作者丨Frankielmy@知乎（已授权）

来源丨

编辑丨极市平台

最近学习CV中的Transformer有感而发，网上关于Deformable DETR通俗的帖子不是很多，因此想分享一下最近学习的内容。第一次发帖经验不足，文章内可能有许多错误或不恰之处欢迎批评指正。

Abstract

DETR消除了目标检任务中的手工设计痕迹，但是存在收敛慢以及Transformer的自注意力造成的特征图分辨率不能太高的问题，这就导致了小目标检测性能很差。我们的Deformable DETR只在参考点附近采样少量的key来计算注意力，因此我们的方法收敛快并且可以用到多尺度特征。

1、Introduction

传统目标检测任务有很多手工设计痕迹，所以不是端到端的网络。DETR运用到了Transformer强大的功能以及全局关系建模能力来取代目标检测中人工设计痕迹来达到端到端的目的。

DETR的两大缺点：

(1)收敛速度慢：因为全局像素之间计算注意力要收敛到几个稀疏的像素点需要消耗很长的时间。

(2)小目标检测差：目标检测基本都是在大分辨率的特征图上进行小目标的检测，但是Transformer中的Self Attention的计算复杂度是平方级别的，所以只能利用到最后一层特征图。

可变形卷积DCN是一种注意稀疏空间位置很好的机制，但是其缺乏元素之间关系的建模能力。

综上所述，Deformable Attention模块结合了DCN稀疏采样能力和Transformer的全局关系建模能力。这个模块可以聚合多尺度特征，不需要FPN了，我们用这个模块替换了Transformer Encoder中的Multi-Head Self- Attention模块和Transformer Decoder中的Cross Attention模块。

Deformable DETR的提出可以帮助探索更多端到端目标检测的探索。提出了bbox迭代微调策略和两阶段方法，其中iterative bounding box refinement类似Cascade R-CNN方法，two stage类似RPN。

2、Related work

Transformer中包含了多头自注意力和交叉注意力机制，其中多头自注意力机制对key的数量很敏感，平方级别的复杂度导致不能有太多的key，解决方法主要可以分为三类。

（1）第一类解决方法为在key上使用预定义稀疏注意力模式，例如将注意力限制在一个固定的局部窗口上，这将导致失去了全局信息。

（2）第二类是通过数据学习到相关的稀疏注意力。

（3）第三类是寻找自注意力中低等级的属性，类似限制关键元素的尺寸大小。

图像领域的注意力方法大多数都局限于第一种设计方法，但是因为内存模式原因速度要比传统卷积慢3倍（相同的FLOPs下）。DCN可以看作是一种自注意力机制，它比自注意力机制更加高效有效，但是其缺少元素关系建模的机制。我们的可变形注意力模块来源于DCN，并且属于第二类注意力方法。它只关注从q特征预测得到的一小部分固定数量的采样点。

目标检测任务一个难点就是高效的表征不同尺度下的物体。现在有的方法比如FPN，PA-FPN，NAS-FPN，Auto-FPN，BiFPN等。我们的多尺度可变形注意力模块可以自然的融合基于注意力机制的多尺度特征图，不需要FPN了。

3、Revisiting Transformers And DETR3.1、Transformer中的Multi-Head Self-Attention

该模块计算复杂度为: , 其中代表特征图维度, 和均为图片中的像素(pixel), 因此有 。所以计算复杂度可以简化为 , 可以得出其与图片像素的数量成平方级别的计算复杂度。

3.2、DETR

DETR在目标检测领域中引入了Transformer结构并且取得了不错的效果。这套范式摒弃了传统目标检测中的anchor和post processing 机制，而是先预先设定100个object queries然后进行二分图匹配计算loss。其具体流程图(pipeline)如下

图1. DETR Pipeline

1、输入图片3×800×1066的一张图片，经过卷积神经网络提取特征，长宽32倍下采样后得到2048×25×34，然后通过一个1×1 Conv进行降维最终得到输出shape为256×25×34.

