\section{Discussion}
\label{discussion}

%Interpret the findings in results, answer to the problem asked in the introduction, contrast with previous articles, draw possible implications. Give limitations of the study.

% But how different is the perception of the haptic augmentation in \AR compared to \VR, with a virtual hand instead of the real hand?
% The goal of this paper is to study the visual rendering of the hand (real or virtual) and its environment (\AR or \VR) on the perception of a tangible surface whose texture is augmented with a wearable vibrotactile device mounted on the finger.

The results showed a difference in vibrotactile roughness perception between the three visual rendering conditions.
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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}).
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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}.
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%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}).
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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}).
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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.
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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).
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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}).
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The \level{Mixed} rendering was always in between, with no significant difference from the other two.
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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.
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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{questions}) in both the \level{Mixed} and \level{Virtual} renderings.
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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{questions}).
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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).
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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 visuo-haptic augmentation system aimed to provide a coherent multimodal virtual rendering integrated with the real environment.
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Yet, it involves different sensory interaction loops between the user's movements and the visuo-haptic feedback (\figref{method/diagram}), which may not feel to be in synchronised with each other or with proprioception.
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%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 hypothesise 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).
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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.
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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{questions}). %, and the exploratory movements typically observed in our study had a fairly constant speed during a passage over the textures.
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\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.
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Another complementary explanation could be a pseudo-haptic effect 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}.
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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.

We can outline recommendations for future \AR/\VR studies or applications using wearable haptics.
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Attention should be paid to the respective latencies of the visual and haptic sensory feedbacks inherent in such systems and, more importantly, to \emph{the perception of their possible asynchrony}.
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%This is in line with embodiment studies in \VR that compared realism, latency and control \cite{waltemate2016impact,fribourg2020avatar}.
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Latencies should be measured \cite{friston2014measuring}, minimised to an acceptable level for users and kept synchronised with each other \cite{diluca2019perceptual}.
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It seems that the visual aspect of the hand or the environment on itself has little effect on the perception of haptic feedback, but the degree of visual reality-virtuality can affect the asynchrony sensation of the latencies, even though they remain identical.
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%As we have shown, the visual representation of the hand or the environment can affect the experience of the unchanged latencies and thus the perception of haptic feedback.
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Therefore, when designing for wearable haptics or integrating it into \AR/\VR, it seems important to test its perception in real, augmented and virtual environments.
%Finally, a visual hand representation in OST-\AR together with wearable haptics should be avoided until acceptable tracking latencies are achieved, as was also observed for virtual object interaction with the bare hand \cite{normand2024visuohaptic}.

The main limitation of our study is the absence of a visual representation of the virtual texture.
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This is indeed a source of information as important as haptic sensations for the perception of both real textures \cite{baumgartner2013visual,bergmanntiest2007haptic,vardar2019fingertip} and virtual textures \cite{degraen2019enhancing,gunther2022smooth}, and their interaction in the overall perception is complex.
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%Specifically, it remains to be investigated how to visually represent vibrotactile textures in an immersive \AR or \VR context, as the visuo-haptic coupling of such grating textures is not trivial \cite{unger2011roughness} even with real textures \cite{klatzky2003feeling}.

Also, our study was conducted with an \OST-\AR headset, but the results may be different with a \VST-\AR headset.
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Finally, we focused on the perception of roughness sensations using wearable haptics in \AR \vs \VR using a square wave vibrotactile signal, but different haptic texture rendering methods should be considered.
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More generally, many other haptic feedbacks could be investigated in \AR \vs \VR using the same system and methodology, such as stiffness, friction, local deformations, or temperature.
