【论文阅读】RAL2022: Make it Dense: Self-Supervised Geometric Scan Completion of Sparse 3D LiDAR Scans in Large Outdoor Environments

0. 参考与前言

论文链接：https://ieeexplore.ieee.org/document/9812507

代码链接：https://github.com/PRBonn/make_it_dense

vdbfusion同组所出，自监督的scan completion，第一幅非常直白的表明了这个工作在做的任务，虽然数据结构 数据集不一样，但是很像grid map，elevation map 2.5D那边的补全，不过这个是mesh的surface mesh输出

1. Motivation

主要是为稀疏的点云输入，给一个dense的输出结果，首先是使用了vdbfusion的框架，然后propose a neural network去帮助frame-to-frame的3D 重建，走到 dense TSDF volume，这个基于一个 geometric scan completion network，是无需label的自监督训练

问题场景

主要是雷达的线束是16-128线，而价格也随线束的增加而线性增加，所以问题随之而来了：是否可以使用一个较为稀疏的信息，也能得到一个dense results map。[37] 中提到了这一问题的重要性，也就是无需积累帧数之间的数据结构也能得到一个dense observation，同时给到导航任务中

Contribution

提出了一个自监督的方法，可以将稀疏的3D激光雷达数据转成dense TSDF representation下的场景；与[10,19,37]不同之处是：we aim at completing single scans instead of completing a scene created from aggregated scans offline. 同时在相关工作中，也再次强调了这点：In contrast to these methods, which work on the aggregated volumes, we target the single scan setting to avoid the time-consuming buffering of scans.

过程主要是：

1. we process the 3D LiDAR data and pass it to our CNN. The output of the network is a TSDF representation
2. TSDF representation encodes the most recent observation plus synthetically completed data, which is then fused into a global map.

2. Method

1. 使用单帧信息构建基于TSDF的volumetric representation，这样可以得到 \(\boldsymbol D_t^S(\bf x)\) 和 权重 \(\boldsymbol W_t^S(\bf x)\) 其中 \(\bf x\) 为voxel在grid中的位置
2. 使用 \(\boldsymbol D_t^S(\bf x)\) 通过网络预测一个新的 TSDF value 我们用 \(\boldsymbol D_t^P(\bf x)\) 表示；网络目的：The network is trained to fill in values in a self-supervised way as if the data would have been recorded with a high-resolution LiDAR.
3. 当 grids之间全局匹配时，我们将 预测的 \(\boldsymbol D_t^P(\bf x)\) 放入 global grid中去 \(\boldsymbol D_t^G(\bf x)\)；然后由global signed distance fields 使用marching cubes [16] 得到surface representation

2.1 框架

输入：instead of raw data, 主要使用batch of TSDF volumes作为网络输入，原因主要是 TSDF的表达可以 split into non-overlapping volumes of 3.2 m^3；These volumes are batched together into a dense multidimensional tensor and then feed to our network

网络主要使用的是3D-UNet [6, 30]，首先使用dense 3D convolutions 去增加通道数量；然后每一步的encoder增加output通道；然后以unet形式，前后 skip connect，具体可以看代码，定义的很清晰：

class ResNetBlock3d(nn.Module):
    def __init__(self, in_channels, out_channels):
        super().__init__()
        self.conv1 = nn.Conv3d(in_channels, out_channels, kernel_size=3, padding=1, bias=False)
        self.bn1 = nn.BatchNorm3d(out_channels)
        self.relu = nn.ReLU(inplace=True)
        self.conv2 = nn.Conv3d(out_channels, out_channels, kernel_size=3, padding=1, bias=False)
        self.bn2 = nn.BatchNorm3d(out_channels)

    def forward(self, x):
        identity = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)
        out = self.conv2(out)
        out = self.bn2(out)
        out += identity
        out = self.relu(out)

        return out

class Unet3D(nn.Module):
    def __init__(self, channels: List[int], layers_down: List[int], layers_up: List[int]):
        super().__init__()

        self.layers_down = nn.ModuleList()
        self.layers_down.append(ResNetBlock3d(channels[0], channels[0]))
        for i in range(1, len(channels)):
            layer = [
                nn.Conv3d(
                    channels[i - 1], channels[i], kernel_size=3, stride=2, padding=1, bias=False
                ),
                nn.BatchNorm3d(channels[i]),
                nn.ReLU(inplace=True),
            ]
            # Do we need 4 resnet blocks here?
            layer += [ResNetBlock3d(channels[i], channels[i]) for _ in range(layers_down[i])]
            self.layers_down.append(nn.Sequential(*layer))