2、positional encoding为绝对位置编码，为了和特征完全匹配形状也为256×25×34，然后和特征进行元素级别的相加后输入到Transformer Encoder中。

3、输入到Encoder的尺寸为(25×34)×256=850×256，代表有256个token每个token的维度为850，Encoder不改变输入的Shape。

4、Encoder的输出和object queries输入到Decoder中形成cross attention，object queries的维度设置为anchor数量×token数量。

5、Decoder输出到FFN进行分类和框定位，其中FFN是共享参数的。

tips: 虽然DETR没有anchor，但是object queries其实就是起到了anchor的作用。

DETR缺点在于：

（1）计算复杂度的限制导致不能利用大分辨率特征图，导致小目标性能差。

（2）注意力权重矩阵往往都很稀疏，DETR计算全部像素的注意力导致收敛速率慢。

4、Method4.1、Deformable Attention Module

图2. Deformable Attention Module

Deformable Attention Module主要思想是结合了DCN和自注意力, 目的就是为了通过在输入特征图上的参考点(reference point)附近只采样少数点(deformable detr设置为3个点)来作为注意力的 。因此要解决的问题就是：（1）确定reference point。（2）确定每个reference point的偏移量 (offset)。(3) 确定注意力权重矩阵 。在Encoder和Decoder中实现方法不太一样, 加下来详细叙述。

在Encoder部分, 输入的Query Feature 为加入了位置编码的特征图(src+pos), value 的计算方法只使用了src而没有位置编码(value_proj函数)。

（1）reference point确定方法为用了torch.meshgrid方法，调用的函数如下(get_reference_points)，有一个细节就是参考点归一化到0和1之间，因此取值的时候要用到双线性插值的方法。而在Decoder中，参考点的获取方法为object queries通过一个nn.Linear得到每个对应的reference point。

def get_reference_points(spatial_shapes, valid_ratios, device):    reference_points_list = []    for lvl, (H_, W_) in enumerate(spatial_shapes):        # 从0.5到H-0.5采样H个点，W同理 这个操作的目的也就是为了特征图的对齐        ref_y, ref_x = torch.meshgrid(torch.linspace(0.5, H_ - 0.5, H_, dtype=torch.float32, device=device),                                        torch.linspace(0.5, W_ - 0.5, W_, dtype=torch.float32, device=device))        ref_y = ref_y.reshape(-1)[None] / (valid_ratios[:, None, lvl, 1] * H_)        ref_x = ref_x.reshape(-1)[None] / (valid_ratios[:, None, lvl, 0] * W_)        ref = torch.stack((ref_x, ref_y), -1)        reference_points_list.append(ref)    reference_points = torch.cat(reference_points_list, 1)    reference_points = reference_points[:, :, None] * valid_ratios[:, None]    return reference_points

（2）计算offset的方法为对过一个nn.Linear，得到多组偏移量，每组偏移量的维度为参考点的个数，组数为注意力头的数量。

（3）计算注意力权重矩阵的方法为过一个nn.Linear和一个F.softmax，得到每个头的注意力权重。

如图2所示，分头计算完的注意力最终会拼接到一起，然后最后过一个nn.Linear得到输入 的最终输出。

4.2、Multi-Scale Deformable Attention Module

图3. Multi-Scale Feature Maps

多尺度的Deformable Attention模块也是在多尺度特征图上计算的。多尺度的特征融合方法则是取了骨干网(ResNet)最后三层的特征图C3，C4，C5，并且用了一个Conv3x3 Stride2的卷积得到了一个C6构成了四层特征图。特别的是会通过卷积操作将通道数量统一为256(也就是token的数量)，然后在这四个特征图上运行Deformable Attention Module并且进行直接相加得到最终输出。其中Deformable Attention Module算子的pytorch实现如下：

