Figure S4.
Visualized explanation of core ILEE algorithm. The core strategy of ILEE thresholding is explained from the perspective of time domain (i.e., image itself) and frequency domain (i.e., after Fourier transformation, FFT). (a) Schematic diagram describing how ILEE generates local threshold based on detected edges. For the purposed of simplicity, we use a “1D image” for demonstration. Suppose there is an example grayscale image (I) with 4 peaks of pixel value (i, ii, iii, iv); the higher peaks ii and iii are true cytoskeleton fluorescence but the lower peaks i and iv are random noise. ILEE first identify edges of cytoskeleton—area with a gradient magnitude higher than a computed threshold (marked cyan). Then these edges are used as “reference values” to generate a threshold image (Ithres, in red color) that smoothly links all the reference area. Finally, the bona-fide cytoskeleton will be defined as area where I is higher than Ithres. The areas not selected as edges will not be referred, which means true florescence with locally high values (ii, iii) are selected and background with locallay low values (i, iv) are excluded, regardless of whether the local level is generally low (i, ii) or high (iii, iv). (b) The comparison of effect of ILEE, classic low-pass filter, and implicit Laplacian smoothing (ILS) on image frequency domain. For low-pass filter, the input image (I) is transformed into frequency domain pattern by FFT, and we artificially define a filter where 0–1 indicates the passing rate of each frequency fraction. We pass the frequency pattern through the filter to render the filtered FFT pattern and restore the image by reverse FFT. For ILS and ILEE, the input image is transformed to frequency domain pattern by FFT; on the other side, the result of ILS and ILEE are pre-computed and transformed to frequency domain pattern as the “filtered FFT.” The (equivalent) frequency filter is deduced by subtracting filtered FFT from FFT of input and make the value relative to the FFT of input, which is comparable to the classic low-pass filter. ILS and ILEE have more fractions low frequency fractions on either x- or y-direction, which are potentially thick line cytoskeleton structures. Scale bar = 20 μm. (c) Comparison of high-frequency filtering of ILS and ILEE. The red rectangle in subplot (b) is maximized to present the detail. ILEE has uneven but well-directed selection of high frequency fractions because ILEE particularly preserves the cytoskeleton edge and tends to neglect the coarse background.

Visualized explanation of core ILEE algorithm. The core strategy of ILEE thresholding is explained from the perspective of time domain (i.e., image itself) and frequency domain (i.e., after Fourier transformation, FFT). (a) Schematic diagram describing how ILEE generates local threshold based on detected edges. For the purposed of simplicity, we use a “1D image” for demonstration. Suppose there is an example grayscale image (I) with 4 peaks of pixel value (i, ii, iii, iv); the higher peaks ii and iii are true cytoskeleton fluorescence but the lower peaks i and iv are random noise. ILEE first identify edges of cytoskeleton—area with a gradient magnitude higher than a computed threshold (marked cyan). Then these edges are used as “reference values” to generate a threshold image (Ithres, in red color) that smoothly links all the reference area. Finally, the bona-fide cytoskeleton will be defined as area where I is higher than Ithres. The areas not selected as edges will not be referred, which means true florescence with locally high values (ii, iii) are selected and background with locallay low values (i, iv) are excluded, regardless of whether the local level is generally low (i, ii) or high (iii, iv). (b) The comparison of effect of ILEE, classic low-pass filter, and implicit Laplacian smoothing (ILS) on image frequency domain. For low-pass filter, the input image (I) is transformed into frequency domain pattern by FFT, and we artificially define a filter where 0–1 indicates the passing rate of each frequency fraction. We pass the frequency pattern through the filter to render the filtered FFT pattern and restore the image by reverse FFT. For ILS and ILEE, the input image is transformed to frequency domain pattern by FFT; on the other side, the result of ILS and ILEE are pre-computed and transformed to frequency domain pattern as the “filtered FFT.” The (equivalent) frequency filter is deduced by subtracting filtered FFT from FFT of input and make the value relative to the FFT of input, which is comparable to the classic low-pass filter. ILS and ILEE have more fractions low frequency fractions on either x- or y-direction, which are potentially thick line cytoskeleton structures. Scale bar = 20 μm. (c) Comparison of high-frequency filtering of ILS and ILEE. The red rectangle in subplot (b) is maximized to present the detail. ILEE has uneven but well-directed selection of high frequency fractions because ILEE particularly preserves the cytoskeleton edge and tends to neglect the coarse background.

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