# A Learnable Viewpoint Evolution Method for Accurate Pose Estimation of Complex Assembled Product
## 2 Proposed Method
### A Learnable Evolutionary Function Optimization  
The evolution functions mentioned above include \(\delta=E^{g}(\overline{vp}^{q})\), \(\lambda=E^{t}\Big{(}vp_{k}^{q}\Big{)}\), \(s=E^{e}\Big{(}vp_{k}^{q}\Big{)}v_{k}\), \(\tau=E^{a}\Big{(}vp_{k}^{q}\Big{)}\), \(\alpha=E^{p}\Big{(}vp_{k}^{q}\Big{)}\), and \(\sigma=E^{s}\Big{(}vp_{k}^{q}\Big{)}\), which are employed to manage evolution parameters and processes based on the performance of the population. The evolution function is initialized as a linear function, and the abscissas of the head and tail are taken as \(\overline{vp}^{q0}\) and \(min\big{\{}\varepsilon\overline{vp}^{q0},1.0\big{\}}\), where \(\varepsilon\) is the termination threshold. \(\delta_{0}\) can be referenced by \(\frac{1}{N_{\text{L}}}\sum_{k}^{N_{i}}cp^{res},vp_{k}\in\mathcal{P}_{1}, \delta_{end}=0.0\). The ordinates of other parameters need to be empirically provided; see Section 3 for details. As shown in Figure 6, a learning mechanism for optimizing the evolution function is proposed. The learning stage consists of three main modules and is designed as a hierarchical cyclic process. In the data collection module, each image of the dataset is repeatedly tested according to the current evolution function, and the evolution trajectory \(\boldsymbol{\ell}\in\boldsymbol{\ell}\) of the viewpoint with the best effectiveness in each test is collected. The effectiveness of the \(i\)-th round \(k\)-th viewpoint is defined as  
\[\rho_{k}^{i}=vp_{i,k}^{q}+\sum_{j=i}\Big{(}vp_{j,k}^{q}+p_{\sigma}vp_{j+1,k}^{ q}\Big{)} \tag{19}\]  
which can be regarded as a reverse tracking of \(vp^{q}\) of the trajectory generated by the final output viewpoint. For each node in \(\ell\), \(\Big{\{}vp^{q},\delta,\sigma,\dot{\lambda},\dot{s},\dot{\tau},\dot{\alpha} \Big{\}}\) are saved to complete the trajectory collection, where \(\dot{\star}\) represents the actual sampled value. Afterward, \(\Big{\{}\delta,\sigma,\dot{\lambda},\dot{s},\dot{\tau},\dot{\alpha}\Big{\}}\) are normalized to prevent overwhelming effects due to the magnitude differences. It can be found that the core purpose of evolution function optimization is to build the mapping relation between the observed population performance and process adjustment through high-quality results. Intuitively, there should be a better way of exploratory decay than six separate descent strategies with fixed slopes. The uneven performance of \(\boldsymbol{\ell}\) (there is a large variance of \(vp^{q}\)) generated by linear function will make further learning difficult to converge. To this end, a guided model based on multi-model fusion is designed to provide a reasonable transition for data distribution learning. The linear model can be extended as \(e=a_{b}\Big{(}vp^{qb}\Big{)}+c_{b},e\in\mathcal{E}_{0}\), where \(b\) controls the downward trend of the evolution curve, and \(e\) is the normalized result of each parameter  
Figure 6: A learnable mechanism based on effective trajectory tracking and guided model. in \(\mathcal{E}_{0}\). Given the head and tail points, \(a_{b},c_{b}\) can be modeled as functions of \(b\). Considering the correlation between parameters, factor fusion is performed as  
\[\sum_{e\in\mathcal{E}_{0}}\left\{a_{b_{e}}\left(vp^{q_{b}}\right)+c_{b_{e}} \right\}=\mathbf{e}^{\mathsf{T}}\mathbf{We} \tag{20}\]  
where \(\mathbf{W}\) is the correlation matrix. In such a way, the relationship between \(vp^{q}\) and \(\mathcal{E}_{0}\) can be comprehensively modeled by (20). The design of this guided model is derived from an empirical understanding of the evolution process from coarse-to-fine and a priori knowledge of the interaction of parameters. For example, the correlation between \(s\) and \(\tau\) should be prioritized over the correlation between \(s\) and other parameters. Furthermore, let the \(b_{e}\) of each parameter be initialized as a constant \(\mathsf{b}0,\mathsf{b}0>1.0\). The fitting of (20) is executed with \(\mathbf{\ell}_{0}\) as the dataset to obtain the guided model.