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摘要
Objective: Image segmentation is the foundation of object-based image analysis (OBIA). Scale set model is an effective image multiscale segmentation model, which can obtain the multiscale expression of images. However, traditional scale set models have several problems, such as low efficiency, complex data structure, and numerous redundant scales. To solve these problems, this study proposes a sparse scale set model based on the global regional dissimilarity threshold sequence. Method: The building of the sparse scale set model is driven by a global regional dissimilarity threshold. Specifically, the sparse scale sets are established by repeatedly expanding the global regional dissimilarity threshold and merging all adjacent regions whose dissimilarity is less than the global regional dissimilarity threshold. In addition, the global regional dissimilarity threshold corresponds to the abstract scale. Moreover, many key problems in the building of sparse scale sets are solved. First, a memorized deep-first search is adopted to obtain adjacent regions whose dissimilarity is less than the global regional dissimilarity threshold in the region adjacency graph (RAG). This process remarkably improves the search efficiency. Second, the true value of the total number of regional mergers corresponding to each scale can be obtained, whereas the accurate functional relationship between the total number of regional mergers and the global regional dissimilarity threshold cannot be obtained; therefore, the global regional dissimilarity threshold for each scale is sequentially obtained by repeatedly predicting the global regional dissimilarity threshold, and then the actual global regional dissimilarity threshold is backstepped on the basis of the actual number of merged regions and the expected number of merged regions. A three-dimensional exponential smoothing method that can achieve a stable number of merged regions between adjacent scales is used by the prediction algorithm of the global regional dissimilarity threshold. Third, the value of the global regional dissimilarity threshold rapidly expands because large scales forcefully merge large dissimilarities of adjacent regions, causing prediction lag. Therefore, this study uses a scale attribute analysis based on local variance (LV) and Moran's index (MI) to stop merging when the image segmentation state reaches undersegmentation. Result: Four experiments are designed to investigate the influence of sparsity on regional merge quality, the control of merging stop scale, the influence of core parameters on the speed of sparse scale set building, and the comparison of the speed of sparse and traditional scale set building. In the experiment on the influence of sparsity on regional merge quality, the values of LV and MI during the traditional scale set merging are used as standard values because traditional scale sets follow the optimal merge criterion. Results show that the root mean square error(RMSE) of LV and MI are only 0.037 and 0.434, respectively, even though the sparsity is expanded to 0.3. We believe that the degree of dissimilarity between the adjacent regions formed by oversegmentation within the same feature is usually much smaller than that between the adjacent regions belonging to different features. Therefore, increasing sparsity does not reduce the quality of the regional merger. The effectiveness of the proposed method based on scale attribute analysis is verified by a merging stop scale control experiment. The scale of the merging stop can be controlled by modifying the value of the penalty factor Q; the smaller the value of Q, the larger the scale of the merging stop. The results of many experiments reveal that the empirical value of Q is 0.6 because the probability of the merging stop scale is large enough to fall in a reasonable undersegmentation scale. The experiment on the influence of core parameters on the speed of sparse scale set building verifies the effect of different values of sparsity d on the building time of the sparse scale sets when N is fixed in the experiment. The building time is divided into two parts: region merger and scale attribute calculation. With the increase in d, the time of region merging and scale attribute calculation decrease. The scale attribute calculation time has a linear decreasing relationship with the reciprocal of d. Specifically, when d=0.017, the number of merged regions between adjacent scales is 50, the total number of theoretical scales is 61, and the total construction time is 22.082 s. When d=0.2, the number of merged regions between adjacent scales is 600, the total number of theoretical scales is 6, and the total build time is only 6.414 s. The smaller the value of d, the smaller the global regional dissimilarity threshold difference between adjacent scales; thus, edges that meet the conditions in RAG become more difficult to retrieve. The time consumption of each scale attribute calculation is only related to the image itself. The scale attribute calculation time of each scale in the experimental image is approximately 0.2 s. The smaller the value of d, the more the intermediate scales, resulting in the time consumption of the scale attribute calculation. In the comparison of the speed of sparse and traditional scale set building, the time for sparse scale set region merging increases from 0.318 s to 9.207 s, whereas the time for calculating the scale attribute remains basically unchanged when the sparsity d of the sparse scale sets is fixed, and the number of initial image segmentation regions N increases from 500 to 3 000. The total building time of the sparse scale sets increases from 4.513 s to 13.521 s, whereas the building time of the traditional scale sets increases from 12.661 s to 37.706 s. The average building speed of the sparse scale sets in the experiment is 3.11 times of the traditional scale sets. Conclusion: In this study, a sparse scale set model based on the global regional dissimilarity threshold sequence is proposed; the implementation method is presented, and several key problems are solved. Experiment results indicate that the sparse scale set model can dramatically improve the speed of scale set model building without reducing the quality of the merger. Furthermore, the sparse scale set model is more widely and flexibly applied in comparison with the traditional scale set model.
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