def ms_deform_attn_core_pytorch(value, value_spatial_shapes, sampling_locations, attention_weights):    # for debug and test only,    # need to use cuda version instead    N_, S_, M_, D_ = value.shape # batch size, number token, number head, head dims    # Lq_: number query, L_: level number, P_: sampling number采样点数    _, Lq_, M_, L_, P_, _ = sampling_locations.shape    # 按照level划分value    value_list = value.split([H_ * W_ for H_, W_ in value_spatial_shapes], dim=1)    # [0, 1] -> [-1, 1] 因为要满足F.grid_sample的输入要求    sampling_grids = 2 * sampling_locations - 1    sampling_value_list = []    for lid_, (H_, W_) in enumerate(value_spatial_shapes):        # N_, H_*W_, M_, D_ -> N_, H_*W_, M_*D_ -> N_, M_*D_, H_*W_ -> N_*M_, D_, H_, W_        value_l_ = value_list[lid_].flatten(2).transpose(1, 2).reshape(N_*M_, D_, H_, W_)        # N_, Lq_, M_, P_, 2 -> N_, M_, Lq_, P_, 2 -> N_*M_, Lq_, P_, 2        sampling_grid_l_ = sampling_grids[:, :, :, lid_].transpose(1, 2).flatten(0, 1)        # N_*M_, D_, Lq_, P_        # 用双线性插值从feature map上获取value，因为mask的原因越界所以要zeros的方法进行填充        sampling_value_l_ = F.grid_sample(value_l_, sampling_grid_l_,                                          mode='bilinear', padding_mode='zeros', align_corners=False)        sampling_value_list.append(sampling_value_l_)    # (N_, Lq_, M_, L_, P_) -> (N_, M_, Lq_, L_, P_) -> (N_, M_, 1, Lq_, L_*P_)    attention_weights = attention_weights.transpose(1, 2).reshape(N_*M_, 1, Lq_, L_*P_)    # 不同scale计算出的multi head attention 进行相加，返回output后还需要过一个Linear层    output = (torch.stack(sampling_value_list, dim=-2).flatten(-2) * attention_weights).sum(-1).view(N_, M_*D_, Lq_)    return output.transpose(1, 2).contiguous()

