Extracting plasma structures in the solar corona (e.g. jets, loops, prominences) from spacecraft imagery data is essential in order to ascertain their unique properties and for our understanding of their evolution. Hence, our aim is to detect all coronal off-limb structures over a solar cycle and to analyse their statistical properties. In particular, we investigated the intensity and density evolution of these coronal structures, with a specific focus on active longitudes in the corona, that is, longitudinal regions where the solar activity is unequivocally dominant. We developed a methodology based on mathematical morphology (MM) algorithms to extract these coronal structures from extreme ultraviolet (EUV) images taken by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) in the 304 wavelength channel during Solar Cycle (SC) 24. The resulting dataset consists of $877,843$ structures spanning the whole period from June 2010 to December 2021 with a three-hour cadence. We assessed the main characteristics of these coronal off-limb structures, such as their length, width, area, perimeter, latitude, and longitude (evaluated at the centre of the structures), as well as their intensity corrected for the charge-coupled device (CCD) sensitivity degradation of the AIA instrument. Regarding most of these properties, we find similar trends to the behaviour of the on-disk features, including the butterfly diagram and the structures that migrate towards the polar regions (also referred to as `rush-to-the-poles' structures) expanding during the rising phase of SC 24 until the reversal of the magnetic field at the solar poles. We uncover an interesting distribution: lower-intensity coronal structures seem to behave differently with respect to higher-intensity structures. The butterfly diagram is clearly shaped by the high-intensity structures, while the lower-intensity structures are more dispersed and survive during the declining phase of SC 24. We also find evidence of the existence of active longitudes in the corona and of their dependence on differential rotation and latitude.
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