A noise-based non-parametric technique for detecting nebulous objects, for example, irregular or clumpy galaxies, and their structure in noise is introduced. "Noise-based" and "non-parametric" imply that this technique imposes negligible constraints on the properties of the targets and that it employs no regression analysis or fittings. The sub-sky detection threshold is defined and initial detections are found independently of the sky value. False detections are then estimated and removed using the ambient noise as a reference. This results in a purity level of 0.88 for the final detections as compared to 0.29 for SExtractor when a completeness of 1 is desired for a sample of extremely faint and diffuse mock galaxy profiles. The difference in the mean of the undetected pixels with the known background of mock images is decreased by 4.6 times depending on the diffuseness of the test profiles, quantifying the success in their detection. A non-parametric approach to defining substructure over a detected region is also introduced. NoiseChisel is our software implementation of this new technique. Contrary to the existing signal-based approach to detection, in its various implementations, signal-related parameters such as the image point-spread function or known object shapes and models are irrelevant here. Such features make this technique very useful in astrophysical applications such as detection, photometry, or morphological analysis of nebulous objects buried in noise, for example, galaxies that do not generically have a known shape when imaged.
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