完整的Multi-Scale Deformable Attention模块代码如下：

class MSDeformAttn(nn.Module):    def __init__(self, d_model=256, n_levels=4, n_heads=8, n_points=4):        """        Multi-Scale Deformable Attention Module        :param d_model      hidden dimension        :param n_levels     number of feature levels        :param n_heads      number of attention heads        :param n_points     number of sampling points per attention head per feature level        """        super().__init__()        if d_model % n_heads != 0:            raise ValueError('d_model must be divisible by n_heads, but got {} and {}'.format(d_model, n_heads))        _d_per_head = d_model // n_heads        # you'd better set _d_per_head to a power of 2 which is more efficient in our CUDA implementation        if not _is_power_of_2(_d_per_head):            warnings.warn("You'd better set d_model in MSDeformAttn to make the dimension of each attention head a power of 2 "                          "which is more efficient in our CUDA implementation.")        self.im2col_step = 64        self.d_model = d_model        self.n_levels = n_levels        self.n_heads = n_heads        self.n_points = n_points        self.sampling_offsets = nn.Linear(d_model, n_heads * n_levels * n_points * 2)        self.attention_weights = nn.Linear(d_model, n_heads * n_levels * n_points)        self.value_proj = nn.Linear(d_model, d_model)        self.output_proj = nn.Linear(d_model, d_model)        self._reset_parameters()    def _reset_parameters(self):        constant_(self.sampling_offsets.weight.data, 0.)        thetas = torch.arange(self.n_heads, dtype=torch.float32) * (2.0 * math.pi / self.n_heads)        grid_init = torch.stack([thetas.cos(), thetas.sin()], -1)        grid_init = (grid_init / grid_init.abs().max(-1, keepdim=True)[0]).view(self.n_heads, 1, 1, 2).repeat(1, self.n_levels, self.n_points, 1)        for i in range(self.n_points):            grid_init[:, :, i, :] *= i + 1        with torch.no_grad():            self.sampling_offsets.bias = nn.Parameter(grid_init.view(-1))        constant_(self.attention_weights.weight.data, 0.)        constant_(self.attention_weights.bias.data, 0.)        xavier_uniform_(self.value_proj.weight.data)        constant_(self.value_proj.bias.data, 0.)        xavier_uniform_(self.output_proj.weight.data)        constant_(self.output_proj.bias.data, 0.)    def forward(self, query, reference_points, input_flatten, input_spatial_shapes, input_level_start_index, input_padding_mask=None):        """        :param query                       (N, Length_{query}, C)        :param reference_points            (N, Length_{query}, n_levels, 2), range in [0, 1], top-left (0,0), bottom-right (1, 1), including padding area                                        or (N, Length_{query}, n_levels, 4), add additional (w, h) to form reference boxes        :param input_flatten               (N, \sum_{l=0}^{L-1} H_l \cdot W_l, C)        :param input_spatial_shapes        (n_levels, 2), [(H_0, W_0), (H_1, W_1), ..., (H_{L-1}, W_{L-1})]        :param input_level_start_index     (n_levels, ), [0, H_0*W_0, H_0*W_0+H_1*W_1, H_0*W_0+H_1*W_1+H_2*W_2, ..., H_0*W_0+H_1*W_1+...+H_{L-1}*W_{L-1}]        :param input_padding_mask          (N, \sum_{l=0}^{L-1} H_l \cdot W_l), True for padding elements, False for non-padding elements        :return output                     (N, Length_{query}, C)        """        # query是 src + positional encoding        # input_flatten是src，没有位置编码        N, Len_q, _ = query.shape        N, Len_in, _ = input_flatten.shape        assert (input_spatial_shapes[:, 0] * input_spatial_shapes[:, 1]).sum() == Len_in        # 根据input_flatten得到v        value = self.value_proj(input_flatten)        if input_padding_mask is not None:            value = value.masked_fill(input_padding_mask[..., None], float(0))        # 多头注意力 根据头的个数将v等分        value = value.view(N, Len_in, self.n_heads, self.d_model // self.n_heads)        # 根据query得到offset偏移量和attention weights注意力权重        sampling_offsets = self.sampling_offsets(query).view(N, Len_q, self.n_heads, self.n_levels, self.n_points, 2)        attention_weights = self.attention_weights(query).view(N, Len_q, self.n_heads, self.n_levels * self.n_points)        attention_weights = F.softmax(attention_weights, -1).view(N, Len_q, self.n_heads, self.n_levels, self.n_points)        # N, Len_q, n_heads, n_levels, n_points, 2        if reference_points.shape[-1] == 2:            offset_normalizer = torch.stack([input_spatial_shapes[..., 1], input_spatial_shapes[..., 0]], -1)            sampling_locations = reference_points[:, :, None, :, None, :] \                                 + sampling_offsets / offset_normalizer[None, None, None, :, None, :]        elif reference_points.shape[-1] == 4:            sampling_locations = reference_points[:, :, None, :, None, :2] \                                 + sampling_offsets / self.n_points * reference_points[:, :, None, :, None, 2:] * 0.5        else:            raise ValueError(                'Last dim of reference_points must be 2 or 4, but get {} instead.'.format(reference_points.shape[-1]))        output = MSDeformAttnFunction.apply(            value, input_spatial_shapes, input_level_start_index, sampling_locations, attention_weights, self.im2col_step)        output = self.output_proj(output)        return output