        channels = channels[::-1]
        self.layers_up_conv = nn.ModuleList()
        for i in range(1, len(channels)):
            self.layers_up_conv.append(
                nn.Sequential(
                    nn.ConvTranspose3d(
                        channels[i - 1], channels[i], kernel_size=2, stride=2, bias=False
                    ),
                    nn.BatchNorm3d(channels[i]),
                    nn.ReLU(inplace=True),
                    nn.Conv3d(channels[i], channels[i], kernel_size=3, padding=1, bias=False),
                    nn.BatchNorm3d(channels[i]),
                    nn.ReLU(inplace=True),
                )
            )

        self.layers_up_res = nn.ModuleList()
        for i in range(1, len(channels)):
            layer = [ResNetBlock3d(channels[i], channels[i]) for _ in range(layers_up[i - 1])]
            self.layers_up_res.append(nn.Sequential(*layer))

    def forward(self, x):
        xs = []
        for layer in self.layers_down:
            x = layer(x)
            xs.append(x)

        xs.reverse()
        out = []
        for i in range(len(self.layers_up_conv)):
            x = self.layers_up_conv[i](x)
            x = (x + xs[i + 1]) / 2.0
            x = self.layers_up_res[i](x)
            out.append(x)

        return out

总网络借鉴的是Atlas [19] ：

class AtlasNet(nn.Module):
    def __init__(self, config: MkdConfig):
				# xxx
				# Network
        self.feature_extractor = FeatureExtractor(channels=self.f_maps[0])
        self.unet = Unet3D(
            channels=self.f_maps,
            layers_down=self.layers_down,
            layers_up=self.layers_up,
        )
        self.decoders = nn.ModuleList(
            [nn.Conv3d(c, 1, 1, bias=False) for c in self.f_maps[:-1]][::-1]
        )

    def forward(self, xs):
        feats = self.feature_extractor(xs)
        out = self.unet(feats)

        output = {}
        mask_occupied = []
        for i, (decoder, x) in enumerate(zip(self.decoders, out)):
            # regress the TSDF
            tsdf = torch.tanh(decoder(x)) * 1.05

            # use previous scale to sparsify current scale
            if i > 0:
                tsdf_prev = output[f"out_tsdf_{self.voxel_sizes[i - 1]}"]
                tsdf_prev = F.interpolate(tsdf_prev, scale_factor=2)
                mask_truncated = tsdf_prev.abs() >= self.occ_th[i - 1]
                tsdf[mask_truncated] = tsdf_prev[mask_truncated].sign()
                mask_occupied.append(~mask_truncated)
            output[f"out_tsdf_{ self.voxel_sizes[i]}"] = tsdf
        return output, mask_occupied

2.2 Multi-Resolution Loss

loss设计很有意思，在提前定好的每个分辨率(32cm, 16cm, 8cm) 都给出了一个l1 loss，然后sum起来，代码对应如下；公式对应，首先是sdf的转换，

\[\phi(x)=\operatorname{sgn}(x) \cdot \log (|x|+1)
\]

然后分辨率下的loss，

\[\mathcal{L}\left(\hat{D}_i, D_i\right)=\sum_{\mathbf{x} \in \mathcal{R}_i}\left\|\phi\left(\hat{D}_i(\mathbf{x})\right)-\phi\left(D_i(\mathbf{x})\right)\right\|_1
\]

class SDFLoss(nn.Module):
    def __init__(self, config: MkdConfig):
        super().__init__()
        self.config = config.loss
        self.voxel_sizes = config.fusion.voxel_sizes
        self.sdf_trunc = np.float32(1.0)
        self.l1_loss = nn.L1Loss()

    @staticmethod
    def log_transform(sdf):
        return sdf.sign() * (sdf.abs() + 1.0).log()

    def forward(self, output, mask_occupied, targets):
        losses = {}
        for i, voxel_size_cm in enumerate(self.voxel_sizes):
            pred = output[f"out_tsdf_{voxel_size_cm}"]
            trgt = targets[f"gt_tsdf_{voxel_size_cm}"]["nodes"]

