  The Kerr black holes possess a photon region with prograde and retrograde
orbits radii, respectively, $M\leq r_p^-\leq 3M$ and $3M\leq r_p^+\leq 4M$, and
thereby always cast a closed photon ring or a shadow silhouette for $a\leq M$.
For $a>M$, it is a no-horizon spacetime (naked singularity) wherein prograde
orbits spiral into the central singularity, and retrograde orbits produce an
arc-like shadow with a dark spot at the center. We compare Kerr black holes'
photon ring structure with those produced by three rotating regular spacetimes,
viz. Bardeen, Hayward, and nonsingular. These are non-Kerr black hole metrics
with an additional deviation parameter of $g$ related to the nonlinear
electrodynamics charge. It turns out that for a given $ a $, there exists a
critical value of $ g $, $g_E$ such that $\Delta=0$ has no zeros for $ g >
g_E$, one double zero at $ r = r_E $ for $ g = g_E $, respectively,
corresponding to a no-horizon regular spacetime and extremal black hole with
degenerate horizon. We demonstrate that, unlike the Kerr naked singularity,
no-horizon regular spacetimes can possess closed photon ring when $g_E< g \leq
g_c$, e.g., for $a=0.10M$, Bardeen ($g_E=0.763332M<g\leq g_c= 0.816792M$),
Hayward ($g_E=1.05297M < g\leq g_c = 1.164846M$) and nonsingular ($g_E=1.2020M
< g \leq g_c= 1.222461M$) no-horizon spacetimes have closed photon ring. These
results confirm that the mere existence of a closed photon ring does not prove
that the compact object is necessarily a black hole. The ring circularity
deviation observable $\Delta C$ for the three no-horizon rotating spacetimes
satisfy $\Delta C\leq 0.10$ as per the M87* black hole shadow observations. We
have also appended the case of Kerr-Newman no-horizon spacetimes (naked
singularities) with similar features.
