可变形卷积DCNv1 & DCNv2
✨✨✨论文及代码详解——可变形卷积（DCNv1）
✨✨✨论文及代码详解——可变形卷积（DCNv2）
DCNv3 是InternImage中提出的，DCNv3在DCNv2版本上进行了改进。
✨✨✨论文详解——《InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions》
InterImage官方代码： https://github.com/OpenGVLab/InternImage

概述

如下图，首先下载InterImage官方代码，然后在segmentation、detection、classification文件夹下均可以找到ops_dcnv3文件夹，该文件夹下的内容就是实现DCNv3算子的核心代码。

• modules
  如下图所示, modules文件夹中的dcnv3.py文件主要定义了DCNv3模块。
  其中DCNv3_pytorch是DCNv3的pytorch实现版本，DCNv3是DCNv3的C++实现版本。
  
• functions
  如下图所示，function文件夹中的dcnv3_func.py文件定义了DCNv3的一些核心操作。
  其中黄色部分的DCNv3Function类被c++版本的DCNv3 调用。
  其中红色部分的dcnv3_core_pytorch方法被pytorch版本的DCNv3_pytorch调用。
  
• src
  src下的代码是用C++来实现DCNv3中核心操作，其下的cpu和cuda分别表示cpu和cuda编程两种实现版本。c++实现的版本需要去编译，否则如上图所示，黄色箭头指向的import DCNv3 有红色波浪线，无法正常导入。
  如果想import DCNv3成功，有两种解决办法：
  （1）需要编译：DCNv3具体编译方法是直接运行make.sh文件（但是这种方法很容易编译失败，对于pytorch,cuda的版本以及c++编译器的配置都有要求）
  （2）不需要编译：去官网上下载轮子https://github.com/OpenGVLab/InternImage/releases/tag/whl_files （更推荐这种方法，但是也需要注意cuda和pytorch的版本）
  
  本文重点介绍DCNv3的pytorch实现部分。

dcnv3.py

to_channels_first

• 功能：将通道维度放在前面，输入(b,h,w,c),输出(b,c,h,w)

# 将通道维度放在前面：(b,h,w,c)->(b,c,h,w)
class to_channels_first(nn.Module):

    def __init__(self):
        super().__init__()

    def forward(self, x): # (b,h,w,c)
        return x.permute(0, 3, 1, 2) #(b,c,h,w)

to_channels_last

• 功能：将通道维度放在后面，输入 (b,c,h,w),输出(b,h,w,c)

# 将通道维度放在后面 (b,c,h,w)->(b,h,w,c)
class to_channels_last(nn.Module):

    def __init__(self):
        super().__init__()

    def forward(self, x): # (b,c,h,w)
        return x.permute(0, 2, 3, 1) # (b,h,w,c)

build_norm_layer

• 功能：构建归一化层，可以选择Batch Norm或者Layer Norm

def build_norm_layer(dim,
                     norm_layer,
                     in_format='channels_last',
                     out_format='channels_last',
                     eps=1e-6):
    layers = []
    if norm_layer == 'BN':
        if in_format == 'channels_last':
            layers.append(to_channels_first())
        layers.append(nn.BatchNorm2d(dim))
        if out_format == 'channels_last':
            layers.append(to_channels_last())
    elif norm_layer == 'LN':
        if in_format == 'channels_first':
            layers.append(to_channels_last()) # (b,c,h,w)->(b,h,w,c)
        layers.append(nn.LayerNorm(dim, eps=eps))
        if out_format == 'channels_first':
            layers.append(to_channels_first())
    else:
        raise NotImplementedError(
            f'build_norm_layer does not support {norm_layer}')
    return nn.Sequential(*layers)

build_act_layer

• 功能：构建激活函数层，可选择RELU / SiLU / GELU激活函数

def build_act_layer(act_layer):
    if act_layer == 'ReLU':
        return nn.ReLU(inplace=True)
    elif act_layer == 'SiLU':
        return nn.SiLU(inplace=True)
    elif act_layer == 'GELU':
        return nn.GELU()

    raise NotImplementedError(f'build_act_layer does not support {act_layer}')