            # Apply masking for the loss function
            mask_observed = trgt.abs() < self.config.mask_occ_weight * self.sdf_trunc
            planes = trgt == self.sdf_trunc
            # Search for truncated planes along the target volume on X, Y, Z directions
            if self.config.mask_plane_loss:
                mask_planes = (
                    planes.all(-1, keepdim=True)
                    | planes.all(-2, keepdim=True)
                    | planes.all(-3, keepdim=True)
                )
                mask = mask_observed | mask_planes
            else:
                mask = mask_observed
            mask &= mask_occupied[i - 1] if (i != 0 and self.config.mask_l1_loss) else True

            if self.config.use_log_transform:
                pred = self.log_transform(pred)
                trgt = self.log_transform(trgt)

            losses[f"{voxel_size_cm}"] = F.l1_loss(pred[mask], trgt[mask])
        return losses

最后是整个sum，代码就是直接output sum起来了

# Compute Loss function
losses = self.loss(outputs, masks, targets)
loss = sum(losses.values())

2.3 Global Update

当我们获得了两个观测值后，一个是sensor data，一个是网络输出的，我们就可以将其整合到全局的grid下了，引入了一个权重，来指定 how much more we want to trust an actual measurement over a predicted TSDF value. 也就是下列公式所表示的，实验过程 让我们经验性的选择了 \(\eta=0.7\)

\[\begin{aligned}\Delta \mathbf{D}(\mathbf{x}) &=\eta \boldsymbol{W}_t^S(\mathbf{x}) \boldsymbol{D}_t^S(\mathbf{x})+(1-\eta) \boldsymbol{W}_t^P(\mathbf{x}) \boldsymbol{D}_{\underline{t}}^P(\mathbf{x}) \\\Delta \mathbf{W}(\mathbf{x}) &=\eta \boldsymbol{W}_t^S(\mathbf{x})+(1-\eta) \boldsymbol{W}_t^P(\mathbf{x})\end{aligned}
\]

当我们获得 \(\Delta \mathbf{D}\) 后 通过 [7] 所示 fuse for all voxels at location x

\[\begin{aligned}
\boldsymbol{D}_t^G(\mathrm{x}) &=\frac{\boldsymbol{W}_{t-1}^G(\mathrm{x}) \cdot \boldsymbol{D}_{t-1}^G(\mathrm{x})+\Delta \mathbf{D}(\mathrm{x})}{\boldsymbol{W}_{t-1}^G(\mathrm{x})+\Delta \mathbf{W}(\mathrm{x})} \\
\boldsymbol{W}_t^G(\mathrm{x}) &=\boldsymbol{W}_{t-1}^G(\mathrm{x})+\Delta \mathbf{W}(\mathrm{x})
\end{aligned}
\]

代码对应 由vdbfusion那边调用的函数：

from vdbfusion import VDBVolume
self._global_map = VDBVolume(
            self._config.voxel_size,
            self._config.vox_trunc * self._config.voxel_size,
            self._config.space_carving,
        )
self._global_map.integrate(scan, pose, weight=self._config.eta)
self._global_map.integrate(grid=self.make_it_dense(scan), weight=1 - self._config.eta)

C++ vdbfusion那边是：

void VDBVolume::Integrate(openvdb::FloatGrid::Ptr grid,
                          const std::function<float(float)>& weighting_function) {
    for (auto iter = grid->cbeginValueOn(); iter.test(); ++iter) {
        const auto& sdf = iter.getValue();
        const auto& voxel = iter.getCoord();
        this->UpdateTSDF(sdf, voxel, weighting_function);
    }
}

void VDBVolume::UpdateTSDF(const float& sdf,
                           const openvdb::Coord& voxel,
                           const std::function<float(float)>& weighting_function) {
    using AccessorRW = openvdb::tree::ValueAccessorRW<openvdb::FloatTree>;
    if (sdf > -sdf_trunc_) {
        AccessorRW tsdf_acc = AccessorRW(tsdf_->tree());
        AccessorRW weights_acc = AccessorRW(weights_->tree());
        const float tsdf = std::min(sdf_trunc_, sdf);
        const float weight = weighting_function(sdf);
        const float last_weight = weights_acc.getValue(voxel);
        const float last_tsdf = tsdf_acc.getValue(voxel);
        const float new_weight = weight + last_weight;
        const float new_tsdf = (last_tsdf * last_weight + tsdf * weight) / (new_weight);
        tsdf_acc.setValue(voxel, new_tsdf);
        weights_acc.setValue(voxel, new_weight);
    }
}

3. 实验及结果

定量分析：

定性分析

更多可查看原文

4. Conclusion

总结方法：We combine traditional TSDF-based volumetric mapping with 3D convolutional neural networks to aid reconstruction on a frame-to-frame basis.

主要局限性是，data本身的稀疏性，可以尝试sparse convolutions 从而有效减少内存消耗和提升运行效率 (确实可以试试

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