Morphological characteristics of the vertically thick inner bar components are studied. At high galaxy inclinations they manifest as Boxy/Peanut/X-shape features, and near to face-on view as barlenses. Using the Spitzer Survey of Stellar Structure in Galaxies (S4G) and the Near-IR S0 galaxy Survey (NIRS0S), we compared the properties of 88 X-shape features, 85 barlenses, and the photometric bulges of 41 non-barred galaxies. Sizes and minor-to-major axis ratios (b/a) of these structures are compared, and interpreted by means of synthetic images using N-body simulation models. Barlenses and their parent galaxies are also divided into different sub-groups. The synthetic images are analyzed in a similar manner as the observations. This is the first time that the observed properties of barlenses and X-shape features are compared, over a large range of galaxy inclinations. Our analysis are consistent with the idea that barlenses and X-shape features are physically the same phenomenon. However, which of the two features is observed depends, not only on galaxy inclination, but also on its central flux concentration. The observed nearly round face-on barlens morphology is expected when at least a few percents of the disk mass is in a central component, within a region much smaller than the size of the barlens itself. We also discuss that the large range of stellar population ages obtained for the photometric bulges in the literature, are consistent with our interpretation.
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