SIMULTANEOUS MULTI-BAND DETECTION OF LOW SURFACE BRIGHTNESS GALAXIES WITH MARKOVIAN MODELING^*

We employ the dedicated MARSIAA (MARkovian Software for Image Analysis in Astronomy) modeling software for the segmentation of multi-band images based on a hierarchical in-scale neighborhood system to overcome strongly noised observations (Laferte et al. 2000; Provost et al. 2004). In the following, we give a brief summary of the method which is described in detail in the Appendix.

The segmentation principle, corresponding to a segmentation (labeling) process, is simple: the segmentation classes (labels) are described on a hierarchical quadtree (see Figure 1). At the bottom of the quadtree each label is linked to the corresponding pixel of the observations Y. Whereas the information contained in the observations is propagated upward within the quadtree, the labels are propagated downward according to Markovian transmission probabilities, i.e., a label at a given level of the quadtree only depends on its parent. The quadtree structure is a well-adapted topology structure to express in-scale Markovian properties (transmission of information from parent to child), providing an efficient way to regularize the segmentation map (Laferte et al. 2000). This regularization maximizes the extent of objects within a segmentation class even in the presence of strong noise.

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Since the labels are unknown at the beginning of the process, they have to be estimated iteratively. The quadtree structure deals with the label estimations at various spatial resolutions: the top represents the lowest resolution (a single label for the whole image) whereas the bottom corresponds to the finest resolution, i.e., the image pixels. At the bottom of the quadtree all labels X are linked to the observations Y through a data-driven term defined as the parametric probability density function (pdf), which is assumed to be a multi-dimensional Gaussian of variable variance. The data-driven term allows the correct connection between the observations (scalar or multi-component at each location, according to the available data) and the label which has to be estimated at the same image location. The rules on labels between scales are managed by the Markovian property: the children labels depend on the parent label according to transition probabilities. The label at the finest resolution represents the end product of our algorithm: true or false for a detection problem, reconstructed surface brightness in a restoration problem, or 1, 2, ..., N for our segmentation problem where we sort image pixels into N subsets of similar behavior. In our case the final map for a given class is a binary mask at the highest resolution. This type of regularization scheme is generic, allowing the detection, segmentation, and classification of raw data:

• 1.  
  in the case of multi-band observations, containing data at different scales (which is not our case), the quadtree is fed by the observations at different scales and the segmentation process takes into account all data simultaneously;
• 2.  
  in the case of missing data, the quadtree can take into account only its prior (parent–children transition probability) to define the label.

Compared to other detection methods our approach is scale free, because the hierarchical quadtree is only applied to the set of labels, whereas the information contained in the data at the highest resolution is not propagated to lower resolution planes within the quadtree. MARSIAA does not handle different point-spread functions (PSFs) explicitly. However, a band with data of significantly different resolution can feed a different level of the quadtree. On the other hand, the method will become scale dependent if applied to data projected toward another representation space (wavelet, curvelet, shapelet, etc.) where the coefficients again may feed the quadtree at different levels (Crouse et al. 1998; Romberg et al. 2001; Murtagh et al. 2005; Starck & Murtagh 2006; Chan et al. 2008), because structures are intuitively selected on dyadic scales. The advantage of our approach consists of the combination of multi-band data in the Bayesian inference process, without any mathematical decomposition on a specific function basis: in this sense the data remain unchanged and the segmentation process is model independent.

The segmentation process assigns image pixels to different classes. The final map of a given class is a binary mask in which all pixels belonging to this class have been assigned a value of 1 and where the rest are all 0. The mean amplitude of a given class depends on the information contained in the whole image and the number of classes. Typically, class 0 is the noise and the LSB galaxies are contained in class 1 and/or 2. The user defines the total number of classes, which in our case was set to 6 for the INT images and 8 for the NGVS images, after tests using values between 4 and 10. Since a given pixel can only be assigned to one class, detected objects with a significant gradient in their surface brightness profiles will be distributed over different classes, e.g., the outer parts are labeled as class 1, the intermediate radii as class 2, and the center of the object as class 3. To obtain binary masks of each entire object in a given class N₀, we therefore have to add the binary masks of classes N ⩾ N₀. The assignment of image pixels to the different classes depends on the total number of classes, the dynamic range of the image, and the surface brightness distribution. Our simulations (Section 4) show that the detection of known LSB galaxies on CCD images is hampered by the high dynamic range, due to the presence of stars. To avoid this problem we clipped the images at the 20σ level (σ being the noise in the images), which affects mainly bright stars but not the galaxies we are searching for. We determined the clipping level heuristically by applying our method to known LSB galaxies from Sabatini et al. (2003) which could not be detected in the image without clipping. The results are not sensitive to the exact value of the clipping level (10σ–30σ). The subsequent LSB detection was conducted on both the original and the 20σ level clipped images for the INT data and on the 30σ level clipped images for the NGVS.