详细代码注释如下，iterative bounding box refinement和two stage改进方法的Encoder不变。

class DeformableTransformerEncoderLayer(nn.Module):    def __init__(self,                 d_model=256, d_ffn=1024,                 dropout=0.1, activation="relu",                 n_levels=4, n_heads=8, n_points=4):        super().__init__()        # self attention        self.self_attn = MSDeformAttn(d_model, n_levels, n_heads, n_points)        self.dropout1 = nn.Dropout(dropout)        self.norm1 = nn.LayerNorm(d_model)        # ffn        self.linear1 = nn.Linear(d_model, d_ffn)        self.activation = _get_activation_fn(activation)        self.dropout2 = nn.Dropout(dropout)        self.linear2 = nn.Linear(d_ffn, d_model)        self.dropout3 = nn.Dropout(dropout)        self.norm2 = nn.LayerNorm(d_model)    @staticmethod    def with_pos_embed(tensor, pos):        return tensor if pos is None else tensor + pos    def forward_ffn(self, src):        src2 = self.linear2(self.dropout2(self.activation(self.linear1(src))))        src = src + self.dropout3(src2)        src = self.norm2(src)        return src    def forward(self, src, pos, reference_points, spatial_shapes, level_start_index, padding_mask=None):        # self attention        src2 = self.self_attn(self.with_pos_embed(src, pos), reference_points, src, spatial_shapes, level_start_index, padding_mask)        src = src + self.dropout1(src2)        src = self.norm1(src)        # ffn        src = self.forward_ffn(src)        return srcclass DeformableTransformerEncoder(nn.Module):    def __init__(self, encoder_layer, num_layers):        super().__init__()        self.layers = _get_clones(encoder_layer, num_layers)        self.num_layers = num_layers    @staticmethod    def get_reference_points(spatial_shapes, valid_ratios, device):        reference_points_list = []        for lvl, (H_, W_) in enumerate(spatial_shapes):            # 从0.5到H-0.5采样H个点，W同理 这个操作的目的也就是为了特征图的对齐            ref_y, ref_x = torch.meshgrid(torch.linspace(0.5, H_ - 0.5, H_, dtype=torch.float32, device=device),                                          torch.linspace(0.5, W_ - 0.5, W_, dtype=torch.float32, device=device))            ref_y = ref_y.reshape(-1)[None] / (valid_ratios[:, None, lvl, 1] * H_)            ref_x = ref_x.reshape(-1)[None] / (valid_ratios[:, None, lvl, 0] * W_)            ref = torch.stack((ref_x, ref_y), -1)            reference_points_list.append(ref)        reference_points = torch.cat(reference_points_list, 1)        reference_points = reference_points[:, :, None] * valid_ratios[:, None]        return reference_points    def forward(self, src, spatial_shapes, level_start_index, valid_ratios, pos=None, padding_mask=None):        output = src        reference_points = self.get_reference_points(spatial_shapes, valid_ratios, device=src.device)        for _, layer in enumerate(self.layers):            output = layer(output, pos, reference_points, spatial_shapes, level_start_index, padding_mask)        return output

详细代码注释如下，这里要控制是否使用iterative bounding box refinement和two stage技巧。iterative bounding box refinement其实就是对参考点的位置进行微调。two stage方法其实就是通过参考点直接生成anchor但是只取最高置信度的前几个，然后再送入decoder进行调整。intermediate数组是一个trick，每层Decoder都是可以输出bbox和分类信息的，如果都利用起来算损失则成为auxiliary loss。

