# A Novel Method Based on Topological Perception Theory for 3D Landmark Building Model Retrieval
## 7 Discussion  
In this study, we propose a novel method for landmark building model retrieval to evaluate the algorithm's performance on a dataset we constructed. The method consists of two parts: a new projection method and the QDAH algorithm. Compared to the Hu moments and the Fourier descriptor algorithm, the QDAH algorithm extracted more stable topological features and performed better when classifying views of the model. This is likely because views with an identical topological structure may be completely different in terms of contours, textures, and other features, which is what makes topological features superior. In contrast to the QDH algorithm, our approach enhances the ability to distinguish between hole, non-concave, and concave unclosed shapes. This is achieved by reclassifying the voting interval of the quotient distance histogram and incorporating angular distribution features to minimize confusion among the three categories. Additionally, we performed model retrieval experiments comparing the new projection method combined with the QDAH algorithm to several classical 3D model retrieval algorithms. Compared with LFD_QDAH, the algorithm in this paper reduced the time cost by appropriately minimizing the projection views, and the retrieval results are comparable. This is in line with our view that topological features are more stable and that too many views will extract a large number of similar features, resulting in redundancy and little enhancement to the algorithm. Furthermore, our algorithm outperformed the SPH, LFD, MVCNN, and GVCNN algorithms in categorizing landmark buildings based on topological structure. We attribute this to our emphasis on the topology of landmark models, deliberately avoiding interference from other features.  
Classification based on topological structure mitigates interference from unrelated features. Nevertheless, in this study, attributes such as color and texture were not considered, potentially causing instances with similar topology but differing semantics to be erroneously grouped. In subsequent research, we aim to alleviate this limitation by integrating topological features with neural network models. One of the major difficulties of view-based methods is utilizing the relationships between features in multiple views effectively, and there is no exception in deep learning-related algorithms. On the one hand, some viewpoints are similar to each other and some are more different, and these similar viewpoints should play an equal role in the representation of 3D object shapes. On the  
Figure 11: Recall–precision curves of each algorithm.  
other hand, there are some perspectives that extract more useful features. If we can group the views by topological features and assign weights to them, the distinguishability of the final feature descriptors will be improved to some extent. Additionally, due to time constraints, the experimental results were exclusively derived from the dataset of landmark building models. Since the majority of building models available on the web are renowned landmark buildings, the process of gathering and generating datasets for other models is anticipated to be time-consuming. In this context, the models employed in this paper lack diversity. In the future, we will collect more building models and further validate the QDAH-related algorithms.