3DGS学习（七）—— 自适应高斯密度控制

3DGS中的优化方案

由于初始化点云可能导致生成高斯在空间中密度过大或过小，3dgs给出一些手段来在学习过程中自适应地密度，具体方法有点密集化和点剪枝。

点密集化

重建过度的区域拆分大高斯

官方代码

    def densify_and_split(self, grads, grad_threshold, scene_extent, N=2):
        n_init_points = self.get_xyz.shape[0]
        # Extract points that satisfy the gradient condition
        padded_grad = torch.zeros((n_init_points), device="cuda")
        padded_grad[:grads.shape[0]] = grads.squeeze()
        selected_pts_mask = torch.where(padded_grad >= grad_threshold, True, False)
        selected_pts_mask = torch.logical_and(selected_pts_mask,
                                              torch.max(self.get_scaling, dim=1).values > self.percent_dense*scene_extent)

        stds = self.get_scaling[selected_pts_mask].repeat(N,1)
        means =torch.zeros((stds.size(0), 3),device="cuda")
        samples = torch.normal(mean=means, std=stds)
        rots = build_rotation(self._rotation[selected_pts_mask]).repeat(N,1,1)
        # 新生成点云信息（由大高斯分割并按一定系数缩放得到）
        new_xyz = torch.bmm(rots, samples.unsqueeze(-1)).squeeze(-1) + self.get_xyz[selected_pts_mask].repeat(N, 1)
        new_scaling = self.scaling_inverse_activation(self.get_scaling[selected_pts_mask].repeat(N,1) / (0.8*N))
        new_rotation = self._rotation[selected_pts_mask].repeat(N,1)
        new_features_dc = self._features_dc[selected_pts_mask].repeat(N,1,1)
        new_features_rest = self._features_rest[selected_pts_mask].repeat(N,1,1)
        new_opacity = self._opacity[selected_pts_mask].repeat(N,1)

        self.densification_postfix(new_xyz, new_features_dc, new_features_rest, new_opacity, new_scaling, new_rotation)

        prune_filter = torch.cat((selected_pts_mask, torch.zeros(N * selected_pts_mask.sum(), device="cuda", dtype=bool)))
        # 裁剪过程参照其不透明度值进行，裁剪掉不必要的点提高效率
        self.prune_points(prune_filter)

实现过程

重建不足的区域克隆小高斯

官方代码

    def densify_and_clone(self, grads, grad_threshold, scene_extent):
        # Extract points that satisfy the gradient condition
        selected_pts_mask = torch.where(torch.norm(grads, dim=-1) >= grad_threshold, True, False)
        selected_pts_mask = torch.logical_and(selected_pts_mask,
                                              torch.max(self.get_scaling, dim=1).values <= self.percent_dense*scene_extent)
        
        new_xyz = self._xyz[selected_pts_mask]
        new_features_dc = self._features_dc[selected_pts_mask]
        new_features_rest = self._features_rest[selected_pts_mask]
        new_opacities = self._opacity[selected_pts_mask]
        new_scaling = self._scaling[selected_pts_mask]
        new_rotation = self._rotation[selected_pts_mask]

        self.densification_postfix(new_xyz, new_features_dc, new_features_rest, new_opacities, new_scaling, new_rotation)

实现过程

1. 根据梯度的阈值条件和点云的缩放因子，生成一个选择点的掩码 selected_pts_mask。
2. 基于选择的点生成新的点云坐标、特征、不透明度、缩放和旋转。
3. 将新生成的点云和特征附加到原始点云中。
4. 调用 densification_postfix 函数对点云进行后处理。

点剪枝

将不透明度小于一定阈值的点减去，将过大的也减去，类似于正则化过程。并且在迭代一定次数后，高斯会被设置为几乎透明。这样就能有控制地增加必要的高斯密度，同时剔除多余的高斯。

官方代码

def densify_and_prune(self, max_grad, min_opacity, extent, max_screen_size):
        grads = self.xyz_gradient_accum / self.denom
        grads[grads.isnan()] = 0.0
		# 点密集化过程
        self.densify_and_clone(grads, max_grad, extent)
        self.densify_and_split(grads, max_grad, extent)

        prune_mask = (self.get_opacity < min_opacity).squeeze()
        if max_screen_size:
            big_points_vs = self.max_radii2D > max_screen_size
            big_points_ws = self.get_scaling.max(dim=1).values > 0.1 * extent
            prune_mask = torch.logical_or(torch.logical_or(prune_mask, big_points_vs), big_points_ws)
        self.prune_points(prune_mask)

        torch.cuda.empty_cache()

    def prune_points(self, mask):
        valid_points_mask = ~mask
        optimizable_tensors = self._prune_optimizer(valid_points_mask)

        self._xyz = optimizable_tensors["xyz"]
        self._features_dc = optimizable_tensors["f_dc"]
        self._features_rest = optimizable_tensors["f_rest"]
        self._opacity = optimizable_tensors["opacity"]
        self._scaling = optimizable_tensors["scaling"]
        self._rotation = optimizable_tensors["rotation"]

        self.xyz_gradient_accum = self.xyz_gradient_accum[valid_points_mask]

        self.denom = self.denom[valid_points_mask]
        self.max_radii2D = self.max_radii2D[valid_points_mask]

实现过程

1. 上述代码根据最小不透明度和最大屏幕尺寸等条件生成剪枝掩码 prune_mask，并调用 prune_points 函数进行点云的剪枝操作。

2. prune_points 函数根据给定的掩码 mask 对点云进行剪枝操作，将不需要的点从点云中删除，并更新相关的张量数据。