_is_power_of_2

• 功能：检查n是否是2的某次方，且n不为0
  如果n & (n - 1)为0，则说明n是2的某次方。

def _is_power_of_2(n):
    if (not isinstance(n, int)) or (n < 0): # 如果n不为整数或者n小于0
        raise ValueError(
            "invalid input for _is_power_of_2: {} (type: {})".format(n, type(n)))

    return (n & (n - 1) == 0) and n != 0

CenterFeatureScaleModule

• 功能：生成缩放系数。
  F.linear的输出取决于传入的实参weight和bias，然后再通过sigmod函数归一化。

class CenterFeatureScaleModule(nn.Module):
    def forward(self,
                query,
                center_feature_scale_proj_weight, # (group,channels)
                center_feature_scale_proj_bias):
        center_feature_scale = F.linear(query,
                                        weight=center_feature_scale_proj_weight,
                                        bias=center_feature_scale_proj_bias).sigmoid() # 全连接层+sigmod
        # F.linear的输出取决于传入的实参weight和bias
        # 输入:(*,channels) -> 输出：(*,group)
        return center_feature_scale

DCNv3_pytorch

class DCNv3_pytorch 是分组可变形卷积DCNv3的pytorch的实现版。

'''分组可变形卷积 pytorch实现版'''
class DCNv3_pytorch(nn.Module):
    def __init__(
            self,
            channels=64, # 通道数
            kernel_size=3, # 卷积核大小
            dw_kernel_size=None, # 深度可分离卷积核大小
            stride=1, # 步长
            pad=1, # 填充
            dilation=1, #空洞率
            group=4,# 分组数
            offset_scale=1.0, 
            act_layer='GELU', # 激活函数
            norm_layer='LN', # 归一化层
            center_feature_scale=False):

        super().__init__()
        if channels % group != 0: # 分组卷积必须保证通道数可以被组数整除
            raise ValueError(
                f'channels must be divisible by group, but got {channels} and {group}')
        _d_per_group = channels // group # 每个组数拥有的通道数
        dw_kernel_size = dw_kernel_size if dw_kernel_size is not None else kernel_size # 设置深度可分离卷积核的大小
        # 最好把_d_per_group设置为2的某次方，方便cuda的具体实现
        if not _is_power_of_2(_d_per_group):
            warnings.warn(
                "You'd better set channels in DCNv3 to make the dimension of each attention head a power of 2 "
                "which is more efficient in our CUDA implementation.")

        self.offset_scale = offset_scale
        self.channels = channels
        self.kernel_size = kernel_size
        self.dw_kernel_size = dw_kernel_size
        self.stride = stride
        self.dilation = dilation
        self.pad = pad
        self.group = group
        self.group_channels = channels // group
        self.offset_scale = offset_scale
        self.center_feature_scale = center_feature_scale
        
        # 深度可分离卷积
        self.dw_conv = nn.Sequential(
            # depth-wise 逐通道卷积
            # H_out=H_in+2*padding-(kernel_size-1) 
            nn.Conv2d(
                channels,
                channels, # 输入输出的通道数不变
                kernel_size=dw_kernel_size,
                stride=1,
                padding=(dw_kernel_size - 1) // 2, # 输出大小不变
                groups=channels), # 分组数和输入通道数相等，也就实现了逐通道的卷积 ！！！
            # 归一化层
            build_norm_layer(
                channels,
                norm_layer,
                'channels_first', #如果是LN, (b,c,h,w)->(b,h,w,c)
                'channels_last'),
            # 激活层
            build_act_layer(act_layer))
            
