## 3 Methods
### Neural Network Architecture of BiResNeRF  
The network used in this paper adopts a framework similar to the joint pose optimization and neural radiance field in BARF [24] and NeRF\(-\)[23]. The overall network architecture is shown in Figure 1. BiResNeRF is an improvement on the neural radiance field model part of NeRF based on this framework. The improved network architecture is shown in Figure 2.  
As shown in Figure 1, the yellow parts represent the training parameters, including \(\{\textbf{p},F_{\theta}\}\). **o** and **d** are the origin and direction in the world coordinate system of the ray, calculated based on \(\textbf{Ray}_{\textbf{cam}}\) and the extrinsic parameter \(p\). Sampling is performed on this ray, and the position of the sample point can be parameterized as \(\textbf{o}+t_{i}\textbf{d}\), where \(t_{i}\) represents the depth of the \(i\)th sample point. The position of the sample point and its direction **d** are input into the neural radiance field model, which returns the density and color of this point. Finally, by integrating the sampled points along the ray, the final color of the ray is obtained.  
As shown in Figure 1, this architecture consists of two modules: (1) the feature fusion module and (2) the rendering module. The feature fusion module is composed of two sub-modules, namely the low-resolution pose estimation module (a) and the high-resolution reconstruction module (b). These two modules have L1 and L2 different resolution layers, respectively. Each resolution layer obtains a feature vector of length F, and after concatenation, the length of the feature vector is (L1 + L2) \(\times\) F. Finally, this module uses a multi-layer perceptron (MLP) with one hidden layer to perform feature fusion and obtain the final feature vector. The primary function of the rendering module is to extract the density and color of the given position. The first component of the feature vector obtains the density \(\sigma\) through the ELU activation function. The other components of the feature vector are concatenated with the ray direction as new input features. Lastly, they pass through an MLP with two hidden layers, each having 64 neurons, and the Sigmoid activation function to obtain the RGB value of that position.  
When multi-resolution hash encoding is directly introduced in scenes with inaccurate poses, the features of a given position are generated under the combined effect of hash encodings of different resolutions. This hinders the pose estimation task due to the high-resolution hash encoding, making it difficult to adjust effectively, thereby affecting the accurate reconstruction of the scene.  
Figure 1: The framework of joint pose optimization.  
Figure 2: NeRF model network architecture.  
We propose the Low-Resolution and High-Resolution Hash Encoding feature fusion module, abbreviated as the feature fusion module, to address the issue of ineffective pose adjustment. As shown in Figure 2, this module consists of two sub-modules: the Low-Resolution pose estimation module (a) and the High-Resolution reconstruction module (b). The pose estimation module has fewer layers of low-resolution hash encoding. The larger grid provides more space for pose adjustment, enabling better completion of pose estimation tasks. Module (b) includes more layers of high-resolution hash encoding. The smaller grid has lesser pose adjustment capabilities but excels at capturing details, resulting in better high-resolution reconstruction.