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CNN Decoder

如patch设置为32x32,patch_scale设置为3，则先在原图上采样96x96大小的像素块，然后每隔三个取一个像素，降采样成32x32的块。

用这32x32个像素render feature，再经过CNN反卷积预测出96x96的像素，与真值对比。

def _patches_from_centers(self,image: torch.Tensor,patch_center_indices: torch.Tensor,rgb_size: int,device: Union[torch.device, str] = "cpu",
):"""Convert patch center coordinates to the full set of ray indices and image patches."""offsets = torch.arange(-(rgb_size // 2), (rgb_size // 2) + rgb_size % 2, device=device)zeros = offsets.new_zeros((rgb_size, rgb_size))relative_indices = torch.stack((zeros, *torch.meshgrid(offsets, offsets, indexing="ij")), dim=-1)[None]  # 1xKxKx3，原图采样大小rgb_indices = patch_center_indices[:, None, None] + relative_indices  # NxKxKx3ray_indices = rgb_indices[:, self.patch_scale // 2 :: self.patch_scale, self.patch_scale // 2 :: self.patch_scale]  # NxKfxKfx3，降采样ray_indices = ray_indices.reshape(-1, 3)  # (N*Kf*Kf)x3img_patches = image[rgb_indices[..., 0], rgb_indices[..., 1], rgb_indices[..., 2]]return ray_indices, img_patches

相机位姿优化

参考nerfstudio/cameras/camera_optimizers.py

每迭代一次优化一次

1. 初始化

self.pose_adjustment = torch.nn.Parameter(torch.zeros((num_cameras, 6), device=device)) # Nx6，前3维表示平移，后三维表示后3维表示切向量，再通过exp_map_SO3xR3，把6维变量映射为位姿和位移变量。相当于优化的是每个相机的标定参数

2. 计算位姿偏移量

def forward(self,indices: Int[Tensor, "camera_indices"],) -> Float[Tensor, "camera_indices 3 4"]:correction_matrices = exp_map_SO3xR3(self._get_pose_adjustment()[indices, :])

3. 应用到相机的原始位姿上

def apply_to_raybundle(self, raybundle: RayBundle) -> None:"""Apply the pose correction to the raybundle"""if self.config.mode != "off":correction_matrices = self(raybundle.camera_indices.squeeze())  # type: ignoreraybundle.origins = raybundle.origins + correction_matrices[:, :3, 3]raybundle.directions = (torch.bmm(correction_matrices[:, :3, :3], raybundle.directions[..., None]).squeeze().to(raybundle.origins))

6. 可学习的6维向量如何转成旋转矩阵

# nerfstudio/cameras/lie_groups.py
# We make an exception on snake case conventions because SO3 != so3.
def exp_map_SO3xR3(tangent_vector: Float[Tensor, "b 6"]) -> Float[Tensor, "b 3 4"]:"""Compute the exponential map of the direct product group `SO(3) x R^3`.This can be used for learning pose deltas on SE(3), and is generally faster than `exp_map_SE3`.Args:tangent_vector: Tangent vector; length-3 translations, followed by an `so(3)` tangent vector.Returns:[R|t] transformation matrices."""# code for SO3 map grabbed from pytorch3d and stripped down to bare-boneslog_rot = tangent_vector[:, 3:]nrms = (log_rot * log_rot).sum(1)rot_angles = torch.clamp(nrms, 1e-4).sqrt()rot_angles_inv = 1.0 / rot_anglesfac1 = rot_angles_inv * rot_angles.sin()fac2 = rot_angles_inv * rot_angles_inv * (1.0 - rot_angles.cos())skews = torch.zeros((log_rot.shape[0], 3, 3), dtype=log_rot.dtype, device=log_rot.device)skews[:, 0, 1] = -log_rot[:, 2]skews[:, 0, 2] = log_rot[:, 1]skews[:, 1, 0] = log_rot[:, 2]skews[:, 1, 2] = -log_rot[:, 0]skews[:, 2, 0] = -log_rot[:, 1]skews[:, 2, 1] = log_rot[:, 0]skews_square = torch.bmm(skews, skews)ret = torch.zeros(tangent_vector.shape[0], 3, 4, dtype=tangent_vector.dtype, device=tangent_vector.device)ret[:, :3, :3] = (fac1[:, None, None] * skews+ fac2[:, None, None] * skews_square+ torch.eye(3, dtype=log_rot.dtype, device=log_rot.device)[None])# Compute the translationret[:, :3, 3] = tangent_vector[:, :3]return ret

Apperance embedding

就是简单的使用torch.nn.Embedding(num_embeds, self.config.appearance_dim)