        self.offset = nn.Linear( # offset： 偏移量
            channels,
            group * kernel_size * kernel_size * 2) # 输出通道数：group*2*kernel_size*kernel_size
            
        self.mask = nn.Linear( # mask: 调制标量
            channels,
            group * kernel_size * kernel_size) # 输出通道数：group*kernel_size*kernel_size
            
        self.input_proj = nn.Linear(channels, channels) # Linear层，输入输出通道数不变
        self.output_proj = nn.Linear(channels, channels) # Linear层，输入输出通道数不变
        self._reset_parameters() # 参数初始化
        
        if center_feature_scale: # 如果需要对特征图进行缩放
            self.center_feature_scale_proj_weight = nn.Parameter(
                torch.zeros((group, channels), dtype=torch.float)) # weighit:大小为(group,channels)的全0 Tensor
            self.center_feature_scale_proj_bias = nn.Parameter(
                torch.tensor(0.0, dtype=torch.float).view((1,)).repeat(group, )) # bias: 大小为(group)的全0 tensor
            self.center_feature_scale_module = CenterFeatureScaleModule()# (*,channels)->(*,groups)

---

_reset_parameters

• 功能：初始化参数，将bias设置为0，weights采用xavier_uniform_ 分布进行初始化。

    # 参数初始化
    def _reset_parameters(self):
        constant_(self.offset.weight.data, 0.)
        constant_(self.offset.bias.data, 0.)
        constant_(self.mask.weight.data, 0.)
        constant_(self.mask.bias.data, 0.)
        xavier_uniform_(self.input_proj.weight.data)
        constant_(self.input_proj.bias.data, 0.)
        xavier_uniform_(self.output_proj.weight.data)
        constant_(self.output_proj.bias.data, 0.)

---

forward
功能：前向传播

    def forward(self, input): # (N,H,W,C)
        N, H, W, _ = input.shape
        x = self.input_proj(input) #Linear层，通道不变 x: (N,H,W,C)
        x_proj = x
        x1 = input.permute(0, 3, 1, 2) # x1: (N,C,H,W)
        '''
        改进点1：将原始卷积权值w_k分离为depth-wise和point-wise两部分，其中depth-wise部分由原始的location-aware modulation scalar m_k负责，point-wise部分是采样点之间的共享投影权值w。
        '''
        # DW_conv(逐通道卷积)+Norm+Act
        x1 = self.dw_conv(x1) # (N,H,W,C)
        ''' 
        改进点2：我们将空间聚集过程分成G组，每个组都有单独的采样偏移offset和调制规模mask
        因此在一个卷积层上的不同组可以有不同的空间聚集模式，从而为下游任务带来更强的特征。
        '''
        offset = self.offset(x1) #生成偏移 (N,H,W,group*2*kernel_size*kernel_size)
        mask = self.mask(x1).reshape(N, H, W, self.group, -1) # mask 表示调制标量
        # mask后：(N,H,W,group*kernel_size*kernel_size)
        # reshape后：(N,H,W,group,kernel_size*kernel_size)
        mask = F.softmax(mask, -1).reshape(N, H, W, -1)  # (N,H,W,group*kernel_size*kernel_size)
        # softmax的dim=-1,表示在kernel_size*kernel_size个样本点进行归一化，其和等于1。
        '''
        改进点3：我们将基于element-wise的sigmoid归一化改为基于样本点的softmax归一化。这样，将调制标量的和限制为1，使得不同尺度下模型的训练过程更加稳定。
        '''
        x = dcnv3_core_pytorch( # 可变形卷积的核心代码
            x, offset, mask, 
            # x: (N,H,W,C) 
            # offset: (N,H,W,group*2*kernel_size*kernel_size)
            # mask: (N,H,W,group*kernel_size*kernel_size)
            self.kernel_size, self.kernel_size,
            self.stride, self.stride,
            self.pad, self.pad,
            self.dilation, self.dilation,
            self.group, self.group_channels,
            self.offset_scale) # (N_, H_out, W_out,group*group_channels)

