Grid-based Spatial Multi-scale Clustering By Synthesizing Edge-preserving Low-pass Filtering And Scale-aware Otsu Method

The existing grid-based multi-scale clustering methods fail to take scale factors as clustering model parameters explicitly,and make it difficult to implement the scaledriven threshold adaptive extraction.This issue impedes clustering parameter adjustment and optimization,and hinders the fully exploration the spatial distribution patterns of the study dataset.Comparing with traditional spatial dataset,the emerging big spatiotemporal point data contains more abundant information and has more complex hierarchical structure,which puts higher requirements on the parameter setting and calculation efficiency of clustering algorithms.To address above issues,this paper designs a multi-scale clustering algorithm that suitable for big spatial point dataset by defining two scale dimensions,i.e.,data scale and view scale.This method achieves data scale transformation and view scale transformation through the scale expansion mechanism of the grid multi-resolution and edge-preserving low-pass filtering respectively.By explicitly introducing the view scale as the model parameter of the clustering algorithm upon classical OTSU method,automatic extraction of multiple view scale density thresholds can be achieved.The main contents of this paper are as follows:1)Extract two scale factors that affect the multi-scale spatial clustering results.In this paper,the definition of data scale is derived from modifiable area unit problem and remote sensing multi-resolution image recognition,and the definition of view scale is derived from multi-scale low-pass filtering of signals.2)Designed a multi-scale clustering algorithm flow.According to the influence of data scale and view scale on clustering results,the overall flow of spatial multi-scale clustering algorithm combined with two dimensions is designed.Firstly,according to the application requirements,the algorithm divides the original spatial data into multiple data scales,and then establishes clustering results on multiple view scales for each data scale,and finally forms a multi-dimensional multi-scale spatial clustering result.3)Design an edge-preserving low-pass filter to extract the low-frequency information of the view scale.Low-frequency information extraction is a key step in the multi-scale clustering algorithm process.This paper improves the problems of common low-pass filtering and designs a simplified edge-preserving low-pass filter.The experimental results show that compared with wavelet filtering,the edgepreserving low-pass filter has better effect on denoising and edge preservation.4)A density threshold extraction method based on the scale constraint Otsu method is designed.Density threshold extraction is another key step in view scale iteration.In this paper,for the problems of threshold segmentation methods such as Otsu method and histogram concavity analysis method,the view scale level is added as a constraint to the target formula to achieve the scale-driven density threshold extraction.The experimental results show that compared with the Otsu method,the method can adaptively extract multiple clustering results,which can guide humans to fully understand the multi-level spatial laws,which has certain rationality.The experimental results show that compared with the DBSCAN clustering method,the algorithm can achieve adaptive extraction of parameter thresholds on multiple observation scales without the loss of precision.The process can also provide a reference for parameter selection of other algorithms.Moreover,the time complexity of the algorithm is low(O(n)),which enables near real-time massive spatial point clustering.In the practical application of infrastructure POI in China,the multi-scale clustering algorithm of this paper can reflect the multi-level economic structure of mainland China to a certain extent,and the results are more consistent with the multilevel spatial cognition results of the observers.The mining and visual analysis of multilevel spatial structure of auxiliary massive spatial point data has certain application value.Compared with the traditional low-pass filtering,the filtering method has good denoising and edge-preserving effect.The adaptive multi-scale density threshold algorithm can capture the rich multi-level information of the data set more effectively,and the computational complexity is low.The method can be used for rapid mining and visual analysis of various multi-level spatial structures of massive spatial point data.