The MARSIAA segmentation map represents the heart of our proposed method for the detection of LSB galaxies in multi-band images. The MARSIAA objects have then to be tested for stellarity and confusion. This is done with a subsequent algorithm called DetectLSB which is based on radial surface brightness profiles to which an exponential profile is fitted. If a cut in exponential scale length (e.g., r_e ⩾ 3'') is applied to the LSB galaxy candidates on images of intermediate depth (μ_B ∼ 26 mag arcsec⁻²), the resulting relatively small number of LSB galaxy candidates permits all to be visually inspected. Since the number of LSB galaxy candidates is huge for deep images (μ_g ∼ 29 mag arcsec⁻²), we developed additional selection software which is based on the source parameters from DetectLSB. The whole processing pipeline consists of five steps: (1) cutting the images into subimages of sizes up to 2048 × 2048 pixels, which represents the limiting image size for MARSIAA, (2) application of MARSIAA simultaneously to the multi-band subimages, (3) application of DetectLSB, (4) cross-identification of the objects identified by DetectLSB via a clustering algorithm, and (5) visual inspection of LSB candidate galaxies or application of an LSB selection software. The pipeline only needs human intervention between step (4) and (5), to change the format of the source catalog from xml to ascii.

Segmentation artifacts such as very small connected components or small holes are removed by using a morphological Open-Close-Close-Open filter⁸ (Gonzalez & Woods 1992; Soille 2003) with a cross structuring element of 3 pixels width. A second filter eliminates objects having a diameter smaller than the PSF FWHM or larger than 200 pixels. Finally, objects too close to image borders (when the distance from center to border is less than 64 pixels) are removed and the remaining objects are labeled.

The isophotes of the galaxy are modeled as ellipses (Figure 2), which are described by five parameters: center c, major axis radius a, minor axis radius b, and major axis position angle α. The initial values are provided by Matlab through the function "regionprops" which determines the ellipse which has the same second moment as the object detected by MARSIAA. The fit is performed through the minimization of a cost function which decreases when symmetry increases. The space is divided into homothetic elliptical rings {e_a} with a width of one PSF FWMH each. We define the partial cost function of each ring as the sum of the absolute difference between the mean value of pixels in each quadrants, whereas the total cost function is the weighted sum of all partial energies. Formally, the cost function e is given by

$$\begin{equation} e=\sum _{r=0}^{a}{G(r)\sum _{i=1}^{4}{\sum _{j=1,j\ne i}^{4}{|B_{i}(r)-B_{j}(r)|}}}, \end{equation} \tag{ 1 }$$

where B_i(r) is the mean pixel value over the ith quadrant of the ring at radius r and G(r) = exp (− r²/2a) is a weighting function which decreases with radius r.

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The major and minor axis radii are defined as the last points on the radial fits whose error bar lies above the noise level. The optimization is done with an adaptive gradient descent algorithm which processes the parameters sequentially, in the following order: center position, position angle, and minor axis radius. The major axis, which is a direct result of MARSIAA, is not optimized. The minor axis radius and center parameters are constrained: the radius and the center have to stay within a range of 10 pixels from their initial values, and the center within ±10° from its initial value. The procedure is run on a mean filtered version of the image (3 × 3 pixel filter) and pixels belonging to other MARSIAA objects are ignored. If the estimated center is not included within the original MARSIAA object, we consider that the fit has failed and the object is eliminated.

In the next step, we compute the mean surface brightness profile using all four quadrants. An exponential profile is fitted by performing a linear regression on the mean surface brightness profile in a single band. Within each ellipse annulus e_a we compute the mean surface brightness value μ_a and its standard deviation σ_a, using a mean filtered version of the image (3 × 3 pixel filter), and ignore all pixels belonging to different MARSIAA objects and to segmentation classes <j − 1 or >j + 1, where j is the class of the majority of pixels in the annulus. The local background level μ_b and local pixel noise σ_b are estimated in a window of 512 × 512 pixels centered on the object with the same iterative clipping algorithm as used in SExtractor (Bertin & Arnouts 1996). The linear regression is performed only on those points whose error bars lie above the background level and whose distance from the object center is smaller than that of the first point which lies below the background level (Figure 2). We also calculate the half-light radius and the magnitude based on the radial profile. For the determination of the half-light radius, the surface brightness profile was not interpolated. The half-light radius has thus discrete values. We extrapolated the magnitudes by assuming an exponential profile and a measured source extent of 3.4 scale lengths. The extracted half-light radii and magnitudes are thus rough estimates and are not intended to replace photometric measurements with more sophisticated methods.

We have defined a set of empirical selection rules based on estimated surface brightness profiles for the removal of spurious detection like stars, HSB galaxies, or multiple objects. An object is discarded if one of the following conditions is met:

• 1.  
  the linear regression includes less than three points;
• 2.  
  multiple objects: the second point is higher than the first one and there exists another point higher than the second one (not necessary the third one);
• 3.  
  surface brightness criterion: the extrapolated central surface brightness is higher than 30σ in the B/g band and 60σ in the I/i band;
• 4.  
  star criterion: the difference between the extrapolated central surface brightness and the measured central surface brightness is more than 2 mag arcsec⁻² (this case applies when the wings of a star are fitted), where the latter is defined as the mean pixel value in a central ellipse with a major axis radius of 4 pixels;
• 5.  
  extension criterion: the width of the extrapolated curve at 20% of its height is less than 1.5 times the width of the PSF at 20% of its height. This criterion rarely applies.

