论文链接：https://bmvc2022.mpi-inf.mpg.de/0239.pdf

代码链接：https://github.com/huiyu8794/LDCNet

1 FAS面临的挑战

（1）与其他cv任务不同，FAS处理的是真假人脸之间高度相似的特征，需要更加精细的特征表示来表征与人脸呈现攻击相关的内在特征；

（2）不同benchmark的数据集有不同的数据分布，在一个数据集上训练的模型，在另一个数据集上的测试结果往往不佳。

2 创新点

（1）提出了Learnable Descriptive Convolution (LDC)来自适应地学习FAS中精细的纹理特征；

（2）结合triplet mining和dual-attention supervision的策略来协同监督 LDCNet 以学习域不变和真假人脸判别特征。

3 方法论

3.1 LDC

（1）标准卷积与中心差分卷积

标准卷积：

R为3×3的局部区域({(-1,-1),(-1,0),…,(0,1),(1,1)})，p为当前像素点。

中心差分卷积：

（2）LDC

虽然中心差分卷积等合并了不同的局部描述符来扩展标准卷积，但它们都采用了预定义好的局部描述符并且仍然保留了卷积核 w 中的学习能力，这些局部描述符不会在模型训练中进行更新。预定义的描述符无法灵活地捕获各种纹理特征。因此，作者提出了LDC，

class conv3x3_learn(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size=3, stride=1,
                 padding=1, dilation=1, groups=1, bias=False):
        # conv.weight.size() = [out_channels, in_channels, kernel_size, kernel_size]
        super(conv3x3_learn, self).__init__()
        self.conv = nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, stride=stride, padding=padding,
                              dilation=dilation, groups=groups, bias=bias)  # [12,3,3,3]
        
        self.center_mask = torch.tensor([[0, 0, 0],
                                         [0, 1, 0],
                                         [0, 0, 0]]).cuda()
        self.base_mask = nn.Parameter(torch.ones(self.conv.weight.size()), requires_grad=False)  # [12,3,3,3]
        self.learnable_mask = nn.Parameter(torch.ones([self.conv.weight.size(0), self.conv.weight.size(1)]),
                                           requires_grad=True)  # [12,3]
        self.learnable_theta = nn.Parameter(torch.ones(1) * 0.5, requires_grad=True)  # [1]
        print(self.learnable_mask[:, :, None, None].shape)

    def forward(self, x):
        mask = self.base_mask - self.learnable_theta * self.learnable_mask[:, :, None, None] * \
               self.center_mask * self.conv.weight.sum(2).sum(2)[:, :, None, None]

        out_diff = F.conv2d(input=x, weight=self.conv.weight * mask, bias=self.conv.bias, stride=self.conv.stride,
                            padding=self.conv.padding,
                            groups=self.conv.groups)
        return out_diff

3.2 LDCNet

FE：feature extractor；CF：live/spoof classifier；LE：live attention estimator；SE：spoof attention estimator

其中，分类器由交叉熵损失函数优化：

3.3 Triplet Mining

作者在LDCNet中采用triplet mining来约束FE，以学习域不变特征。如下图所示，假设不同源域均有3个类别的标签(live, print attack, and replay attack)，triplet mining使intra-class pairs相互靠近，inter-class pairs相互远离，

class HardTripletLoss(nn.Module):
    """Hard/Hardest Triplet Loss
    (pytorch implementation of https://omoindrot.github.io/triplet-loss)
    For each anchor, we get the hardest positive and hardest negative to form a triplet.
    """
    def __init__(self, margin=0.1, hardest=True, squared=False):
        """
        Args:
            margin: margin for triplet loss
            hardest: If true, loss is considered only hardest triplets.
            squared: If true, output is the pairwise squared euclidean distance matrix.
                If false, output is the pairwise euclidean distance matrix.
        """
        super(HardTripletLoss, self).__init__()
        self.margin = margin
        self.hardest = hardest
        self.squared = squared

    def forward(self, embeddings, labels, device_id='cuda:0'):
        """
        Args:
            labels: labels of the batch, of size (batch_size,)
            embeddings: tensor of shape (batch_size, embed_dim)
        Returns:
            triplet_loss: scalar tensor containing the triplet loss
        """
        pairwise_dist = _pairwise_distance(embeddings, squared=self.squared)  # [bs, bs]
        #print("pairwise_dist:",pairwise_dist)


        if self.hardest:
            # Get the hardest positive pairs
            mask_anchor_positive = _get_anchor_positive_triplet_mask(labels, device_id).float()
            valid_positive_dist = pairwise_dist * mask_anchor_positive
            hardest_positive_dist, _ = torch.max(valid_positive_dist, dim=1, keepdim=True)

            # Get the hardest negative pairs
            mask_anchor_negative = _get_anchor_negative_triplet_mask(labels).float()
            max_anchor_negative_dist, _ = torch.max(pairwise_dist, dim=1, keepdim=True)
            anchor_negative_dist = pairwise_dist + max_anchor_negative_dist * (
                    1.0 - mask_anchor_negative)
            hardest_negative_dist, _ = torch.min(anchor_negative_dist, dim=1, keepdim=True)

            # Combine biggest d(a, p) and smallest d(a, n) into final triplet loss
            triplet_loss = F.relu(hardest_positive_dist - hardest_negative_dist + self.margin)
            triplet_loss = torch.mean(triplet_loss)
        else:
            anc_pos_dist = pairwise_dist.unsqueeze(dim=2)
            #print("anc_pos_dist shape",anc_pos_dist.shape)
            anc_neg_dist = pairwise_dist.unsqueeze(dim=1)
            #print("anc_neg_dist shape", anc_neg_dist.shape)