        if self.center_feature_scale: # 如果需要特征缩放
            center_feature_scale = self.center_feature_scale_module(
                x1, self.center_feature_scale_proj_weight, self.center_feature_scale_proj_bias)
            # x1：(N,H,W,C) ->(N,H,W,groups)
            center_feature_scale = center_feature_scale[..., None].repeat(
                1, 1, 1, 1, self.channels // self.group).flatten(-2)
            #  (N, H, W, groups) -> (N, H, W, groups, 1) -> (N, H, W, groups, _d_per_group) -> (N, H, W, channels)
            x = x * (1 - center_feature_scale) + x_proj * center_feature_scale
            # x_proj和x按照一定的系数相加
        x = self.output_proj(x) # (N,H,W,C)
        return x

在forward函数中体现了InterImage论文中提出的三个改进点。

• 改进点1：将原始卷积权值w_k分离为depth-wise和point-wise两部分，其中depth-wise部分由原始的location-aware modulation scalar m_k负责，point-wise部分是采样点之间的共享投影权值w。
  如下图所示，DCNv3的实现代码offset和mask是由经过dw_conv的depth-wise convolution得到的x1生成，但是一同输入dcnv3的是原始的x_proj。
  
  如下图是DCNv2的实现代码，其中它的m(mask)和offset 是原始输入x分别通过普通卷积p_conv和m_conv生成。
  
  假设卷积核的大小是(kernel_h,kernel_w), 输入的大小是(c_in,h,w)。卷积核需要滑动t次。
  那么普通卷积需要的总乘法运算数是c_out*kernel_h*kernel_w*c_in*t
  而depth-wise 卷积需要的总乘法数是kernel_h*kernel_w*c_in*t， 相比下减少了c_out倍。
  因此用dw_conv生成offset和mask，可以提升模型的效率。

• 改进点2：我们将空间聚集过程分成$G$组，每个组都有单独的采样偏移$∆p_{gk}$和调制规模$m_{gk}$，
  DCNv3生成的mask大小是(N,H,W,group*kernel_size*kernel_size), offset的大小是(N,H,W,2*group*kernel_size*kernel_size)，每个组都有不同的采样偏移和调制规模。
  而DCNv2生成的mask大小是(N,H,W,kernel_size*kernel_size), offset的大小是(N,H,W,2*kernel_size*kernel_size)。

• 改进点3：将基于element-wise的sigmoid归一化改为基于样本点的softmax归一化。
  如下图，DCNv3的softmax函数在最后一个维度上进行归一化，保证了最后一个维度的kernel_size*kernel_size个元素的和为1。
  
  如下图所示，DCNv2的softmax函数只是将所有的element通过sigmod 函数，保证每个element的值在[0,1]范围内。
  

DCNv3

DCNv3是C++实现版本，唯一和DCNv3_pytorch不同的是, dcnv3_core_pytorch 被替换成了DCNv3Function类中的apply函数（这个是dcnv3_func.py中定义的autograd function）。

'''分组可变形卷积 C++实现版'''
class DCNv3(nn.Module):
    def __init__(
            self,
            channels=64,
            kernel_size=3,
            dw_kernel_size=None,
            stride=1,
            pad=1,
            dilation=1,
            group=4,
            offset_scale=1.0,
            act_layer='GELU',
            norm_layer='LN',
            center_feature_scale=False):
        """
        DCNv3 Module
        :param channels
        :param kernel_size
        :param stride
        :param pad
        :param dilation
        :param group
        :param offset_scale
        :param act_layer
        :param norm_layer
        """
        super().__init__()
        if channels % group != 0:
            raise ValueError(
                f'channels must be divisible by group, but got {channels} and {group}')
        _d_per_group = channels // group
        dw_kernel_size = dw_kernel_size if dw_kernel_size is not None else kernel_size
        # you'd better set _d_per_group to a power of 2 which is more efficient in our CUDA implementation
        if not _is_power_of_2(_d_per_group):
            warnings.warn(
                "You'd better set channels in DCNv3 to make the dimension of each attention head a power of 2 "
                "which is more efficient in our CUDA implementation.")

