  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.
