The quantificational comparison of robustness of ILEE and other algorithms by index rendering stability. Like Fig. S14, the dataset of Fig. 4 is added with a series of Gaussian noise (μ = 0, σ as variable), segmented by aforementioned algorithms, and their indices are computed and presented as the relative value to the ground truth. Each sample-noise combination is technically repeated by 12 times and the averaged result was used. The transparent area with light color indicates 95% confidence interval of each algorithm. For each figure, the lines with plainer slope indicate higher robustness (resistance to noise); being closer to 1.0 by value indicates higher accuracy. (a–c) Index class of density; (b), index class of bundling; (c), indices of other classes. For most of the indices, ILEE provide an extremely stable result against increasing noise, while other algorithms have very obvious change of value of output indices and are therefore no longer accurate (if they were), which echoes the visual observation of Fig. S14. Interestingly, skewness and CV are two exceptions, where ILEE shows more instability and tends to have a bifurcated direction of change.