            # Compute a 3D tensor of size (batch_size, batch_size, batch_size)
            # triplet_loss[i, j, k] will contain the triplet loss of anc=i, pos=j, neg=k
            # Uses broadcasting where the 1st argument has shape (batch_size, batch_size, 1)
            # and the 2nd (batch_size, 1, batch_size)
            loss = anc_pos_dist - anc_neg_dist + self.margin
            #print("loss shape",loss.shape)

            mask = _get_triplet_mask(labels).float()
            triplet_loss = loss * mask

            # Remove negative losses (i.e. the easy triplets)
            triplet_loss = F.relu(triplet_loss)

            # Count number of hard triplets (where triplet_loss > 0)
            hard_triplets = torch.gt(triplet_loss, 1e-16).float()
            num_hard_triplets = torch.sum(hard_triplets)

            triplet_loss = torch.sum(triplet_loss) / (num_hard_triplets + 1e-16)

        return triplet_loss


def _pairwise_distance(x, squared=False, eps=1e-16):
    # Compute the 2D matrix of distances between all the embeddings.

    # got the dot product between all embeddings
    #print("x shape",x.shape)
    cor_mat = torch.matmul(x, x.t())

    #print("cor_mat shape:", cor_mat.shape)

    # Get squared L2 norm for each embedding. We can just take the diagonal of `dot_product`.
    # This also provides more numerical stability (the diagonal of the result will be exactly 0).
    norm_mat = cor_mat.diag()  # 输出矩阵主对角线上的元素
    #print("norm_mat shape:", norm_mat)

    # Compute the pairwise distance matrix as we have:
    # ||a - b||^2 = ||a||^2  - 2 <a, b> + ||b||^2
    # shape (batch_size, batch_size)
    #print("norm_mat.unsqueeze(0) shape:", norm_mat.unsqueeze(0).shape)

    distances = norm_mat.unsqueeze(1) - 2 * cor_mat + norm_mat.unsqueeze(0)

    # Because of computation errors, some distances might be negative so we put everything >= 0.0
    distances = F.relu(distances)

    if not squared:
        # Because the gradient of sqrt is infinite when distances == 0.0 (ex: on the diagonal)
        # we need to add a small epsilon where distances == 0.0
        mask = torch.eq(distances, 0.0).float()
        distances = distances + mask * eps
        distances = torch.sqrt(distances)

        # Correct the epsilon added: set the distances on the mask to be exactly 0.0
        distances = distances * (1.0 - mask)

    return distances


def _get_anchor_positive_triplet_mask(labels, device_id):
    # Return a 2D mask where mask[a, p] is True iff a and p are distinct and have same label.

    device = torch.device(device_id if torch.cuda.is_available() else "cpu")

    indices_not_equal = torch.eye(labels.shape[0]).to(device).byte() ^ 1  # 对角矩阵取反

    # Check if labels[i] == labels[j]
    labels_equal = torch.unsqueeze(labels, 0) == torch.unsqueeze(labels, 1)

    mask = indices_not_equal * labels_equal

    return mask


def _get_anchor_negative_triplet_mask(labels):
    # Return a 2D mask where mask[a, n] is True iff a and n have distinct labels.

    # Check if labels[i] != labels[k]
    labels_equal = torch.unsqueeze(labels, 0) == torch.unsqueeze(labels, 1)
    mask = labels_equal ^ 1

    return mask


def _get_triplet_mask(labels):
    """Return a 3D mask where mask[a, p, n] is True iff the triplet (a, p, n) is valid.
    A triplet (i, j, k) is valid if:
        - i, j, k are distinct
        - labels[i] == labels[j] and labels[i] != labels[k]
    """
    device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")

    # Check that i, j and k are distinct
    indices_not_same = torch.eye(labels.shape[0]).to(device).byte() ^ 1
    i_not_equal_j = torch.unsqueeze(indices_not_same, 2)
    i_not_equal_k = torch.unsqueeze(indices_not_same, 1)
    j_not_equal_k = torch.unsqueeze(indices_not_same, 0)
    distinct_indices = i_not_equal_j * i_not_equal_k * j_not_equal_k

    # Check if labels[i] == labels[j] and labels[i] != labels[k]
    label_equal = torch.eq(torch.unsqueeze(labels, 0), torch.unsqueeze(labels, 1))
    i_equal_j = torch.unsqueeze(label_equal, 2)
    i_equal_k = torch.unsqueeze(label_equal, 1)
    valid_labels = i_equal_j * (i_equal_k ^ 1)

    mask = distinct_indices * valid_labels   # Combine the two masks

    return mask

3.4 Dual Attention Supervision

由于二分类标签无法满足FAS的需求，作者提出了dual-attention supervision，包含live attention和spoof attention，为LDCNet提供具有细粒度信息的监督。作者使用Class Activation Map为LE和SE生成quasi-ground truth。具体来说，先预训练FE和CF，以获得live activation map 和spoof activation map ，

使用MSE约束和，和均为1×32×32的tensor，

其中，假体图片的和真人图片的为0

3.5 Total Loss and Live/Spoof Classification

其中，β=0.1，γ=0.004

在推理阶段，检测分数为：

4 实验结果