Since the same object can be detected and identified as an LSB galaxy using masks of different classes, DetectLSB can yield up to five sets of derived parameters for the original and clipped image each (see Section 2.2). We gather these sets of parameters to form one single object using a clustering algorithm based on the projected distances between the different identifications.

In order to evaluate the performance and the limits of our method, we performed several tests on simulated images. All simulations were done using single- and multi-band (2 and 3 bands) images. We considered two classes of sources—elliptically shaped LSB disk galaxies with an exponential surface brightness profile and point sources—and a flat background. These images are convolved with the point-spread function and Gaussian noise is added to them:

$$\begin{equation} Y = H * m +b, \end{equation} \tag{ 2 }$$

where * stands for a convolution, Y is the simulated image, H is the point-spread function, m is the sum of all components of the simulation (LSB galaxy, point sources, background), and b is the noise (assumed to be Gaussian with zero mean).

We use the following image characteristics which are close to the INT observations to which we applied MARSIAA (see Section 5); the intensities are given in arbitrary units:

• 1.  
  pixel scale: 033 pixel⁻¹ (in all bands);
• 2.  
  PSF FWHM: 21 in the first band (B) and 20 in the second (I);
• 3.  
  background level μ: 779.6 in the first band and 3717.1 in the second;
• 4.  
  noise deviation σ: 16.9 (25.98 mag arcsec⁻²) in the B band and 31.6 (24.82 mag arcsec⁻²) in the I band.

The free parameters of our simulations are: scale length and central surface brightness of the LSB galaxy in both bands and the number of point sources. The size of the simulated images is 512 × 512 pixels. To avoid border effects, the LSB galaxy is always placed at the center of the image. It has a constant eccentricity of $\sqrt{3}/2$ (i.e., the major axis is two times longer than the minor axis) and a major axis position angle of 0 deg. Point sources are generated randomly in an annulus with an inner radius of 75 pixels and outer radius of 128 pixels. Their peak brightness is also chosen randomly between 25σ and 1000σ.

We performed 10 sets of LSB detection simulations which are designed to reproduce INT data of Sabatini et al. (2003; see Section 5). For each set an LSB galaxy with a central surface brightness between 0.3σ and 3σ and a characteristic scale length between 2'' and 15'' was hidden in a 512 × 512 image. Three, five, and seven point sources were then added to the image in 21 different configurations. For each set, MARSIAA and DetectLSB were applied on a clipped and a non-clipped test image, because the division of the image pixels into the different classes depends on the dynamic range of the image and the surface brightness distribution (see Section 2.2). Figures 3 and 4 show the detection statistics for the following six different scenarios:

• 1.  
  single band (a);
• 2.  
  2 bands with LSB galaxies of the same central surface brightness and characteristic scale length in both bands (b);
• 3.  
  3 bands with LSB galaxies of the same central surface brightness and characteristic scale length in both bands (c);
• 4.  
  single band with a 20σ level clipping (d);
• 5.  
  2 bands with LSB galaxies of the same central surface brightness and characteristic scale length in both bands, with 20σ level clipping (e);
• 6.  
  3 bands with LSB galaxies of the same central surface brightness and characteristic scale length in both bands, with 20σ level clipping (f).

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While in the simulations shown in Figure 3 no point sources were added, the simulated images of Figure 4 contained either 3, 5, or 7 polluting point sources. The results of 21 simulations with different numbers of polluting sources were included in the detection statistics of Figure 4. The detection fractions are upper limits of what can be expected for observations, because (1) the simulated galaxies are designed to have exponential profiles and (2) real LSB galaxies might be located near or overlap with other extended sources.

In the case of no polluting point sources the detection statistics becomes worse for 2 and 3 bands. This is the well-known curse of dimensionality (Hughes phenomenon): the number of pixels in a segmentation class (containing the LSB structure) may become relatively small and the segmentation process fails. Because MARSIAA is applied to subimages with sizes between 512 × 512 pixels and 1024 × 1024 pixels, this scenario is never met in astronomical images where a large number of polluting point sources is always present.

As expected, the presence of polluting point sources makes single-band detection statistics worse (Figure 4). On the other hand, the addition of multiple bands improves the detection statistics in this case. Our method is able to detect with a 90% success rate LSB galaxies with a characteristic scale length of ⩾4'' down to the 1.5σ central surface brightness level. For the unclipped images the detection rate increases only slightly for objects larger than 6'' when MARSIAA is applied to 2 and 3 bands simultaneously. When applied to images which are clipped at a 20σ level, the detection limit at the 90% success rate for extended objects (⩾8'') decreases from 1.5σ to the 1σ level. This illustrates the effect of the surface brightness distribution on the segmentation process and justifies the approach to apply our method on clipped images. We want to emphasize here that the test images are idealized cases and that the application of our method on actual INT observations (Section 5) has shown that our detection limit in practice lies between 1.5σ and 2σ in both the original and the clipped images.

