Correct vhar system equations

2-related-work/1-haptic-hand.tex

@@ -379,7 +379,7 @@ That is, \textcite{bergmanntiest2009cues} showed the perception of hardness reli
 \label{haptic_sense_conclusion}
 
 Haptic perception and manipulation of objects with the hand involve several simultaneous mechanisms with complex interactions.
-Exploratory movements of the hand are performed on contact with the object to obtain multiple sensory information from several cutaneous and kinaesthetic receptors.
+Exploratory movements of the hand are performed on contact with the object to obtain multiple sensory information from several cutaneous and kinesthetic receptors.
 These sensations express physical parameters in the form of perceptual cues, which are then integrated to form a perception of the property being explored.
 For the perception of roughness (texture) or hardness, one perceptual cue is particularly important, but perceptual constancy is possible by compensating for its absence with others.
 In turn, these perceptions help to guide the grasping and manipulation of the object by adapting the grasp type and the forces applied to the shape of the object and the task to be performed.

2-related-work/3-augmented-reality.tex

@@ -339,7 +339,7 @@ Taken together, these results suggest that a visual augmentation of the hand in
 \label{ar_conclusion}
 
 \AR systems integrate virtual content into the user's perception as if it were part of the \RE.
-\AR headsets now enable real-time tracking of the head and hands, and high-quality display of virtual content, while being portable and mobile.
+\AR headsets now enable real-time pose estimation of the head and hands, and high-quality display of virtual content, while being portable and mobile.
 They enable highly immersive augmented environments that users can explore with a strong sense of the presence of the virtual content.
 However, without direct and seamless interaction with the virtual objects using the hands, the coherence of the augmented environment experience is compromised.
 In particular, when manipulating virtual objects in \OST-\AR, there is a lack of mutual occlusion and interaction cues between the hands and the virtual content, which could be mitigated by a visual augmentation of the hand.

2-related-work/4-visuo-haptic-ar.tex

@@ -26,11 +26,11 @@ The \MLE model then predicts that the integrated estimated property $\tilde{s}$
 \begin{equation}{MLE}
   \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:
+where the individual weights $w_i$ are proportional to their inverse variances:
 \begin{equation}{MLE_weights}
   w_i = \frac{1/\sigma_i^2}{\sigma^2}
 \end{equation}
-And the integrated variance $\sigma^2$ is the inverse of the sum of the individual variances:
+and the integrated variance $\sigma^2$ is the inverse of the sum of the individual variances:
 \begin{equation}{MLE_variance}
   \sigma^2 = \left( \sum_i \frac{1}{\sigma_i^2} \right)^{-1}
 \end{equation}