In this paper, we extend to the Mueller imaging framework a formerly introduced Bayesian approach dealing with polarimetric data reduction and robust clustering of polarization encoded images in the piecewise constant case. The extension was made possible thanks to a suitable writing of the observation model in the Mueller context that relies on the system's coherency matrix and Cholesky decomposition such that the admissibility constraints are easily captured. This generalization comes at the cost of nonlinearity with respect to the parameters that have to be estimated. This estimation-clustering problem is tackled in a Bayesian framework where a hierarchical stochastic model based on a Markov random field proposed by Potts is used. This fully unsupervised approach is extensively tested over synthetic data as well as real Mueller images.

We present to the astronomical community an algorithm for the detection of Low Surface Brightness (LSB) galaxies in images, called MARSIAA (MARkovian Software for Image Analysis in Astronomy), which is based on multi-scale Markovian modeling. MARSIAA can be applied simultaneously to different bands. It segments an image into a user-defined number of classes, according to their surface brightness and surroundings -typically, one or two classes contain the LSB structures. We have developed an algorithm, called DetectLSB, which allows the efficient identification of LSB galaxies from among the candidate sources selected by MARSIAA. The application of the method to two and three bands simultaneously was tested on simulated images. Based on our tests we are confident that we can detect LSB galaxies down to a central surface brightness level of only 1.5 times the standard deviation from the mean pixel value in the image background. To assess the robustness of our method, the method was applied to a set of 18 B and I band images (covering 1.3 square degrees in total) of the Virgo cluster to which Sabatini et al. (2003Sabatini et al. ( , 2005 previously applied a matched-filters dwarf LSB galaxy search algorithm. We have detected all 20 objects from the Sabatini et al. catalog which we could classify by eye as 1 bona fide LSB galaxies. Our method has also detected 4 additional Virgo cluster LSB galaxy candidates undetected by Sabatini et al. To further assess the completeness of the results of our method, both MARSIAA, SExtractor, and DetectLSB were applied to search for (i) mock Virgo LSB galaxies inserted into a set of deep Next Generation Virgo Survey (NGVS) gri-band subimages and (ii) Virgo LSB galaxies identified by eye in a full set of NGVS square degree gri images. MARSIAA/DetectLSB recovered ∼ 20 % more mock LSB galaxies and ∼ 40 % more LSB galaxies identified by eye than SExtractor/DetectLSB. With a 90 % fraction of false positives from an entirely unsupervised pipeline, a completeness of 90 % is reached for sources with r e > 3 ′′ at a mean surface brightness level of µ g = 27.7 mag arcsec −2 and a central surface brightness of µ 0 g = 26.7 mag arcsec −2 . About 10 % of the false positives are artifacts, the rest being background galaxies. We have found our proposed Markovian LSB galaxy detection method to be complementary to the application of matched filters and an optimized use of SExtractor, and to have the following advantages: it is scale-free, can be applied simultaneously to several bands, and is well adapted for crowded regions on the sky.

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