        self.offset_scale = offset_scale
        self.channels = channels
        self.kernel_size = kernel_size
        self.dw_kernel_size = dw_kernel_size
        self.stride = stride
        self.dilation = dilation
        self.pad = pad
        self.group = group
        self.group_channels = channels // group
        self.offset_scale = offset_scale
        self.center_feature_scale = center_feature_scale
        
        self.dw_conv = nn.Sequential(
            nn.Conv2d(
                channels,
                channels,
                kernel_size=dw_kernel_size,
                stride=1,
                padding=(dw_kernel_size - 1) // 2,
                groups=channels),
            build_norm_layer(
                channels,
                norm_layer,
                'channels_first',
                'channels_last'),
            build_act_layer(act_layer))
        self.offset = nn.Linear(
            channels,
            group * kernel_size * kernel_size * 2)
        self.mask = nn.Linear(
            channels,
            group * kernel_size * kernel_size)
        self.input_proj = nn.Linear(channels, channels)
        self.output_proj = nn.Linear(channels, channels)
        self._reset_parameters()
        
        if center_feature_scale:
            self.center_feature_scale_proj_weight = nn.Parameter(
                torch.zeros((group, channels), dtype=torch.float))
            self.center_feature_scale_proj_bias = nn.Parameter(
                torch.tensor(0.0, dtype=torch.float).view((1,)).repeat(group, ))
            self.center_feature_scale_module = CenterFeatureScaleModule()

    def _reset_parameters(self):
        constant_(self.offset.weight.data, 0.)
        constant_(self.offset.bias.data, 0.)
        constant_(self.mask.weight.data, 0.)
        constant_(self.mask.bias.data, 0.)
        xavier_uniform_(self.input_proj.weight.data)
        constant_(self.input_proj.bias.data, 0.)
        xavier_uniform_(self.output_proj.weight.data)
        constant_(self.output_proj.bias.data, 0.)

    def forward(self, input):
        """
        :param query                       (N, H, W, C)
        :return output                     (N, H, W, C)
        """
        N, H, W, _ = input.shape

        x = self.input_proj(input)
        x_proj = x
        dtype = x.dtype

        x1 = input.permute(0, 3, 1, 2)
        x1 = self.dw_conv(x1)
        offset = self.offset(x1)
        mask = self.mask(x1).reshape(N, H, W, self.group, -1)
        mask = F.softmax(mask, -1).reshape(N, H, W, -1).type(dtype)

        x = DCNv3Function.apply(  # ！！！
            x, offset, mask,
            self.kernel_size, self.kernel_size,
            self.stride, self.stride,
            self.pad, self.pad,
            self.dilation, self.dilation,
            self.group, self.group_channels,
            self.offset_scale,
            256)
        
        if self.center_feature_scale:
            center_feature_scale = self.center_feature_scale_module(
                x1, self.center_feature_scale_proj_weight, self.center_feature_scale_proj_bias)
            # N, H, W, groups -> N, H, W, groups, 1 -> N, H, W, groups, _d_per_group -> N, H, W, channels
            center_feature_scale = center_feature_scale[..., None].repeat(
                1, 1, 1, 1, self.channels // self.group).flatten(-2)
            x = x * (1 - center_feature_scale) + x_proj * center_feature_scale
        x = self.output_proj(x)