A galaxy might have a different characteristic scale length in each band. This can be the case for both late-type spirals, lenticulars, or ellipticals with a dominant old stellar population and only a small amount of recent star formation. To model such LSB galaxies of different colors, we have put an LSB galaxy of fixed size (10''), central surface brightness, and axis ratio in one band and varied the properties of the second LSB galaxy in the second band (Figure 5):

• 1.  
  2 bands, with an LSB galaxy with a central surface brightness of 1σ in one band (a);
• 2.  
  2 bands, with an LSB galaxy with a central surface brightness of 1σ in one band, and 20σ level clipping (b);
• 3.  
  2 bands, with an LSB galaxy with a central surface brightness of 0.5σ in one band (c);
• 4.  
  2 bands, with an LSB galaxy with a central surface brightness of 0.5σ in one band, and 20σ level clipping (d).

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For LSB galaxies with different colors, i.e., different central surface brightness and/or different scale length in the two bands, an object with a large scale length (10'') and a central surface brightness of 1σ in one band can be detected with 90% probability if the surface brightness and scale length in the second band are greater than 1.5σ and 4'', respectively. For the clipped image the limiting surface brightness decreases below 1σ for LSB galaxies with a scale length >6''. In an extreme case, where a large LSB galaxy (10'') has a central surface brightness of only 0.5σ, its scale length has to be larger than 9'' in the second band to be detected at the 90% level with a central surface brightness of 1.5σ. In this case, clipping does not significantly enhance the detection rate.

In conclusion, we are confident that in images with a PSF FWHM of about 2'' we can detect LSB galaxies with a radius ⩾4'' down to a central peak S/N  ∼ 1.5. Large LSB galaxy (scale length ∼10'') located in one band can in principle be detected down to S/N  ∼  1. Clipping of the images always increases the detection probability.

The optical images we use in this paper are part of the 2.5 m Isaac Newton Telescope Wide Field Camera (INT WFC) survey of the Virgo Cluster which was used by Sabatini et al. (2003, 2005) in their search for LSB dwarf galaxies in the cluster. Here, we present results from the west–east B- and I-band strips in the cluster. The data were preprocessed and reduced using the Wide-Field Survey pipeline, see Sabatini et al. for details—the photometric zero points are accurate to 1%–2%. The results are given in the B and I magnitudes of the Johnson–Cousin photometric system. Each 2048 × 4100 pixel INT image has a size of 1126 × 2255, a pixel size of 033 × 033, a mean PSF FWHM of 21 and 20 in the B and I bands, respectively, and the B band sky noise level corresponds to ∼26 mag arcsec⁻².

After the source identification by DetectLSB, ∼40–50 objects were found per INT image, giving in total 800 objects on 18 INT images. However, this total includes not only genuine Virgo LSB galaxies, but also background galaxies and confused sources. An inspection by eye represents the most secure way to separate these different classes of sources. To facilitate the checking of the DetecLSB identifications by eye, we developed the java tool LSBExplorer which displays the object together with its measured parameters, surface brightness profiles, image cut-outs, and segmentation maps. This readily permits the user to flag a source as an LSB galaxy candidate. At the end of the inspection the selected sources can be saved in xml or VOtable format. Despite the automatic rejection criteria (Section 4.1), there are still many spurious objects. As a first test, three of the authors (S.S., W.v.D., B.V.) independently sorted the sources in one INT image (v234c4) by eye and rejected the spurious sources. In this way, respectively, 70%, 60%, and 52% of the sources were rejected by the three examiners; 47% were rejected by all three, 13% were rejected by two, and 12% were rejected by only one. Thus, more than half of the sources are spurious. We did not attempt to make the automatic rejection criteria more stringent, because this might lead to uncontrolled rejections of relevant sources.

To investigate the nature of the spurious sources, the same three authors then sorted the sources in 10 INT images into different categories (Table 1). The overall rejection rate is 50%–70%, consistent with the aforementioned statistics of the simultaneous inspection of one INT image. Of these rejections 50%–70% are classified as multiple sources which are sometimes confused and 20%–40% could not be distinguished from extended low-level variations in the sky noise. After the inspection about 15–20 sources were left per INT image. Most of them are cosmologically dimmed background galaxies which are typically compact and elongated, and have characteristic scale lengths smaller than 3'' (Sabatini et al. 2003).

