## 4 Proposed Method
### See-Then-Grasp: Two-Stage Robotic Full 3D Reconstruction Pipeline
#### 4.3.2 Stage 2 (Grasp-Assisted Full Coverage)  
In stage 2, the manipulator grasps the object and utilizes another fixed external camera to cover all areas of the object by showing the uncertain regions. Specifically, to obtain data regarding the NBV pose \(\mathcal{T}_{\mathbf{\Theta}}\) that allows for capturing the complete view of the object, the robot grasps the object and moves its end effector, satisfying \(\mathcal{T}_{\mathbf{\Theta}}\) relative to the external camera. The robot first employs a grasp pose generator such as Contact-GraspNet [48] to generate the grasp pose \(\mathcal{T}_{\text{grasp\_eef}}^{\text{base}}\) for grasping the object. Subsequently, we release the view space constraints from stage 1, expanding the view space around the object to a full spherical range. Then, the robot end-effector pose \(\mathcal{T}_{\text{move}}^{\text{base}}\) is generated following the transformation order. \[\mathcal{T}_{\text{move}}^{\text{base}}=\mathcal{T}_{\text{cam2}}^{\text{base }}(\mathcal{T}_{\mathbf{\Theta}})^{-1}(\mathcal{T}_{\text{obj}}^{\text{base}}) ^{-1}\mathcal{T}_{\text{grasp\_eef}}^{\text{base}}, \tag{19}\]  
where \(\mathcal{T}_{\text{cam2}}^{\text{base}}\) and \(\mathcal{T}_{\text{obj}}^{\text{base}}\) represent the pose of the external camera and the object canonical pose placed on the table, both relative to the robot's base frame. Note that \((\mathcal{T}_{\text{obj}}^{\text{base}})^{-1}\mathcal{T}_{\text{grasp\_eef}}^ {\text{base}}\) represents the transformation between the object pose and the end-effector frame after the object has been grasped and attached. By planning the path of the end effector according to \(\mathcal{T}_{\text{move}}^{\text{base}}\) while the robot grasps the object, the object pose as seen from the external camera can satisfy \(\mathcal{T}_{\mathbf{\Theta}}\). When stage 2 begins, the Voxurf model initiates the active learning process, incorporating the training dataset obtained from stage 1. By optimizing \(\mathcal{L}_{\text{NBV}}\), the full-coverage NBV pose \(\mathcal{T}_{\mathbf{\Theta}}\) is determined, and the robot's end effector is moved to \(\mathcal{T}_{\text{move}}^{\text{base}}\) to align with\(\mathcal{T}_{\mathbf{\Theta}}\) as seen from the external camera. Subsequently, an image is captured with the external camera and a segmentation mask is applied, adding the new image and pose pair to the current training dataset: \(\{\mathcal{I}_{i},\mathcal{T}_{i}\}_{i=1}^{t+1+\text{stage}\,1}\leftarrow\mathcal{ I}_{t},\mathcal{T}_{\mathbf{\Theta}}\). Similar to stage 1, the training process continues by optimizing the reconstruction loss \(\mathcal{L}_{\text{recon}}\) in Equation (18). The process is concluded when the object uncertainty \(\mathbf{U}(\mathcal{T}_{\mathbf{\Theta}})\) drops below the predefined threshold \(\epsilon_{2}\). Due to the use of two cameras, the backgrounds of the views from each camera differ, making it challenging to satisfy the view consistency of the object. To ensure the view consistency for each camera, we applied HQ-SAM [49] to generate object segmentation masks from the captured images. Furthermore, to retain the geometric information obtained in stage 1 during stage 2, we prevent gradients from flowing in areas outside the mask, thus preserving the information in regions occluded by the gripper. Specifically, a binary segmentation mask \(\mathcal{M}\), which has the same size as the raw image \(\mathcal{I}_{\text{raw}}\), is defined as follows:  
\[\mathcal{M}(\mathcal{I}_{\text{raw}})= \begin{cases}1&\text{if the pixel in }\mathcal{I}_{\text{raw}}\in\text{ object},\\ 0&\text{if the pixel in }\mathcal{I}_{\text{raw}}\in\text{background}.\end{cases}