        return x

dcnv3_func.py

DCNv3Function

DCNv3Function是一个自定义的autograd function, 用于C++实现的DCNv3。

class DCNv3Function(Function): # 自定义 autograd function
    @staticmethod
    @custom_fwd
    def forward( # 前向传播
            ctx, input, offset, mask,
            kernel_h, kernel_w, stride_h, stride_w,
            pad_h, pad_w, dilation_h, dilation_w,
            group, group_channels, offset_scale, im2col_step):
        ctx.kernel_h = kernel_h
        ctx.kernel_w = kernel_w
        ctx.stride_h = stride_h
        ctx.stride_w = stride_w
        ctx.pad_h = pad_h
        ctx.pad_w = pad_w
        ctx.dilation_h = dilation_h
        ctx.dilation_w = dilation_w
        ctx.group = group
        ctx.group_channels = group_channels
        ctx.offset_scale = offset_scale
        ctx.im2col_step = im2col_step
        output = DCNv3.dcnv3_forward(
            input, offset, mask, kernel_h,
            kernel_w, stride_h, stride_w, pad_h,
            pad_w, dilation_h, dilation_w, group,
            group_channels, offset_scale, ctx.im2col_step)
        ctx.save_for_backward(input, offset, mask)
        # # 保存所需内容，以备backward时使用，所需的结果会被保存在saved_tensors元组中；
        # 此处仅能保存tensor类型变量，若其余类型变量（Int等），可直接赋予ctx作为成员变量，也可以达到保存效果
        return output

    @staticmethod
    @once_differentiable
    @custom_bwd
    def backward(ctx, grad_output): # 反向传播
        input, offset, mask = ctx.saved_tensors  # 取出forward中保存的result
        # 计算梯度并返回
        grad_input, grad_offset, grad_mask = \
            DCNv3.dcnv3_backward(
                input, offset, mask, ctx.kernel_h,
                ctx.kernel_w, ctx.stride_h, ctx.stride_w, ctx.pad_h,
                ctx.pad_w, ctx.dilation_h, ctx.dilation_w, ctx.group,
                ctx.group_channels, ctx.offset_scale, grad_output.contiguous(), ctx.im2col_step)

        return grad_input, grad_offset, grad_mask, \
            None, None, None, None, None, None, None, None, None, None, None, None

    @staticmethod
    def symbolic(g, input, offset, mask, kernel_h, kernel_w, stride_h,
                 stride_w, pad_h, pad_w, dilation_h, dilation_w, group,
                 group_channels, offset_scale, im2col_step):
        """Symbolic function for mmdeploy::DCNv3.

        Returns:
            DCNv3 op for onnx.
        """
        return g.op(
            'mmdeploy::TRTDCNv3',
            input,
            offset,
            mask,
            kernel_h_i=int(kernel_h),
            kernel_w_i=int(kernel_w),
            stride_h_i=int(stride_h),
            stride_w_i=int(stride_w),
            pad_h_i=int(pad_h),
            pad_w_i=int(pad_w),
            dilation_h_i=int(dilation_h),
            dilation_w_i=int(dilation_w),
            group_i=int(group),
            group_channels_i=int(group_channels),
            offset_scale_f=float(offset_scale),
            im2col_step_i=int(im2col_step),
        )

dcnv3_core_pytorch

def dcnv3_core_pytorch(
        input, offset, mask, kernel_h,
        kernel_w, stride_h, stride_w, pad_h,
        pad_w, dilation_h, dilation_w, group,
        group_channels, offset_scale):
    # for debug and test only,
    # need to use cuda version instead
    '''
    输入参数说明：
    input: (N,H,W,C)
    offset: (N,H,W,group*2*kernel_size*kernel_size)
    mask: (N,H,W,group*2*kernel_size*kernel_size)
    pad_h=pad_w 在h,w方向的填充（默认是1）
    dilation_h,dilation_w : 空洞卷积率
    group：分组数
    group_channels: 每个组中的通道数
    '''
    input = F.pad(
        input,
        [0, 0, pad_h, pad_h, pad_w, pad_w]) # 用0填充 大小变为 (N_,H_in,W_in,C)
    N_, H_in, W_in, _ = input.shape 
    _, H_out, W_out, _ = offset.shape # (N_,H_out,W_out,C)=(N,H,W,C)

