Open Access
Table 1
List of all the symbols used in the paper.
| A | Initial map of intensity I |
| I | Intensity in a broad sense (intensity, column density, or temperature) |
| B | Smoothed map resulting from the convolution of A with a 2D top-hat kernel of radius R |
| R | Radius of the 2D top-hat kernel |
| C | Binary map derived from A-B |
| i | Index of the considered pixel of map C for the detection of bar-like filaments |
| Wb | Width of the model bar |
| Lb | Length of the model bar |
| rb = Lb /Wb | Aspect ratio of the model bar |
| ψb | Orientation angle of the model bar |
| ψf | Orientation angle of a filament |
| fM | Measured orientation function |
| σf | Median absolute deviation of fM |
| f1 | Ideal orientation function |
| Δψ | Width of the angular window over which fM is compared to fI |
 |
Measure of the normalized difference between fM and fI (Eq. (2)) |
| I0 | Central intensity of synthetic filaments |
| j | Index of the considered pixel of map A in one Monte-Carlo iteration |
 |
Standard deviation of sub-region Aj of map A, centered on pixel j |
 |
Signal-to-noise ratio of the ideal filament in the Monte-Carlo simulations |
| fS | Synthetic orientation function |
 |
Measure of the normalized difference between fS and f1 |
| (χr)th | Statistical threshold on χr |
| S = (χr)th /χr | Significance of filament detection |
| C′ | Binary map composed of the model bars associated with all the significant filaments |
| R | Map of reconstructed filaments |
| i′ | Index of the considered pixel of map R |
 |
Orientation angle of the most significant filament |
 |
bar width of the most significant filament |
| σW | Standard deviation of white noise in the sets of simulations |
| σB | Standard deviation of Brownian noise in the sets of simulations |
| Npix | Number of pixels whose most significant bar width is  |
| Nmap | Total number of pixels in the map |
 |
Most prevalent bar width for the entire map |
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