5.2.1. Virgo Cluster LSB Galaxies

We applied MARSIAA simultaneously to 18 INT B- and I-band images (1.3 square degree), and then applied DetectLSB separately to the B and I images using the MARSIAA segmentation masks (see Section 2.2). Table 2 shows the 52 LSB galaxy candidates we found with a characteristic scale length greater or equal than 3''. Since the observed fields are overlapping, some sources appear twice in the table. We decided to leave these doubles, because they represent independent MARSIAA detections/DetectLSB identifications on images with different S/N. The table columns are: (1) galaxy number from this work (a star marks the nine LSB galaxy candidates not found by Sabatini et al. 2003), (2) galaxy number from Sabatini et al. (2005), (3) right ascension, (4) declination, (5) central B-band surface brightness, (6) B-band scale length, (7) I-band characteristic scale length, (8) I-band central surface brightness, (9) color gradient ∇_{B − I} = 1/(log (r^B_d) − log (r^I_d)), (10) total apparent B magnitude, (11) total apparent I magnitude, (12) B − I color, and (13) background flag. Based on the galaxy morphology we labeled 18 objects as background galaxies (bg in Column 13). Among the remaining 34 objects we did not classify as background, we detected 9 that are not included in the Sabatini et al. (2005) catalog. Of these objects four ([VPC2011] 2, 11, 30, 43) have characteristic scale lengths in the B band greater than 3'' and three ([VPC2011] 1, 11, 43) have characteristic scale lengths in the I band greater than 3''. [VPC2011] 1, 11, and 30 have other sources close to them (at 6''–10'' distance) which could be removed by DetectLSB from their surface brightness profile, because they were identified by MARSIAA (see Figure 6). MARSIAA and DetectLSB are thus able to identify LSB galaxy candidates even in crowded regions of the sky. The recovered Virgo LSB galaxies are dwarf ellipticals and dwarf irregulars.

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In Table 3, we compare our detections of LSB galaxies with characteristic scale lengths ⩾3'' with those of Sabatini et al. (2005) based on matched filters. In addition, we used SExtractor (Bertin & Arnouts 1996) in a non-standard way tuned for our purpose (cut at 1.2σ and with at least 200 connected pixels).

Out of 28 objects detected with the matched filter analysis, MARSIAA+DetectLSB detect 20. Of the eight objects that were not identified as LSBs by our method, [SDV2005] 57 is too close to an image edge to be detected by our method, [SDV2005] 2, 39, and 45 are very faint and not recognizable by eye as LSB galaxies on the images, and [SDV2005] 3, 38, 42, and 52 are most probably confused sources. Three objects were found by MARSIAA+DetectLSB but not by SExtractor: [SDV2005] 0, 1, and 35. On the other hand, two sources ([SDV2005] 3 and 41) were found by SExtractor and not by DetectLSB (although MARSIAA detected these, they were qualified as non-LSB by DetectLSB).

We conclude that we detected all 20 LSB objects on the 18 INT images included in Sabatini et al. (2005) which we could classify by eye as bona fide LSB galaxies, and that we detected 3 objects that SExtractor, even in an optimized configuration, was not able to find. Furthermore, we detected four new LSB galaxy candidates ([VPC2011] 2, 11, 30, 43) with characteristic scale lengths >3'' which are not included in the Sabatini et al. (2005) catalog. Two of these candidates are very LSB μ_B ∼ 25 mag arcsec⁻² ([VPC2011] 2 and 30) and the others show pollution by nearby sources.

In Figure 7, we compare our total B- and I-band magnitudes and B-band characteristic scale lengths with those of Sabatini et al. (2005). The correlation has a scatter of 0.5 mag in magnitude and 23 in radius. Given the approximate determination of our magnitudes based on simple exponential profiles, the large scatter is expected.

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The Next Generation Virgo Cluster Survey (NGVS) uses the MegaCam instrument on the 3.8 m Canada–France–Hawaii Telescope (CFHT) to carry out a comprehensive optical imaging survey of the Virgo Cluster, from its core to its virial radius covering a total area of 104 deg² in the u*griz bandpasses (Ferrarese et al. 2012). The results are given in CFHT magnitudes which are close to the SDSS magnitudes. All preprocessing of NGVS data is performed at the CFHT using the Elixir-LSB pipeline (see Ferrarese et al. 2012 for details), while the primary stacking for the NGVS is performed using a variant of the MegaPipe pipeline (Gwyn 2008). Each ∼20000 × 20000 pixel NGVS stacked image has a size of 1 deg² with a pixel size of 0186 × 0186. The mean PSF FWHM is ∼08 in the g and r bands, and ∼06 in the i band. The NGVS reaches a point-source depth of g ∼ 25.9 mag (10σ) and a surface brightness limit of μ_g ∼ 29 mag arcsec⁻² (at 2σ above the mean sky level). The NGVS is thus ∼3 mag deeper than the INT observations presented in Section 5.