class DeformableTransformerDecoderLayer(nn.Module):    def __init__(self, d_model=256, d_ffn=1024,                 dropout=0.1, activation="relu",                 n_levels=4, n_heads=8, n_points=4):        super().__init__()        # cross attention        self.cross_attn = MSDeformAttn(d_model, n_levels, n_heads, n_points)        self.dropout1 = nn.Dropout(dropout)        self.norm1 = nn.LayerNorm(d_model)        # self attention        self.self_attn = nn.MultiheadAttention(d_model, n_heads, dropout=dropout)        self.dropout2 = nn.Dropout(dropout)        self.norm2 = nn.LayerNorm(d_model)        # ffn        self.linear1 = nn.Linear(d_model, d_ffn)        self.activation = _get_activation_fn(activation)        self.dropout3 = nn.Dropout(dropout)        self.linear2 = nn.Linear(d_ffn, d_model)        self.dropout4 = nn.Dropout(dropout)        self.norm3 = nn.LayerNorm(d_model)    @staticmethod    def with_pos_embed(tensor, pos):        return tensor if pos is None else tensor + pos    def forward_ffn(self, tgt):        tgt2 = self.linear2(self.dropout3(self.activation(self.linear1(tgt))))        tgt = tgt + self.dropout4(tgt2)        tgt = self.norm3(tgt)        return tgt    def forward(self, tgt, query_pos, reference_points, src, src_spatial_shapes, level_start_index, src_padding_mask=None):        # self attention        q = k = self.with_pos_embed(tgt, query_pos)        tgt2 = self.self_attn(q.transpose(0, 1), k.transpose(0, 1), tgt.transpose(0, 1))[0].transpose(0, 1)        tgt = tgt + self.dropout2(tgt2)        tgt = self.norm2(tgt)        # cross attention        tgt2 = self.cross_attn(self.with_pos_embed(tgt, query_pos),                               reference_points,                               src, src_spatial_shapes, level_start_index, src_padding_mask)        tgt = tgt + self.dropout1(tgt2)        tgt = self.norm1(tgt)        # ffn        tgt = self.forward_ffn(tgt)        return tgtclass DeformableTransformerDecoder(nn.Module):    def __init__(self, decoder_layer, num_layers, return_intermediate=False):        super().__init__()        self.layers = _get_clones(decoder_layer, num_layers)        self.num_layers = num_layers        self.return_intermediate = return_intermediate        # hack implementation for iterative bounding box refinement and two-stage Deformable DETR        self.bbox_embed = None        self.class_embed = None    def forward(self, tgt, reference_points, src, src_spatial_shapes, src_level_start_index, src_valid_ratios,                query_pos=None, src_padding_mask=None):        output = tgt        # 用来存储中间decoder输出的 可以考虑是否用auxiliary loss        intermediate = []        intermediate_reference_points = []        for lid, layer in enumerate(self.layers):            if reference_points.shape[-1] == 4:                reference_points_input = reference_points[:, :, None] \                                         * torch.cat([src_valid_ratios, src_valid_ratios], -1)[:, None]            else:                assert reference_points.shape[-1] == 2                reference_points_input = reference_points[:, :, None] * src_valid_ratios[:, None]            output = layer(output, query_pos, reference_points_input, src, src_spatial_shapes, src_level_start_index, src_padding_mask)            # hack implementation for iterative bounding box refinement            # iterative refinement是对decoder中的参考点进行微调，类似cascade rcnn思想            if self.bbox_embed is not None:                tmp = self.bbox_embed[lid](output)                if reference_points.shape[-1] == 4:                    new_reference_points = tmp + inverse_sigmoid(reference_points)                    new_reference_points = new_reference_points.sigmoid()                else:                    assert reference_points.shape[-1] == 2                    new_reference_points = tmp                    new_reference_points[..., :2] = tmp[..., :2] + inverse_sigmoid(reference_points)                    new_reference_points = new_reference_points.sigmoid()                reference_points = new_reference_points.detach()            if self.return_intermediate:                intermediate.append(output)                intermediate_reference_points.append(reference_points)        if self.return_intermediate:            return torch.stack(intermediate), torch.stack(intermediate_reference_points)        return output, reference_points