# Appearance embedding settings
# num_sensor指的是相机个数，如果配置temporal，则每一帧都有单独的embedding 
if self.config.use_temporal_appearance:self._num_embeds_per_sensor = math.ceil(self._duration * self.config.temporal_appearance_freq)num_embeds = num_sensors * self._num_embeds_per_sensor
else:num_embeds = num_sensors# num_embeds=6，self.config.appearance_dim=16，表示6个相机，每个相机有16维的Embedding特征
self.appearance_embedding = torch.nn.Embedding(num_embeds, self.config.appearance_dim)def _get_appearance_embedding(self, ray_bundle, features):sensor_idx = ray_bundle.metadata.get("sensor_idxs")if sensor_idx is None:assert not self.training, "Sensor sensor_idx must be present in metadata during training"sensor_idx = torch.full_like(features[..., :1], self.fallback_sensor_idx.value, dtype=torch.long)if self.config.use_temporal_appearance:time_idx = ray_bundle.times / self._duration * (embd_per_sensor := self._num_embeds_per_sensor)before_idx = time_idx.floor().clamp(0, embd_per_sensor - 1)after_idx = (before_idx + 1).clamp(0, embd_per_sensor - 1)ratio = time_idx - before_idx# unwrap to true embedding indices, which also account for the sensor index, not just the time indexbefore_idx, after_idx = (x + sensor_idx * embd_per_sensor for x in (before_idx, after_idx))before_embed = self.appearance_embedding(before_idx.squeeze(-1).long())after_embed = self.appearance_embedding(after_idx.squeeze(-1).long())embed = before_embed * (1 - ratio) + after_embed * ratioelse:embed = self.appearance_embedding(sensor_idx.squeeze(-1))return embed

lidar建模和采样

lidar发射射线和camer类似，只需要根据世界坐标系下lidar原点的坐标和点云的坐标，就能确定一条射线了，沿这条射线采样点，真值是这条射线上真正扫描到的点。

采样时，根据每次迭代设置的采样点数N如16384，平均到每帧的每个点上。

采样方式是把全部帧的点云concate起来，每个点有个全局的序号和帧的idx，假设总点数为100万，采样时在0-100万之间随机生成N个随机数。

    def get_lidar_batch_and_ray_bundle(self):if not len(self.lidar_dataset.lidars):return None, Nonebatch = self.point_sampler.sample(self.cached_points)ray_indices = batch.pop("indices") # Nx2, 0: lidar index, 1: point index，共采样16384个点，每帧采样点数一样ray_bundle: RayBundle = self.lidar_ray_generator(ray_indices, points=batch["lidar"]) #把所有的点都concate起来了return batch, ray_bundle # batch存储lidar原始点，ray_bundle存储采样的方向，原点信息

另外，pixel_area的作用没太看懂，有点像是MipNerf里面的用锥形体界面去积分，而不是直接的射线？

    dx = self.horizontal_beam_divergence[lidar_indices.squeeze(-1)]  # ("num_rays":...,)dy = self.vertical_beam_divergence[lidar_indices.squeeze(-1)]  # ("num_rays":...,)pixel_area = dx * dy  # ("num_rays":..., 1)

sdf实现

如果使用sdf，直接根据下面公式预测出不透明度α；否则便是先预测出密度density，再根据density积分得到不透明度。

因此两种render weight的方式是不同的。

if self.config.use_sdf:signed_distance = geo_out  # 直接把mlp的输出当作signed distanceoutputs[FieldHeadNames.SDF] = signed_distanceoutputs[FieldHeadNames.ALPHA] = self.sdf_to_density(signed_distance)
else:outputs[FieldHeadNames.DENSITY] = trunc_exp(geo_out) # 调用了torch.exp(), 为什么不能直接用geo_out作为density?有两个原因：1.因为density的物理意义是大于0的，geo_out不保证大于0  2. 网络输出的值可能非常小，使用epx放大，可以保持数值稳定性self.sdf_to_density = SigmoidDensity(self.config.sdf_beta, learnable_beta=self.config.learnable_beta)

这个名字应该叫SigmoidAlpha，最后输出的被当做α，不是density了

class SigmoidDensity(nn.Module):"""Learnable sigmoid density"""def __init__(self, init_val, beta_min=0.0001, learnable_beta=False):super().__init__()self.register_buffer("beta_min", torch.tensor(beta_min))self.register_parameter("beta", nn.Parameter(init_val * torch.ones(1), requires_grad=learnable_beta))def forward(self, sdf: Tensor, beta: Union[Tensor, None] = None) -> Tensor:"""convert sdf value to density value with beta, if beta is missing, then use learable beta"""if beta is None:beta = self.get_beta()# negtive sdf will have large densityreturn torch.sigmoid(-sdf * beta) #这里就是上面的公式，这里叫α，和density不是一个东西def get_beta(self):"""return current beta value"""beta = self.beta.abs() + self.beta_minreturn beta

render_weight_from_alpha()直接处理不透明度，而[render_weight_from_density()]则需要先从密度计算不透明度。

def _render_weights(self, outputs, ray_samples):value = outputs[FieldHeadNames.ALPHA if self.config.field.use_sdf else                 FieldHeadNames.DENSITY].squeeze(-1)if self.device.type in ("cpu", "mps"):# Note: for debugging on devices without cudaweights = torch.zeros_like(value) + 0.5elif self.config.field.use_sdf:weights, _ = nerfacc.render_weight_from_alpha(value)else:weights, _, _ = nerfacc.render_weight_from_density(t_ends=ray_samples.frustums.ends.squeeze(-1),t_starts=ray_samples.frustums.starts.squeeze(-1),sigmas=value,)return weights