\section{Discussion}
\label{discussion}

The results showed a difference in vibrotactile roughness perception between the three visual rendering conditions.
Given the estimated \PSEs, the textures were on average perceived as \enquote{rougher} in the \level{Real} rendering than in the \level{Virtual} (\percent{-2.8}) and \level{Mixed} (\percent{-6.0}) renderings (\figref{results/trial_pses}).
A \PSE difference in the same range was found for perceived stiffness, with the \VR perceived as \enquote{stiffer} and the \AR as \enquote{softer} \cite{gaffary2017ar}.
%
%However, the difference between the \level{Virtual} and \level{Mixed} conditions was not significant.
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Surprisingly, the \PSE of the \level{Real} rendering was shifted to the right (to be "rougher", \percent{7.9}) compared to the reference texture, whereas the \PSEs of the \level{Virtual} (\percent{5.1}) and \level{Mixed} (\percent{1.9}) renderings were perceived as \enquote{smoother} and closer to the reference texture (\figref{results/trial_predictions}).
The sensitivity of participants to roughness differences also varied, with the \level{Real} rendering having the best \JND (\percent{26}), followed by the \level{Virtual} (\percent{30}) and \level{Virtual} (\percent{33}) renderings (\figref{results/trial_jnds}).
These \JND values are in line with and at the upper end of the range of previous studies \cite{choi2013vibrotactile}, which may be due to the location of the actuator on the top of the finger middle phalanx, being less sensitive to vibration than the fingertip.
Thus, compared to no visual rendering (\level{Real}), the addition of a visual rendering of the hand or environment reduced the roughness sensitivity (\JND) and the roughness perception (\PSE), as if the virtual vibrotactile textures felt \enquote{smoother}.

Differences in user behaviour were also observed between the visual renderings (but not between the haptic textures).
On average, participants responded faster (\percent{-16}), explored textures at a greater distance (\percent{+21}) and at a higher speed (\percent{+16}) without visual augmentation (\level{Real} rendering) than in \VR (\level{Virtual} rendering) (\figref{results_finger}).
The \level{Mixed} rendering was always in between, with no significant difference from the other two.
This suggests that touching a virtual vibrotactile texture on a tangible surface with a virtual hand in \VR is different from touching it with one's own hand: users were more cautious or less confident in their exploration in \VR.
This does not seem to be due to the realism of the virtual hand or the environment, nor to the control of the virtual hand, all of which were rated high to very high by the participants (\secref{results_questions}) in both the \level{Mixed} and \level{Virtual} renderings.
Very interestingly, the evaluation of the vibrotactile device and the textures was also the same between the visual rendering, with a very high sense of control, a good realism and a very low perceived latency of the textures (\secref{results_questions}).
Conversely, the perceived latency of the virtual hand (\response{Hand Latency} question) seemed to be related to the perceived roughness of the textures (with the \PSEs).
The \level{Mixed} rendering had the lowest \PSE and highest perceived latency, the \level{Virtual} rendering had a higher \PSE and lower perceived latency, and the \level{Real} rendering had the highest \PSE and no virtual hand latency (as it was not displayed).

Our wearable visuo-haptic texture augmentation system, described in \chapref{vhar_system}, aimed to provide a coherent visuo-haptic renderings registered with the \RE.
Yet, it involves different sensory interaction loops between the user's movements and the visuo-haptic feedback (\figref{method/diagram} and \figref[introduction]{interaction_loop}), which may not feel to be in synchronized with each other or with proprioception.
%When a user runs their finger over a vibrotactile virtual texture, the haptic sensations and eventual display of the virtual hand lag behind the visual displacement and proprioceptive sensations of the real hand.
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Thereby, we hypothesize that the differences in the perception of vibrotactile roughness are less due to the visual rendering of the hand or the environment and their associated differences in exploration behaviour, but rather to the difference in the \emph{perceived} latency between one's own hand (visual and proprioception) and the virtual hand (visual and haptic).
The perceived delay was the most important in \AR, where the virtual hand visually lags significantly behind the real one, but less so in \VR, where only the proprioceptive sense can help detect the lag.
This delay was not perceived when touching the virtual haptic textures without visual augmentation, because only the finger velocity was used to render them, and, despite the varied finger movements and velocities while exploring the textures, the participants did not perceive any latency in the vibrotactile rendering (\secref{results_questions}).
\textcite{diluca2011effects} demonstrated similarly, in a \VST-\AR setup, how visual latency relative to proprioception increased the perception of stiffness of a virtual piston, while haptic latency decreased it (\secref[related_work]{ar_vr_haptic}).
Another complementary explanation could be a pseudo-haptic effect (\secref[related_work]{visual_haptic_influence}) of the displacement of the virtual hand, as already observed with this vibrotactile texture rendering, but seen on a screen in a non-immersive context \cite{ujitoko2019modulating}.
Such hypotheses could be tested by manipulating the latency and tracking accuracy of the virtual hand or the vibrotactile feedback. % to observe their effects on the roughness perception of the virtual textures.
