## 2 Our Proposal
### Dynamic MSL Signs Classifier
Algorithm 2 begins by detecting \"p\" with the selected AI model, then verifies the presence of vertical movement associated with the tips of the index and middle fingers, while also ensuring that there is no significant horizontal displacement. The parameter \(\alpha\) allows for some tolerance in the classification, accounting for imperfections in the sign's execution. In Algorithm 2, the variable \(d\) represents the Euclidean distance. Figure 8: Classifiers for “k” and double letters “rr” and “ll”. ```
Data: \(coordNorm\)- Normalized key points. \(\alpha\)- Error tolerance. letter- String Input: letter, \(coordNorm\), \(\alpha\) Output: letter ifletter is \(p\)then \(p1\leftarrow(coordNorm[8],coordNorm[29])\) \(p2\leftarrow(coordNorm[12],coordNorm[33])\) \(detectionCount\gets 3\) while\(detectionCount>0\)do  Get a new frame \(coordNorm\leftarrow\)Normalized coordinates of current frame \(k1\leftarrow(coordNorm[8],coordNorm[29])\) \(k2\leftarrow(coordNorm[12],coordNorm[33])\) if\(p2_{y}-p2_{y}*\alpha>k1_{y}>p2_{y}+p2_{y}*\alpha\)then \(detectionCount\gets detectionCount-1\) continue if\(k2_{y}-k2_{y}*\alpha>d(p1_{y},p2_{y})+p2_{y}>k2_{y}+k2_{y}*\alpha\)then \(detectionCount\gets detectionCount-1\) continue if\(k1_{x}-k1_{x}*\alpha>p1_{x}>k1_{x}+k1_{x}*\alpha\)then \(detectionCount\gets detectionCount-1\) continue if\(k2_{x}-k2_{x}*\alpha>p2_{x}>k2_{x}+k2_{x}*\alpha\)then \(detectionCount\gets detectionCount-1\) continue  end if \(k1_{x}-k2_{x}*\alpha>p2_{x}>k2_{x}+k2_{x}*\alpha\)then \(detectionCount\gets detectionCount-1\) continue  end if  end if returnletter
```  
**Algorithm 2**K letter classification  
The movement of the letter \"k\" is modeled using four conditions based on the behavior of coordinates 8 and 12 obtained from the MediaPipe API, which will be referred to as points \(P1\) and \(P2\) for simplicity. After classifying the sign as the letter \"p\", the coordinates of points \(P1\) and \(P2\) are recorded, and the subsequent three frames are monitored to obtain points 8 and 12 again, now referred to as \(K1\) and \(K2\), respectively. If the following four conditions are met during these frames, the sign is classified as the letter \"k\":  
1. The \(y\) coordinate of point \(K1\) should be similar to that of point \(P2\). This condition is illustrated in Figure 9a, where the green arrow, representing the distance from the origin to \(P2\), should match the purple arrow, which represents the distance from the origin to \(K1\). 2. The sum of the distances between the \(y\) coordinates of \(P1\) and \(P2\) should be close to the value of the \(K2\) coordinate. In Figure 9b, this condition is shown as the sum of the green arrows' magnitudes similar to that of the purple arrow. 3. There should be no significant variation in the \(x\) coordinates of points \(K1\) and \(P1\), as the movement is purely vertical. The \(x\) coordinates should remain constant throughout the trajectory. This is depicted in Figure 9c, where the green arrow (representing \(P1\)'s position along the x-axis) should match the purple arrow (representing \(K1\)'s position along the x-axis). 4. Similarly, there should be no considerable variation in the \(x\) coordinates of points \(K2\) and \(P2\), indicating the absence of horizontal movement. Figure 9d illustrates this,where the green arrow (representing \(P2\)'s position along the x-axis) should align with the purple arrow (representing \(K2\)'s position along the x-axis). In summary, the algorithm for detecting the letter \"k\" was developed by tracking the positions of the index and middle fingertips. The conditions are not rigid, as an error margin is allowed through the parameter \(\alpha\), which accommodates the natural imperfections in human execution. The double letters in MSL, such as \"rr\" and \"ll\", are characterized by a left-to-right movement. The classification Algorithm 3 starts with the prior detection of the letter \"r\" or \"l\" and then checks for horizontal wrist movement in the correct direction while ensuring minimal vertical displacement.