综合模块代码如下

class DeformableTransformer(nn.Module):    def __init__(self, d_model=256, nhead=8,                 num_encoder_layers=6, num_decoder_layers=6, dim_feedforward=1024, dropout=0.1,                 activation="relu", return_intermediate_dec=False,                 num_feature_levels=4, dec_n_points=4,  enc_n_points=4,                 two_stage=False, two_stage_num_proposals=300):        super().__init__()        self.d_model = d_model        self.nhead = nhead        self.two_stage = two_stage        self.two_stage_num_proposals = two_stage_num_proposals        encoder_layer = DeformableTransformerEncoderLayer(d_model, dim_feedforward,                                                          dropout, activation,                                                          num_feature_levels, nhead, enc_n_points)        self.encoder = DeformableTransformerEncoder(encoder_layer, num_encoder_layers)        decoder_layer = DeformableTransformerDecoderLayer(d_model, dim_feedforward,                                                          dropout, activation,                                                          num_feature_levels, nhead, dec_n_points)        self.decoder = DeformableTransformerDecoder(decoder_layer, num_decoder_layers, return_intermediate_dec)        self.level_embed = nn.Parameter(torch.Tensor(num_feature_levels, d_model))        if two_stage:            self.enc_output = nn.Linear(d_model, d_model)            self.enc_output_norm = nn.LayerNorm(d_model)            self.pos_trans = nn.Linear(d_model * 2, d_model * 2)            self.pos_trans_norm = nn.LayerNorm(d_model * 2)        else:            self.reference_points = nn.Linear(d_model, 2)        self._reset_parameters()    def _reset_parameters(self):        for p in self.parameters():            if p.dim() > 1:                nn.init.xavier_uniform_(p)        for m in self.modules():            if isinstance(m, MSDeformAttn):                m._reset_parameters()        if not self.two_stage:            xavier_uniform_(self.reference_points.weight.data, gain=1.0)            constant_(self.reference_points.bias.data, 0.)        normal_(self.level_embed)    def get_proposal_pos_embed(self, proposals):        num_pos_feats = 128        temperature = 10000        scale = 2 * math.pi        dim_t = torch.arange(num_pos_feats, dtype=torch.float32, device=proposals.device)        dim_t = temperature ** (2 * (dim_t // 2) / num_pos_feats)        # N, L, 4        proposals = proposals.sigmoid() * scale        # N, L, 4, 128        pos = proposals[:, :, :, None] / dim_t        # N, L, 4, 64, 2        pos = torch.stack((pos[:, :, :, 0::2].sin(), pos[:, :, :, 1::2].cos()), dim=4).flatten(2)        return pos    def gen_encoder_output_proposals(self, memory, memory_padding_mask, spatial_shapes):        N_, S_, C_ = memory.shape        base_scale = 4.0        proposals = []        _cur = 0        for lvl, (H_, W_) in enumerate(spatial_shapes):            mask_flatten_ = memory_padding_mask[:, _cur:(_cur + H_ * W_)].view(N_, H_, W_, 1)            valid_H = torch.sum(~mask_flatten_[:, :, 0, 0], 1)            valid_W = torch.sum(~mask_flatten_[:, 0, :, 0], 1)            grid_y, grid_x = torch.meshgrid(torch.linspace(0, H_ - 1, H_, dtype=torch.float32, device=memory.device),                                            torch.linspace(0, W_ - 1, W_, dtype=torch.float32, device=memory.device))            grid = torch.cat([grid_x.unsqueeze(-1), grid_y.unsqueeze(-1)], -1)            scale = torch.cat([valid_W.unsqueeze(-1), valid_H.unsqueeze(-1)], 1).view(N_, 1, 1, 2)            grid = (grid.unsqueeze(0).expand(N_, -1, -1, -1) + 0.5) / scale            wh = torch.ones_like(grid) * 0.05 * (2.0 ** lvl)            proposal = torch.cat((grid, wh), -1).view(N_, -1, 4)            proposals.append(proposal)            _cur += (H_ * W_)        output_proposals = torch.cat(proposals, 1)        output_proposals_valid = ((output_proposals > 0.01) & (output_proposals < 0.99)).all(-1, keepdim=True)        output_proposals = torch.log(output_proposals / (1 - output_proposals))        output_proposals = output_proposals.masked_fill(memory_padding_mask.unsqueeze(-1), float('inf'))        output_proposals = output_proposals.masked_fill(~output_proposals_valid, float('inf'))        output_memory = memory        output_memory = output_memory.masked_fill(memory_padding_mask.unsqueeze(-1), float(0))        output_memory = output_memory.masked_fill(~output_proposals_valid, float(0))        