Since the u* and z band NGVS data are at half-depth, LSB structures are generally detected at a lower significance level in these bands. Therefore, the detection statistics for the simultaneous application of MARSIAA to u*griz images are worse than that for the application to the gri filters only. As already stated in Section 4.2, in empty bands the number of pixels in the segmentation class that contains the LSB structures may become relatively small and the segmentation process fails (Hughes phenomenon). Therefore, we applied MARSIAA simultaneously to the g, r, and i bands only, using the following pipeline: (1) each NGVS gri image is cut into 144 subimages of size 2048 × 2048 each, with overlapping regions of 256 pixels, (2) MARSIAA is applied simultaneously to the gri subimages, (3) DetectLSB, based on the MARSIAA segmentation maps, is applied sequentially to the NGVS g, r, and i subimages, (4) a clustering algorithm cross-identifies the sources detected by DetectLSB, and (5) selection software (see Section 6.2) identifies the final LSB galaxy candidates. The pipeline only needs human intervention between step (4) and (5) to change the format of the source catalog from xml to ascii. We produced binary masks based on a clipping of the g-band images at a surface brightness level of 26.7 mag arcsec⁻² (∼30σ). Higher and lower clipping values did not improve the results. After testing MARSIAA with 6 to 10 classes on a selected NGVS image from the Virgo Cluster core (NGVS+0+1) in the gri bands, we set the number of MARSIAA classes to 8. The source clustering algorithm was run with cluster radii from 1'' to 10''. We adopted a cluster radius of 2'', which gave the best results.

The pipeline was run on a single processor, and required 90 hr for MARSIAA, 90 hr for DetectLSB, and 1 hr for the clustering and selection software for a set of gri images of one NGVS square degree field. For comparison we also applied SExtractor with the following parameter sets: 2.5σ and 5 connected pixels, and 1.5σ and 200 connected pixels. The resulting binary maps were added to yield a SExtractor segmentation map. DetectLSB and the selection software were then applied to these data as in the case of MARSIAA. Obviously, SExtractor is significantly faster than MARSIAA: SExtractor needs less than 1 hr of processor time for a set of gri images of 1 deg² NGVS field, and the application of DetectLSB to the SExtractor maps needs 80 hr. Using the pipeline with SExtractor on a set of 3 band images of 1 deg² NGVS field thus needs about four days, or half of the eight days needed with MARSIAA.

The advantage of MARSIAA lies in the increased depth of the segmentation maps compared to SExtractor. MARSIAA/DetectLSB allowed us to identify up to 40% more LSB galaxies than SExtractor/DetectLSB (Sections 6.3 and 6.4).

As for the INT images, DetectLSB was applied to the g, r, and i images separately. The resulting catalogs were merged to yield a final source catalog. In addition, an extra software searched for extended MARSIAA class 1 objects without higher classes. The shallower depth of the INT images made it possible to select LSB galaxy candidates from the final catalog based on the characteristic radius and to do the final identification by eye. This was not possible for the NGVS images where MARSIAA/DetectLSB finds 20,000–40,000 LSB galaxy candidates per square degree. On the other hand, out of this large number only 138 objects were identified by eye as Virgo Cluster LSBs by the NGVS team on one of the NGVS images (NGVS+0+1) near the center of the cluster—only about 1% of the candidates in our catalog. Although our method is intended to detect and identify additional LSB galaxies, we have to select less than ∼10% of real Virgo LSB galaxies out of our LSB galaxy candidates. This is a very challenging task. To do so, we developed an additional software which is based on the MARSIAA segmentation maps and the results of DetectLSB for the different filter bands and segmentation classes. In particular, it takes advantage of the MARSIAA segmentation classes to separate objects in crowded fields and to exclude objects which are too small (half-light radius smaller than 1''), have unphysical colors or surface brightness profiles, are too compact (many MARISAA classes contained in the object), or highly asymmetric. This LSB identification led to about 1500–2000 candidate LSB galaxies. An inspection by eye of 400 of these showed that the majority (∼90%) are bona fide LSB galaxy candidates. Most of the candidates are not in the Virgo Cluster, i.e., they are background galaxies. Spurious detections are mostly located in halos of extended sources (stars or galaxies). The majority of recovered Virgo LSB galaxies are dwarf irregulars, the recovered background galaxies are mostly spirals. It thus turned out that we detect and identify elliptical (dEs on the INT images), disk (background), and irregular galaxies (dIs in the Virgo Cluster).

At the faint surface brightness levels of the NGVS, source crowding and the merging of source halos become important problems. As an example, Figure 8 shows a MARSIAA/DetectLSB false LSB identification of multiple aligned sources. Nevertheless, the LSB galaxy identification by DetectLSB is quite robust in crowded fields with merging source halos (Figure 9) since for the surface brightness profiles, different MARSIAA objects and pixels belonging to segmentation classes <j − 1 and >j + 1, where j is the class of the majority of pixels in an ellipse annulus, are rejected. A typical detection and identification of an isolated LSB galaxy is presented in Figure 10.

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In Figures 8–10, we also show SExtractor masks for the two parameter sets (2.5σ and 5 connected pixels, and 1.5σ and 200 connected pixels). In general, MARSIAA produces deeper masks than SExtractor. On the other hand, the increasing depth of the masks increases confusion. MARSIAA/DetectLSB detects and identifies about 25% more sources than SExtractor/DetectLSB.

