# EOR: An Enhanced Object Registration Method for Visual Images and High-Definition Maps
## 3 Materials and Methods
### Enhanced Pose Estimation
#### 3.5.2 Enhanced Pose Optimization  
To maximize the advantages of combining multiple sources of information, we enhance the pose optimization by integrating SDF and SSC with traditional intensity constraints on distance transform images [10]. We assume the object categories \(C=[lanemarking,pole,sign]\). The process begins by extracting the binary image \(B_{c}\) for each object category \(c(c\in C)\) from the segmented image. Using OpenCV [29], we calculate the distance transform image \(D_{c}\) on \(B_{c}\) and normalize it to the range [0, 1]. The pose \(P\) (\(P\in\mathrm{SE}(3)\)) represents the 6-DoF transformation from the ego to the camera frame, encompassing both translational and rotational components. The target of this enhanced pose optimization module is to construct the cost function \(\xi(P)\) using SDF and SSC to solve for \(P\). The point \(p,Pp\), and \(\pi\)P\(p\) correspond to the HD map objects in the ego, camera, and image coordinate systems, respectively, with the category \(c\). \(\xi(P)\) comprises two parts: the intensity cost function \(I\) and the geometric cost function \(G\), as expressed in (13):  
\[\xi(P)=\sum_{p\in S,c\in C}I\big{(}p,c\big{)}+\alpha\cdot G(p,c) \tag{13}\] \[=\sum_{p\in S,c\in C}I\big{(}\pi Pp,c\big{)}+\alpha\cdot G(Pp,c)\]  
where \(\alpha\) is a weight parameter for the balance between the intensity constraint and the geometric constraint. \(I(p,c)(I\in[0,1])\) is the intensity difference at each pixel \(p_{i}(u,v)\) between the distance segmented image \(D_{c}\) and the projected HD map image, as described by (14):  
\[I(p,c)=1.0-D_{c}(f_{SDF}(p,c)) \tag{14}\]  
When \(I(p,c)=0\), it indicates that the map point \(p\) perfectly aligns with a segmented feature in \(D_{c}\). On the other hand, when \(I(p,c)=1\), it means \(p\) is projected onto a blank area of \(D_{c}\). The function \(f_{SDF}(p,c)\) maps the inputs to the corresponding object weights and optimized dimensions, as given in (15):  
\[f_{SDF}(p,c)=\Big{(}w_{lm},w_{pol},w_{sign},d\Big{)} \tag{15}\]  
Here, \(w_{lm}\), \(w_{pole}\), and \(w_{sign}\) denote the weights assigned to each object category. \(d\) represents the optimized dimensions within the 6-DoF using a specific index: \((0,1,2,3,4,5)\) corresponds to \((x,y,z,pitch,yaw,roll)\), respectively. As shown in Table 3, the initial weights for lane markings and poles are set to 1.0, indicating their importance as reference objects. The weight for traffic signs is set to 0.5, considering the potential limitations of bounding box post-processing and manual labeling procedures from LiDAR point clouds, which may not capture the complete shape of the signs. The initial dimensions contain 6-DOF. The adjustment of object weights and optimized dimensions based on different scenario conditions 1-5 can be summarized as follows:  
1. If the object category occupancy ratio \(\text{Occ}^{c}_{3d}=0\) or \(\text{Occ}^{c}_{2d}=0\): Set the weight assigned to that category to 0. This adjustment is due to the absence of occupancy in the respective modality, which restricts the ability to establish meaningful relationships or constraints between modalities. 2. If the longitudinal difference of lane markings \(L_{lm}<l(l=0.1)\): Increase the weights for poles and traffic signs and prevent the optimization of translation. \(L_{lm}<l\) (\(l=0.1\)) indicates the vehicle's location entering a road intersection. This accounts for unreliable lane markings in intersections, prioritizing independent objects and preserving spatial relationships. 3. If the longitudinal difference of lane markings \(L_{lm}\geq l(l=0.1)\) and \(\text{Occ}^{c}_{3d}>\text{Occ}^{lm}_{3d}\): Increase the weights for poles and traffic signs. This compensates for unreliable lane markings in normal road sections, enhancing the influence of poles and traffic signs in the analysis. 4. If the longitudinal difference of object \(L_{c}<l(l=0.1)\): Prevent longitudinal translation.