Volume 518, July-August 2010
Herschel: the first science highlights
Article Number L103
Number of page(s) 7
Section Letters
Published online 16 July 2010

Online Material

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\end{figure} Figure 2:

Composite 3-color images left of the sub-fields of Aquila ( top) and Polaris ( bottom) produced from the high-contrast ``single-scale'' decompositions (red comes from all SPIRE bands, green and blue correspond to the PACS bands at 160 and 70 ${\mu }$m, respectively); the sub-fields and decompositions are the same as in Fig. 1. Curvelet components ( right) extracted from the original SPIRE 350 ${\mu }$m images overlaid with ellipses for selected cores extracted by getsources (shown are starless cores: those detected at S/N $\ge $ 7.5 levels in at least two SPIRE bands and not detected in emission or detected in absorption in the PACS 70 ${\mu }$m band, with SED dust temperatures $T_{\rm d}\le 18$ K; see also Könyves et al. 2010; André et al. 2010). Most objects lie in the narrow and long filaments spanning orders of magnitude in intensity (MJy/sr).

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Appendix A: Extraction techniques

A.1 Existing source extraction algorithms

Here we summarize (very briefly) the concepts of different techniques, to place getsources described in Sect. 3 in a wider context. The algorithms trying to solve the same problem of source extraction originated from different ideas. Note that they have also been developed (oriented) for use in different areas of astronomy, thus their performance for a specific project must be carefully tested before an appropriate method can be chosen.

Stutzki & Guesten (1990)'s gaussclumps (originally created for position-velocity cubes) fits a Gaussian profile to the brightest peak, subtracting the fit from the image, then fitting a new profile to the brightest peak in the image of residuals, iterating until some termination criteria are met. Williams et al. (1994)'s clumpfind contours an image at a number of levels, starting from the brightest peak in the image and descending down to a minimum contour level, marking as clumps along the way all connected areas of pixels that are above the contour level. Bertin & Arnouts (1996)'s sextractor estimates and subtracts background, then uses thresholding to find objects, deblends them if they overlap, and measures their positions and sizes using intensity moments. CUPID[*]'s reinhold identifies pixels within the image which mark the edges of clumps of emission, producing a set of rings around the clumps. After cleaning noise effects on the edges, all pixels within each ring are assumed to belong to a single clump. CUPID's fellwalker ascends image peaks by following the line of the steepest ascent, considering every pixel in the image as a starting point for a walk to a significant peak, marking along the way all visited pixels with a clump identifier. Motte et al. (2007)'s mre-gcl combines cloud filtering techniques based on wavelet multi-resolution algorithms (e.g., Starck & Murtagh 2006) with gaussclumps. Molinari et al. (2010)'s derivatives analyzes multi-directional second derivatives of the original image and performs curvature thresholding to isolate compact objects, then fits variable-size elliptical Gaussians (adding also a planar background) at their positions. Another method that defines cores in terms of connected pixels is csar, which was developed for use with BLAST and Herschel (Harry et al. 2010, in preparation).

Whereas clumpfind, reinhold, fellwalker, and csar merely partition the image between objects not allowing them to overlap, gaussclumps, sextractor, and mre-gcl can deblend overlapping objects, which is quite essential for obtaining correct results in crowded regions. None of the methods was designed to handle multi-wavelength data, making it necessary to match thecatalogs obtained at different wavelengths using an association radius as a parameter.

A.2 More details on the new method

In getsources the extraction of objects is performed in each of the combined detection images by going from the smallest to the largest scales and finding segmentation masks of the objects at each scale using the tint fill algorithm (Smith 1979)[*]. The masks are the areas of connected pixels in a segmentation image, and the algorithm fills the pixels' values with the number of a detected object and allows tracking of all pixels belonging to the object across all scales. The segmentation masks expand toward larger scales, and the evolution of each object's mask is followed, as is appearance of new objects at any scale and disappearance of those which become too faint at the current and larger scales. When two or more objects touch each other in a single-scale image, the segmentation masks are not allowed to overlap, but overlapping does happen between objects of different scales. The largest extent of any source defines its footprint, and this is determined at the scale where the object's contrast above the cut-off level is at maximum. The scale itself provides an initial estimate for the object's FWHM size.

The positions of sources are computed from the first moments of intensities in a combined detection image at a range of single scales, from where an object first appeared and to the scale twice as large. The objects' sizes are computed from the first and second intensity moments in the original background-subtracted image. The background subtraction is done by linearly interpolating pixel intensities off the observed image under the footprints, in the four main directions (two axes and two diagonals), based on the pixel values just outside the footprints. Our iterative deblending algorithm employs two-dimensional shapes with peak intensities and sizes of the extracted objects in order to divide the intensity of a pixel between surrounding objects according to the fraction of the shapes' intensities at the pixel. For the shapes we adopted a two-dimensional analog of the Gaussian-like function  $f_0(1+(r/r_0)^2)^{-\alpha}$ (Moffat 1969) with $\alpha=10$.

The end result of the processing is an extraction catalog (one line per object) containing coordinates of all detections (independent of $\lambda$) and estimates of the objects' S/N ratios, peak and total fluxes (with their uncertainties), and sizes and orientations for each wavelength. In addition, getsources produces catalogs of all possible colors, as well as the azimuthally-averaged intensity profiles (their full, background-subtracted, and deblended versions) and deblended images for each object.

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