    ref = _get_reference_points(
        input.shape, input.device, kernel_h, kernel_w, dilation_h, dilation_w, pad_h, pad_w, stride_h, stride_w)
    # ref (1,H_out_cov,W_out_cov,1,2)
    grid = _generate_dilation_grids(
        input.shape, kernel_h, kernel_w, dilation_h, dilation_w, group, input.device)
    # grid (1,1,1,group * kernel_h * kernel_w,2)
    spatial_norm = torch.tensor([W_in, H_in]).reshape(1, 1, 1, 2).\
        repeat(1, 1, 1, group*kernel_h*kernel_w).to(input.device)
    # spatial_norm (1,1,1,group*kernel_h*kernel_w)
    sampling_locations = (ref + grid * offset_scale).repeat(N_, 1, 1, 1, 1).flatten(3, 4) + \
        offset * offset_scale / spatial_norm # 得到最终的采样点位置
    # repeat 后(N_,H_out,W_out,group*kernel_h*kernel_w,2)
    # flatten 后(N_,H_out,W_out,group*kernel_h*kernel_w*2)
    # offset: (N_,H_out,W_out,group*kernel_h*kernel_w*2)
    P_ = kernel_h * kernel_w
    sampling_grids = 2 * sampling_locations - 1 # 把大小规范化到[-1,1]之间,方便F.grid_sample函数进行采样

    input_ = input.view(N_, H_in*W_in, group*group_channels).transpose(1, 2).\
        reshape(N_*group, group_channels, H_in, W_in)
    # input: (N_,H_in,W_in,group*group_channels)
    # view后:(N_, H_in*W_in, group*group_channels)
    # transpose后：(N_, group*group_channels, H_in*W_in)
    # reshape后：(N_*group, group_channels, H_in, W_in)

    
    sampling_grid_ = sampling_grids.view(N_, H_out*W_out, group, P_, 2).transpose(1, 2).\
        flatten(0, 1)
    # sampling_grids:(N_, H_out, W_out, group*P_*2)
    # transpose后：(N_, H_out*W_out, group, P_, 2)
    # flatten后：( N_*group, H_out*W_out, P_, 2)

    
    sampling_input_ = F.grid_sample( # 偏移后的采样位置
        input_, sampling_grid_, mode='bilinear', padding_mode='zeros', align_corners=False) # 双线性插值
    # input_: (N_*group, group_channels, H_in, W_in)
    # sampling_grid_: (N_*group, H_out*W_out, P_, 2)
    # sampling_input_: (N_*group, group_channels, H_out*W_out, P_)
    
    mask = mask.view(N_, H_out*W_out, group, P_).transpose(1, 2).\
        reshape(N_*group, 1, H_out*W_out, P_) # 调制标量
    # mask: (N_, H_out, W_out, group*P_)
    # view后: (N_, H_out*W_out, group, P_)
    # transpose后：(N_, group, H_out*W_out, P_)
    # reshape后：(N_*group, 1, H_out*W_out, P_)

    output = (sampling_input_ * mask).sum(-1).view(N_,group*group_channels, H_out*W_out)
    # *后：(N_*group,  group_channels, H_out*W_out, P_)
    # sum(-1)后：(N_*group,  group_channels, H_out*W_out) 
    # view后：(N_,group*group_channels, H_out*W_out)

    return output.transpose(1, 2).reshape(N_, H_out, W_out, -1).contiguous()
    # transpose后：(N_, H_out*W_out，group*group_channels)
    # reshape后：(N_, H_out, W_out,group*group_channels)=(N,H,W,C)

初始设置：

这里的sum(-1)是将kernel_size*kernel_size个像素的值简单求和，并没有和对应的weight相乘后再求和，因为此处对应的是上文所述=改进点1中的point-wise的操作。

