的维度为 H W C 2 HW\frac{C}{2} HW2C​， ϕ \phi ϕ的维度也为 H W C 2 HW\frac{C}{2} HW2C​，将二者矩阵相乘得到 H W × H W HW\times HW HW×HW，这里和Self-attention好像不太一样？Transformer中的self-attention好像是特征进行attention，而这里是channel进行了attention

代码讲解

Non-local的PyTorch实现有四个版本，这里描述Embed Gaussian版本，我们只对二维图片进行处理，所以这里代码把1D和3D的给删除，如下所示

class _NonLocalBlockND(nn.Module):
    def __init__(self, in_channels, inter_channels=None, dimension=2, 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

        conv_nd = nn.Conv2d
        max_pool_layer = nn.MaxPool2d(kernel_size=(2, 2))
        bn = nn.BatchNorm2d

        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(
            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:
        '''

        batch_size = x.size(0)

        g_x = self.g(x).view(batch_size, self.inter_channels, -1)
        g_x = g_x.permute(0, 2, 1)

        # (b, c, N, 1)
        theta_x = self.theta(x).view(batch_size, self.inter_channels, -1, 1)
        # (b, c, 1, N)
        phi_x = self.phi(x).view(batch_size, self.inter_channels, 1, -1)

        h = theta_x.size(2)
        w = phi_x.size(3)
        theta_x = theta_x.repeat(1, 1, 1, w)
        phi_x = phi_x.repeat(1, 1, h, 1)

        concat_feature = torch.cat([theta_x, phi_x], dim=1)
        f = self.concat_project(concat_feature)
        b, _, h, w = f.size()
        f = f.view(b, h, w)

        N = f.size(-1)
        f_div_C = f / N

        y = torch.matmul(f_div_C, g_x)
        y = y.permute(0, 2, 1).contiguous()
        y = y.view(batch_size, self.inter_channels, *x.size()[2:])
        W_y = self.W(y)
        z = W_y + x

        if return_nl_map:
            return z, f_div_C
        return z