\section{Discussion}
\label{sec: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.
%
Given the estimated point of subjective equality (PSE), the textures in the \level{Real} rendering were on average perceived as \enquote{rougher} than in the \level{Virtual} (\percent{-2.8}) and \level{Mixed} (\percent{-6.0}) renderings (see \figref{results/trial_pses}).
%
\textcite{gaffary2017ar} found a PSE difference in the same range between AR and VR for perceived stiffness, with the VR perceived as \enquote{stiffer} and the AR as \enquote{softer}.
%
%However, the difference between the \level{Virtual} and \level{Mixed} conditions was not significant.
%
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 closer to the reference texture, being perceived as \enquote{smoother}  (see \figref{results/trial_predictions}).
%
The sensitivity of participants to roughness differences (just-noticeable differences, JND) also varied between all the visual renderings, with the \level{Real} rendering having the best JND (\percent{26}), followed by the \level{Virtual} (\percent{30}) and \level{Virtual} (\percent{33}) renderings (see \figref{results/trial_jnds}).
%
These JND values are in line with and at the upper end of the range of previous studies~\autocite{choi2013vibrotactile}, which may be due to the location of the actuator on the top of the middle phalanx of the finger, 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 average roughness perception (PSE), as if the virtual haptic 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) (see \figref{results_finger}).
%
The \level{Mixed} rendering, displaying both the real and virtual hands, was always in between, with no significant difference from the other two renderings.
%
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 seems not due to the realism of the virtual hand or environment, nor the control of the virtual hand, that were all rated high to very high by the participants (see \secref{questions}) in both the \level{Mixed} and \level{Virtual} renderings.
%
Very interestingly, the evaluation of the vibrotactile device and textures was also the same between the visual rendering, with a very high sensation of control, a good realism and a very low perceived latency of the textures (see \secref{questions}).
%
However, the perceived latency of the virtual hand (\response{Hand Latency} question) seems 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 visuo-haptic augmentation system aimed to provide a coherent multimodal virtual rendering integrated with the real environment.
%
Yet, it involves different sensory interaction loops between the user's movements and the visuo-haptic feedback (see \figref{method/diagram}), which are subject to different latencies and may not be in synchronised with each other, or may even being inconsistent with other sensory modalities such as 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.
%
Conversely, when interacting with a real texture, there is no lag between any of these sensory modalities.
%
Thereby, we hypothesise that the differences in the perception of vibrotactile roughness are less due to the visual rendering of the hand or environment and their associated difference in exploration behaviour, but rather to the difference in the perceived latency between one's own hand (visually and proprioceptively) and the virtual hand (visually and haptically).
%
\textcite{diluca2011effects} demonstrated, 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.
%
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~\autocite{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.

The main limitation of our study is, of course, the absence of a visual representation of the touched virtual texture.
%
This is indeed a source of information as important as haptic sensations for perception for both real textures~\autocite{baumgartner2013visual,bergmanntiest2007haptic,vardar2019fingertip} and virtual textures~\autocite{degraen2019enhancing,gunther2022smooth,normand2024augmenting}.
%
%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~\autocite{unger2011roughness} even with real textures~\autocite{klatzky2003feeling}.
%
The interactions between the visual and haptic sensory modalities is complex and deserves further investigations, in particular in the context of visuo-haptic AR.
%
Also, our study was conducted with an OST-AR headset, but the results may be different with a VST-AR headset.
%
More generally, we focused on the perception of roughness sensations using wearable haptics in AR \vs VR, but many other haptic feedbacks could be investigated using the same system and methodology, such as stiffness, friction, local deformations, or temperature.