_get_reference_points

• 功能：生成大小为(1,H_out,W_out,1,2) 的reference_points, 其中H_out和W_out 和生成的offset的高宽相同。

def _get_reference_points(spatial_shapes, device, kernel_h, kernel_w, dilation_h, dilation_w, pad_h=0, pad_w=0, stride_h=1, stride_w=1):
	# spatial_shapes: 原始输入pad后大小 (N_,H_in,W_in,C)
    _, H_, W_, _ = spatial_shapes  
    # 等于offset的宽和高(pad=1,stride=1)
    H_out = (H_ - (dilation_h * (kernel_h - 1) + 1)) // stride_h + 1 # H_out
    W_out = (W_ - (dilation_w * (kernel_w - 1) + 1)) // stride_w + 1 # W_out

    ref_y, ref_x = torch.meshgrid(
        torch.linspace(
            (dilation_h * (kernel_h - 1)) // 2 + 0.5,
            (dilation_h * (kernel_h - 1)) // 2 + 0.5 + (H_out - 1) * stride_h,
            H_out,
            dtype=torch.float32,
            device=device),
        # 在[pad_h + 0.5,H_ - pad_h - 0.5]范围内，生成H_out个等分点
        torch.linspace(
            (dilation_w * (kernel_w - 1)) // 2 + 0.5,
            (dilation_w * (kernel_w - 1)) // 2 + 0.5 + (W_out - 1) * stride_w,
            W_out,
            dtype=torch.float32,
            device=device))
        # 在[pad_w + 0.5,W_ - pad_w - 0.5]范围内，生成W_out个等分点
    # ref_y:(H_out,W_out)
    # ref_x:(H_out,W_out)
    ref_y = ref_y.reshape(-1)[None] / H_ # 归一化
    # reshape后(H_out*W_out)
    # None后(1,H_out*W_out)
    ref_x = ref_x.reshape(-1)[None] / W_
    # (1,H_out*W_out)

    ref = torch.stack((ref_x, ref_y), -1).reshape(
        1, H_out, W_out, 1, 2)
    # stack后 (1,H_out*W_out,2)
    # reshape 后 (1,H_out,W_out,1,2)

    return ref # (1,H_out_cov,W_out_cov,1,2)

_generate_dilation_grids

• 功能：用于生成大小为(1,1,1,group * kernel_h * kernel_w,2)的采样点。

def _generate_dilation_grids(spatial_shapes, kernel_h, kernel_w, dilation_h, dilation_w, group, device):
    _, H_, W_, _ = spatial_shapes #(N_,H_in,W_in,C)
    points_list = []
    x, y = torch.meshgrid(
        torch.linspace(
            -((dilation_w * (kernel_w - 1)) // 2),
            -((dilation_w * (kernel_w - 1)) // 2) +
            (kernel_w - 1) * dilation_w, kernel_w,
            dtype=torch.float32,
            device=device),
        torch.linspace(
            -((dilation_h * (kernel_h - 1)) // 2),
            -((dilation_h * (kernel_h - 1)) // 2) +
            (kernel_h - 1) * dilation_h, kernel_h,
            dtype=torch.float32,
            device=device))
    # x: (kernel_w,kernel_h)
    # y: (kernel_w,kernel_h)
    points_list.extend([x / W_, y / H_])
    grid = torch.stack(points_list, -1).reshape(-1, 1, 2).\
        repeat(1, group, 1).permute(1, 0, 2)
    # stack后：(kernel_w,kernel_h,2)
    # reshape后：(kernel_w*kernel_h,1,2)
    # repeat后：(kernel_w*kernel_h,group,2)
    # permute后：(group,kernel_w*kernel_h,2)
    grid = grid.reshape(1, 1, 1, group * kernel_h * kernel_w, 2)
    #(1,1,1,group * kernel_h * kernel_w,2)
    return grid