# Research on Multi-Scale Fusion Method for Ancient Bronze Ware X-ray Images in NSST Domain
## 2 Materials and Methods
### CNP-Based Low-Pass Subband Fusion Rule  
In general, the fusion strategy for the low-pass subbands has a significant impact on the final fused image. These subbands contain a significant amount of energy from the source image, which in turn has a significant influence on the fusion result. These low-frequency data are essential during the fusion process to maintain the overall structure, detail, and color balance. Therefore, selecting a suitable low-pass subband fusion approach is essential to achieving superior fused images. In order to fully guarantee the energy and extract as much detail as possible, a rule based on a localized topological CNP system is used in this paper for the fusion of low-pass subband components in the NSST domain. Inspired by the synchronized pulse bursts in mammalian visual cortex, [PERSON] et al. [19] proposed a similar neural P system called the coupled neural P system (CNP). The CNP system is a computational model consisting of multiple inter-coupled neurons linked together, each containing receptive fields, modulation, and output modules. These neurons form a directed graph structure among themselves, resembling a spiking neural P system, utilized for distributed parallel computation. The CNP system has unique characteristics. Firstly, it has a nonlinear coupling modulation property, which means that the interactions between neurons are nonlinear, and the coupling strength can be modulated. This feature allows the CNP system to exhibit enhanced computational abilities for complex tasks. And secondly, the CNP system also has a dynamic thresholding mechanism. The output of a neuron depends on its input, as well as on a dynamically adjusted threshold. By adjusting the thresholds dynamically, the CNP can adapt to various environments and task demands, thus enhancing computation's flexibility and adaptability. In order to better handle the image fusion problem, [PERSON] et al. [20] designed the CNP system as a neural array with local topology, which is a CNP system with local topology. A CNP system with an m \(\times\) n sublocal topology is defined as follows:  
\[\Pi=(O,\sigma_{11},\sigma_{12},\ldots,\sigma_{1n},\ldots,\sigma_{m1},\sigma_{ m2},\ldots,\sigma_{mn},\text{ syn }) \tag{8}\]  
where \(O=\{a\}\) is an alphabet, and the object \(a\) is called a spike. In this model, the spikes play a neuronal role. Spikes can generate and propagate pulse signals, simulating action potentials in neurons. These pulsed signals are used to transfer and process information in the computational model. The connection and coupling between the spikes form the network structure for parallel computing through the interactions in the network. \(\sigma_{11},\sigma_{12},\ldots,\sigma_{mn}\) is an array of coupled neurons of \(m\times n\) in the specific form of \(\sigma_{ij}=\left(u_{ij},v_{ij},\tau_{ij},R_{ij}\right)\), where \(1\leq i\leq m,1\leq j\leq n\). \[\text{syn}=\{(\text{ij},\text{kl})|1\leq\text{i}\leq\text{m},1\leq\text{j}\leq \text{n},|\text{k}-\text{i}\leq\text{r}|,|1-\text{j}|\leq\text{r},\text{i} \
eq\text{k},\text{j}\
eq 1\} \tag{9}\]  
where \(r\) is the neighborhood radius. According to the spike mechanism, the state equation of neuron \(\sigma_{ij}\) is as follows:  
\[u_{ij}(t+1)=\left\{ \begin{aligned} & u_{ij}(t)-u+\text{C}_{ij}+\sum _{\sigma_{kl}\in\delta_{\ell}}\omega_{kl}p_{kl}(t),\text{(if }\sigma_{ij}\text{ fires)}\\ & u_{ij}(t)+\text{C}_{ij}+\sum_{\sigma_{kl}\in\delta_{\ell}} \omega_{kl}p_{kl}(t),\text{(otherwise)}\end{aligned} \right. \tag{10}\]  
\[v_{ij}(t+1)=\left\{ \begin{aligned} & v_{ij}(t)-v+\sum_{\sigma_{kl}\in \delta_{\ell}}\omega_{kl}p_{kl}(t),\text{(if }\sigma_{ij}\text{ fires)}\\ & v_{ij}(t)+\sum_{\sigma_{kl}\in\delta_{\ell}}\omega_{kl}p_{kl}(t),\text{(otherwise)}\end{aligned} \right. \tag{11}\]  
\[\tau_{ij}(t+1)=\left\{ \begin{aligned} &\tau_{ij}(t)-\tau+p,\text{(if }\sigma_{ij}\text{ fires)}\\ &\tau_{ij}(t),\text{(otherwise)}\end{aligned} \right.