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Erwan Normand
2024-09-20 16:50:31 +02:00
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1-introduction/related-work/4-visuo-haptic-ar.tex
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@@ -21,14 +21,14 @@
\label{sensations_perception}
A \emph{perception} is the merge of multiple sensations from different sensory modalities (visual, cutaneous, proprioceptive, etc.) about the same event or object property~\cite{ernst2004merging}.
For example, it is the haptic hardness perceived through skin pressure and force sensations~\secref{hardness}, the hand movement from proprioception and a visual hand avatar~\secref{ar_displays}, or the perceived size of a tangible with a co-localized \VO~\secref{ar_tangibles}.
For example, it is the haptic hardness perceived through skin pressure and force sensations (\secref{hardness}), the hand movement from proprioception and a visual hand avatar (\secref{ar_displays}), or the perceived size of a tangible with a co-localized \VO (\secref{ar_tangibles}).
When the sensations can be redundant, \ie when only one sensation could be enough to estimate the property, they are integrated to form a single coherent perception~\cite{ernst2004merging}.
No sensory information is completely reliable, and can provide different answers to the same property when measured multiple times, \eg the weight of an object.
Therefore, each sensation $i$ is said to be an estimate $\hat{s}_i$ with variance $\sigma_i^2$ of the property $s$.
The \MLE model predicts then that the integrated estimated property $\hat{s}$ is the weighted sum of the individual sensory estimates:
Therefore, each sensation $i$ is said to be an estimate $\tilde{s}_i$ with variance $\sigma_i^2$ of the property $s$.
The \MLE model predicts then that the integrated estimated property $\tilde{s}$ is the weighted sum of the individual sensory estimates:
\begin{equation}{MLE}
\hat{s} = \sum_i w_i \hat{s}_i \quad \text{with} \quad \sum_i w_i = 1
\tilde{s} = \sum_i w_i \tilde{s}_i \quad \text{with} \quad \sum_i w_i = 1
\end{equation}
Where the individual weights $w_i$ are proportional to their inverse variances:
\begin{equation}{MLE_weights}
@@ -137,11 +137,11 @@ Adding a visual delay increased the perceived stiffness of the reference piston,
\end{subfigs}
%explained how these delays affected the integration of the visual and haptic perceptual cues of stiffness.
The stiffness $k$ of the piston is indeed estimated by both sight and proprioception as the ratio of the exerted force $F$ and the displacement $D$ of the piston, following \eqref{stiffness}, but with a delay $\Delta t$:
The stiffness $\tilde{k}(t)$ of the piston is indeed estimated at time $t$ by both sight and proprioception as the ratio of the exerted force $F(t)$ and the displacement $D(t)$ of the piston, following \eqref{stiffness}, but with potential visual $\Delta t_v$ or haptic $\Delta t_h$ delays:
\begin{equation}{stiffness_delay}
k = \frac{F(t_H)}{D(t_V)} \quad \text{with} \quad t_H = t_V + \Delta t
\tilde{k}(t) = \frac{F(t + \Delta t_h)}{D(t + \Delta t_v)}
\end{equation}
Therefore, the perceived stiffness $k$ increases with a haptic delay in force (positive $\Delta t$) and decreases with a visual delay in displacement (negative $\Delta t$)~\cite{diluca2011effects}.
Therefore, the perceived stiffness $\tilde{k}(t)$ increases with a haptic delay in force and decreases with a visual delay in displacement~\cite{diluca2011effects}.
In a similar \TIFC user study, participants compared perceived stiffness of virtual pistons in \OST-\AR and \VR~\cite{gaffary2017ar}.
However, the force-feedback device and the participant's hand were not visible (\figref{gaffary2017ar}).