Comparison of the calculated Jacobi sets in the Cylinder Flow dataset for the Loop Subdivision (a), the Binomial filter (b), the Gaussian filter (c), the Collapse Algorithm variant B with t = 0.0001 (d), Collapse Algorithm variant C with t = 0.0001 (e), and Collapse Algorithm variant D with t = 0.0001 (f). Three regions of interest (ROI) are highlighted in color for visual comparison.

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... filter, a reduction of the Jacobi set components can already be recognized. The smoothing is further intensified with the Gaussian filter, which even leads to the removal of all Jacobi set components in this ROI. A similar result is obtained after applying the CA variants. Here, all Jacobi set components can also be removed, which can be seen in Fig. 5d, e, f. Only in variant A do individual Jacobi set components remain. The second ROI is marked in brown in the top center of the original data. A larger reddish Jacobi set component can be seen here, with several smaller components adjacent to it , which should be removed. After applying the loop subdivision, the large Jacobi set ...

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... of the original data. A larger reddish Jacobi set component can be seen here, with several smaller components adjacent to it , which should be removed. After applying the loop subdivision, the large Jacobi set component is visible and the small ones are no longer recognizable. When smoothing with the binomial filter, there is hardly any effect in Fig. 5b and the large and small Jacobi set components are still present. In contrast, the effect of smoothing by the Gaussian filter is too large and all components are removed, which is visible in Fig. 5c. When using the CA variant D, the result is similar to the binomial filter, and all components are still present. CA variants B and C do ...

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... Jacobi set component is visible and the small ones are no longer recognizable. When smoothing with the binomial filter, there is hardly any effect in Fig. 5b and the large and small Jacobi set components are still present. In contrast, the effect of smoothing by the Gaussian filter is too large and all components are removed, which is visible in Fig. 5c. When using the CA variant D, the result is similar to the binomial filter, and all components are still present. CA variants B and C do better here, where the large Jacobi set component remains and almost all small components disappear. In CA variant A, only the large component remains, as can be seen in Fig. 1 at the bottom left. The ...

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... the loop subdivision, several large Jacobi set components are separated from each other as can be seen in Fig. 5a. This indicates that the small components are caused by noise or numerical errors and should disappear. With the smoothing filters, the result is similar to before. The binomial filter smoothes too little and the Gaussian filter too much, whereby in this ROI the Gaussian filter does not remove all the small Jacobi set components, but ...

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... Fig. 3a, Fig. 4a, Fig. 5a, Fig. 6a, and Fig. 7a an overall view of the hurricane Isabelle dataset is shown after applying the binominal filter and the gaussian filter with σ ∈ {10, 50, 100, 500}. These smoothing filters also show visually that the Jacobi set components can be simplified visually. In detail, the cutout of Fig. 3b, Fig. 4b, and Fig. 5b shows that the ...

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... Fig. 3a, Fig. 4a, Fig. 5a, Fig. 6a, and Fig. 7a an overall view of the hurricane Isabelle dataset is shown after applying the binominal filter and the gaussian filter with σ ∈ {10, 50, 100, 500}. These smoothing filters also show visually that the Jacobi set components can be simplified visually. In detail, the cutout of Fig. 3b, Fig. 4b, and Fig. 5b shows that the reduction is present in the center of the hurricane and that the structures remain largely intact when compared with the original data. In the Fig. 6b, and Fig. 7b, the filter effect is already too strong, and important structures are no longer fully recognizable. The cutout in Fig. 3c, Fig. 4c, Fig. 5c, Fig. 6c, and ...

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... In detail, the cutout of Fig. 3b, Fig. 4b, and Fig. 5b shows that the reduction is present in the center of the hurricane and that the structures remain largely intact when compared with the original data. In the Fig. 6b, and Fig. 7b, the filter effect is already too strong, and important structures are no longer fully recognizable. The cutout in Fig. 3c, Fig. 4c, Fig. 5c, Fig. 6c, and Fig. 7c provides a slightly different picture, whereby a real simplification and thus the recognition of structures has not been improved. This is particularly evident in the comparison with the loop subdivision and the CA variant A. The image of the visual analysis is confirmed in the values from the Tab. 2, whereby a ...