output_memory = self.enc_output_norm(self.enc_output(output_memory))        return output_memory, output_proposals    def get_valid_ratio(self, mask):        _, H, W = mask.shape        valid_H = torch.sum(~mask[:, :, 0], 1)        valid_W = torch.sum(~mask[:, 0, :], 1)        valid_ratio_h = valid_H.float() / H        valid_ratio_w = valid_W.float() / W        valid_ratio = torch.stack([valid_ratio_w, valid_ratio_h], -1)        return valid_ratio    def forward(self, srcs, masks, pos_embeds, query_embed=None):        assert self.two_stage or query_embed is not None        # prepare input for encoder        src_flatten = []        mask_flatten = []        lvl_pos_embed_flatten = []        spatial_shapes = []        for lvl, (src, mask, pos_embed) in enumerate(zip(srcs, masks, pos_embeds)):            # 得到每一层feature map的batch size 通道数量 高宽            bs, c, h, w = src.shape            spatial_shape = (h, w)            spatial_shapes.append(spatial_shape)            # 将每层的feature map、mask、位置编码拉平，并且加入到相关数组中            src = src.flatten(2).transpose(1, 2)            mask = mask.flatten(1)            pos_embed = pos_embed.flatten(2).transpose(1, 2)            # 位置编码和可学习的每层编码相加，表征类似 3D position            lvl_pos_embed = pos_embed + self.level_embed[lvl].view(1, 1, -1)             lvl_pos_embed_flatten.append(lvl_pos_embed)            src_flatten.append(src)            mask_flatten.append(mask)        # 在hidden_dim维度上进行拼接，也就是number token数量一样的那个维度        src_flatten = torch.cat(src_flatten, 1)        mask_flatten = torch.cat(mask_flatten, 1)        lvl_pos_embed_flatten = torch.cat(lvl_pos_embed_flatten, 1)        spatial_shapes = torch.as_tensor(spatial_shapes, dtype=torch.long, device=src_flatten.device)        # 记录每个level开始的索引以及有效的长宽(因为有mask存在，raw image的分辨率可能不统一) 具体查看get_valid_ratio函数        # prod(1)计算h*w，cumsum(0)计算前缀和        level_start_index = torch.cat((spatial_shapes.new_zeros((1, )), spatial_shapes.prod(1).cumsum(0)[:-1]))        valid_ratios = torch.stack([self.get_valid_ratio(m) for m in masks], 1)        # encoder         memory = self.encoder(src_flatten, spatial_shapes, level_start_index, valid_ratios, lvl_pos_embed_flatten, mask_flatten)        # prepare input for decoder        bs, _, c = memory.shape        # 是否使用两阶段模式        if self.two_stage:            output_memory, output_proposals = self.gen_encoder_output_proposals(memory, mask_flatten, spatial_shapes)            # hack implementation for two-stage Deformable DETR            enc_outputs_class = self.decoder.class_embed[self.decoder.num_layers](output_memory)            enc_outputs_coord_unact = self.decoder.bbox_embed[self.decoder.num_layers](output_memory) + output_proposals            topk = self.two_stage_num_proposals            topk_proposals = torch.topk(enc_outputs_class[..., 0], topk, dim=1)[1]            topk_coords_unact = torch.gather(enc_outputs_coord_unact, 1, topk_proposals.unsqueeze(-1).repeat(1, 1, 4))            topk_coords_unact = topk_coords_unact.detach()            reference_points = topk_coords_unact.sigmoid()            init_reference_out = reference_points            pos_trans_out = self.pos_trans_norm(self.pos_trans(self.get_proposal_pos_embed(topk_coords_unact)))            query_embed, tgt = torch.split(pos_trans_out, c, dim=2)        else:            # 这是非双阶段版本的Deformable DETR            # 将query_embed划分为query_embed和tgt两部分            query_embed, tgt = torch.split(query_embed, c, dim=1)            # 复制bs份            query_embed = query_embed.unsqueeze(0).expand(bs, -1, -1)            tgt = tgt.unsqueeze(0).expand(bs, -1, -1)            # nn.Linear得到每个object queries对应的reference point, 这是decoder参考点的方法!!!            reference_points = self.reference_points(query_embed).sigmoid()            init_reference_out = reference_points        # decoder        hs, inter_references = self.decoder(tgt, reference_points, memory,                                            spatial_shapes, level_start_index, valid_ratios, query_embed, mask_flatten)        inter_references_out = inter_references        if self.two_stage:            return hs, init_reference_out, inter_references_out, enc_outputs_class, enc_outputs_coord_unact        return hs, init_reference_out, inter_references_out, None, None

图4. Deformable DETR性能对比

由图4可知，Deformable DETR不仅收敛速率比DETR快并且小目标精度也高了许多。

6、Conclusion

Deformable DETR效率高并且收敛快，核心是Multi-Scale Deformable Attention Module。解决了DETR中收敛慢以及小目标性能低的问题。

Reference

Deformable DETR：

官方代码仓库：

DCNv2：