A secondary rejection based on color (r − i>1.25 − (g − r)), size, and inclination (half-light radii smaller than 2'' and inclinations >45°), and area +i band surface brightness lead to a total number of ∼1000 LSB galaxy candidates per square degree NGVS image with only a small decrease (<5%) in the identification statistics. Since the number of Virgo Cluster LSB galaxies per NGVS square degree image is about 100 (Section 6.4), we are thus left with ∼90% of sources which are not Virgo Cluster LSB galaxies. Thus, about 1000 have to be examined manually or by a smart unsupervised fitting routine (e.g., GALFIT; Peng et al. 2010), which is beyond the scope of our work.

The NGVS team kindly provided us gri subimages of field NGVS-1+1 (18000 × 18000 pixel) to which they added 396 mock Virgo Cluster LSB galaxies with g-band magnitudes between 19 and 25. The galaxy luminosity profiles are Sersic profiles (Sersic 1963) with variable effective radii (06 ⩽ r_e ⩽ 56), exponents (0.6 ⩽ n ⩽ 2.0), and axis ratios (0.2 ⩽ b/a ⩽ 1.0). Moreover, a nucleus was added to each mock object with m_nuc = m_gal + 6.5, r^nuc_e = 0.1 × r_e^gal, and n = 1. In addition to the mock Virgo galaxies, NGVS-1+1 also contains real LSB and HSB galaxies. Both MARSIAA/DetectLSB and SExtractor/DetectLSB were applied to these images. The two SExtractor binary masks (2.5σ and 5 connected pixels, and 1.5σ and 200 connected pixels) were added to produce a segmentation map. DetectLSB was then applied to this map.

DetectLSB based on the MARSIAA segmentation map found 40,635 objects separately in the g, r, and i bands, the final source catalog (after cross-identification via a cluster algorithm) contains 11,417 sources, and 263 out of the 396 mock Virgo LSB galaxies were detected. DetectLSB based on the SExtractor segmentation map found 21, 915 separately in the g, r, and i bands, the final source catalog contains 8721 sources, and 242 out of 396 mock Virgo LSB galaxies were detected. We then applied the additional software described in Section 6.2 to the final source catalogs which reduced the number of positive sources significantly: with MARSIAA/DetectLSB we obtained 2089 LSB galaxy candidates: 191 out of the 396 mock Virgo LSB galaxies were identified. With SExtractor/DetectLSB we obtained 1606 LSB galaxy candidates: 157 out of 396 mock Virgo LSB galaxies were identified. As stated in Section 6.2, the application of secondary rejection criteria based on color, size, and inclination reduces the number of LSB galaxy candidates to ∼1000 with a less than 5% decrease of the identification statistics. A visual inspection of a portion of the LSB galaxy candidates not identified as mock galaxies showed that about 90% are real galaxies located in the background.

Thus, DetectLSB/MARSIAA detected and identified ∼30% more LSB sources than DetectLSB/SExtractor on the NGVS images (11,417 compared to 8721). Concerning the mock data, DetectLSB/MARSIAA detected ∼10% more mock Virgo LSB galaxies and identified ∼20% more of them than DetectLSB/SExtractor. It should be noted here that, since the mock Virgo LSB galaxies are relatively small, confusion is less important and SExtractor gives results comparable to MARSIAA. LSB galaxies identified by eye by the NGVS team can be much more extended than the mock objects and their identification based on SExtractor maps becomes more difficult (see Section 6.4).

While SExtractor directly yields the magnitude and half-light radius for a given object, the application of DetectLSB results in several magnitudes and half-light radii depending on the fitted MARSIAA segmentation class. During the LSB galaxy identification, DetectLSB assigns a unique magnitude and half-light radius to each MARSIAA object. The g mean surface brightness of the identified mock Virgo LSB galaxies as a function of the effective radius is presented in Figure 11. The completeness for r_e > 15 and m_g < 22 mag is 90% for DetectLSB/MARSIAA and 83% for DetectLSB/SExtractor. The completeness of both methods decreases significantly for sources with m_g > 22 mag. DetectLSB/MARSIAA identified twice as many mock Virgo LSB galaxies in this magnitude range than DetectLSB/SExtractor. Whereas DetectLSB/MARSIAA is able to detect and identify LSB galaxy candidates up to a mean surface brightness of m_g = 28.5 mag (S/N =1.6; the NGVS surface brightness limit is ∼29 mag arcsec⁻² at 2σ above the mean sky level), confirming the results obtained from pure simulations (Section 4.2), a completeness of 90% is reached for sources with r_e >15 at μ_g = 26 mag arcsec⁻² and for sources with r_e > 3'' at μ_g = 27.7 mag arcsec⁻².

