## 3 Dynamic Sampling Rate Adjustment Method
Once the dynamic sampling rate for mobile environments (\(SR_{mobile}\)) is determined based on Algorithm 1, this algorithm uses the movement of hand keypoints across frames to identify the exact points where a sign language utterance starts and ends. As shown in Algorithm 2, it leverages the calculated \(SR_{mobile}\) to compute the number of frames to be analyzed for changes, denoted as \(N_{change}\) (where \(S_{r}\) is replaced by \(SR_{mobile}\)). By assessing the cumulative movement of keypoints between frames (\(C_{i}\)) and comparing it to the average movement (\(C_{avg}\)), the algorithm detects the start point (\(S_{start}\)) and end point (\(S_{end}\)) of the utterance. ```
1:Input:\(SR_{mobile}\), \(K_{info}\), \(F_{total}\), \(K_{max}\)
2:Output:\(S_{start}\), \(S_{end}\)
3:Initialize\(C_{total}\gets 0\), \(N_{change}\gets 0\), \(C_{i}\gets 0\), \(C_{avg}\gets 0\), \(S_{start}\leftarrow-1\), and \(S_{end}\leftarrow-1\)
4:Calculate \(N_{change}\) using Equation (1) (replacing \(S_{r}\) with \(SR_{mobile}\)):
5:\(N_{change}\leftarrow\lfloor\frac{F_{total}}{SR_{mobile}}\rfloor\)
6:for\(i=1\) to \(N_{change}\)do
7: Calculate \(C_{i}\) using Equation (2):
8:\(C_{i}\leftarrow\sum_{k=1}^{K_{max}}\sqrt{(x_{i}^{k_{idx}}-x_{i-1}^{k_{idx}})^ {2}+(y_{i}^{k_{idx}}-y_{i-1}^{k_{idx}})^{2}}\)
9: Accumulate \(C_{total}\):
10:\(C_{total}\gets C_{total}+C_{i}\)
11:endfor
12: Calculate \(C_{avg}\) using Equation (4):
13:\(C_{avg}=\frac{C_{total}}{N_{change}}\)
14:for\(i=1\) to \(N_{change}\)do\(\triangleright\) Determine Start and End Points
15:if\(C_{i}\geq C_{avg}\)then
16:if\(S_{start}=-1\)then
17:\(S_{start}\gets i\)\(\triangleright\) First time exceeding \(C_{avg}\)
18:endif
19:\(S_{end}\gets i\)\(\triangleright\) Update end point to current frame
20:endif
21:endfor
22:return\(S_{start}\), \(S_{end}\)
```  
**Algorithm 2** Detecting start and end points of sign language utterances through dynamic sampling rate  
By dynamically determining the sampling rate based on the number of frames extracted in mobile environments, we can gain the following advantages. First, we can provide adaptability to different mobile device capabilities and conditions by adjusting the sampling rate in real time based on frame rates. Second, we can ensure accuracy in detecting the start and end points of sign language utterances, leading to better overall recognition performance. Lastly, we can reduce the use of computational resources, minimizing unnecessary processing, and lowering the computational load. Figure 1 illustrates an example of the service flow using the proposed dynamic sampling rate adjustment method in a mobile computing environment. As shown in Figure 1, the process begins with the user initiating a sign language utterance, which is captured by the mobile device's camera. The mobile device processes the captured frames in real time, applying algorithms to detect the start and end points of the utterance, thereby optimizing the input data for recognition. After detecting these key segments, the processed images are transmitted to a sign language recognition model, typically located on a server or in the cloud. This model performs inference on the input data to identify the specific sign language gestures. Once the inference is completed, the recognition results are sent back to the mobile device for display or further use. The mobile device focuses on capturing and preprocessing the gesture data, using dynamic sampling rate adjustments to enhance efficiency, particularly in resource-constrained environments. The recognition model then performs the computationally intensive task of interpreting the gestures. By dividing the workload in this manner, the proposed method ensures reliable and effective sign language recognition, despite the limited computational power available on mobile devices.