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We note that our magnitudes and sizes are rough estimates and are not intended to replace proper magnitudes and sizes derived from more sophisticated methods. The recovered DetectLSB and SExtractor magnitudes are compared to the mock input magnitudes in Figure 12. For the SExtractor magnitudes, we use preferentially those of the run with (1.5σ, 200 connected pixels). In the case of the application of DetectLSB based on SExtractor masks, the magnitude offsets and dispersions are comparable (offset: DetectLSB =0.13 mag, SExtractor =0.11 mag; dispersion: DetectLSB =0.18 mag, SExtractor =0.14 mag). This result validates the flux extraction by DetectLSB compared to SExtractor. In the case of the application of DetectLSB based on MARSIAA masks, the DetectLSB magnitudes show a larger dispersion and a larger offset from the input magnitudes than the SExtractor magnitudes (offset: DetectLSB =0.19 mag, SExtractor =0.11 mag; dispersion: DetectLSB =0.22 mag, SExtractor =0.15 mag). The DetectLSB magnitude offset and dispersion is due to the quality of the unsupervised ellipse fit, which mainly depends on the first ellipse fit on the SExtractor or MARSIAA mask of the object. MARSIAA provides the deeper masks, SExtractor the cleaner masks. Since only pixels of similar segmentation classes are taken into account during the extraction of the surface brightness profile and the magnitude is derived from this profile, the fluxes based on MARSIAA masks are lower than those based on SExtractor masks, despite the higher depth of the MARSIAA masks.

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The DetectLSB and SExtractor half-light radii are compared to the mock input half-light radii in Figure 13. For input half-light radii exceeding 15 SExtractor underestimates the input radii on average by 1'', and the offset increases with increasing half-light radius. On the other hand, DetectLSB overestimates the input half-light radii by an approximately constant offset of 05. The dispersion of the differences between the input and estimated half-light radii is in all cases ∼08. As stated in Section 3.3 the DetectLSB half-light radius is discrete and critically depends on the first ellipse fit on the SExtractor or MARSIAA mask of the object.

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As a further test, we applied MARSIAA/DetectLSB and SExtractor/DetectLSB to the NGVS image NGVS+0+1, the field east of NGVS-1+1. On this image the NGVS team identified 138 Virgo LSB members after visual inspection. This identification was based on surface brightness, extent, color, and morphology. While the completeness of this by-eye catalog cannot be rigorously quantified, it is expected to be fairly complete. The average source extent of this sample is significantly larger than that of the Virgo mock galaxies, and about 20 of these LSB galaxies have half-light radii exceeding 10''.

We applied MARISAA, SExtractor, and DetectLSB with the same parameters as before. DetectLSB based on the MARSIAA segmentation map found 125, 787 objects separately in the g, r, and i bands, resulting in a final source catalog with 33, 119 sources. This catalog contains 124 out of 138 Virgo LSB galaxies. DetectLSB based on the SExtractor segmentation map found 76, 797 separately in the g, r, and i bands, resulting in a final source catalog with 25, 913 sources containing 105 out of 138 Virgo LSB galaxies. As for the mock data, we then applied the additional software described in Section 6.2 to the final source catalogs. With MARSIAA/DetectLSB we obtained 2554 LSB galaxy candidates: 115 out of 138 Virgo LSB galaxies were identified. The non-detected LSB galaxies were confused, too faint (no object in the MARSIAA segmentation map), or too small (apparent size on the g-band image smaller than 2''). In addition, one LSB galaxy is split into two parts by an image artifact (Figure 14). With SExtractor/DetectLSB we obtained 1813 LSB galaxy candidates: 82 out of 138 Virgo LSB galaxies were identified. Thus, DetectLSB/MARSIAA detected and identified ∼40% more LSB sources than DetectLSB/SExtractor on the two NGVS images. As stated in Section 6.2, the application of secondary rejection criteria based on color, size, and inclination reduces the number of LSB galaxy candidates to ∼1000 with a less than 5% decrease of the identification statistics. As for the mock data, a visual inspection ∼400 LSB galaxy candidates not identified as Virgo LSB galaxies showed that about 90% are real galaxies located in the background.

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The recovered g mean surface brightness of the identified LSB galaxies as a function of the effective radius is presented in Figure 15. The completeness for r_e > 15 and m_g < 22 mag is 92% for DetectLSB/MARSIAA and 72% for DetectLSB/SExtractor. A completeness of 90% is reached for sources with r_e > 3'' at a mean surface brightness of μ_g = 27.7 mag arcsec⁻² and a central surface brightness of μ⁰_g = 26.7 mag arcsec⁻².

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The DetectLSB and SExtractor g-band magnitudes are compared to the magnitudes extracted by the NGVS team in Figure 16. The latter magnitudes were measured with three independent methods (two-dimensional, one-dimensional, and non-parametric) with extremely good agreement. Both methods show a magnitude offset of 0.3 mag with respect to the values measured by the NGVS team, with a dispersion of 0.4 mag. The application of MARSIAA/DetectLSB results in a bimodal structure in the magnitude difference distribution: a prominent peak with an offset of 0.3 mag and a dispersion of 0.2 mag, and a secondary peak around an offset of −0.8 mag. This bimodal structure is also present, although less pronounced, in the distribution of the SExtractor magnitude differences. As expected, DetectLSB recovers less flux than a manual photometric extraction.

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The DetectLSB and SExtractor half-light radii are compared to the input half-light radii in Figure 17. As for the mock data (Section 6.3), the difference between the half-light radii estimated by SExtractor and those measured by the NGVS team increases with increasing radius. On the other hand, the half-light radii estimated by DetectLSB have an offset of less than 1'', with a dispersion of 08–1''.

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