## 3 Proposed Conceptual Framework
### Proposed Step 2: Conceptualizing Model and Data Preprocessing  
The quality of our data is vital. Recognizing the importance of data quality, it is essential to initiate comprehensive preprocessing steps. Here, we would recommend considering the implementation of a framework based on conceptual mathematical modeling, though it is yet to be experimented with. These steps are geared towards enhancing the video data's adaptability for future analysis. The introduction of meticulous noise reduction and artifact removal techniques can substantially improve the clarity of the video content. Using the latest technologies can aid in discarding any unnecessary disturbances, aiming for the most refined data quality. Additionally, addressing real-world challenges, such as camera movements and vibrations, is crucial. Adopting sophisticated video stabilization techniques can be an excellent strategy in this context. By doing so, any unintended camera movements and vibrations can be neutralized, resulting in impressively smooth video outputs. Such stabilization ensures the model's steadfast performance, even under varied environmental scenarios. Beyond noise management and stabilization, we would recommend the application of frame extraction techniques tailored to single out specific frames from a video stream. Such a strategy not only streamlines the analysis, but also cuts down on computational demands, thereby enhancing the model's efficiency in later stages. By taking these preprocessing measures into account, there is an opportunity to achieve data of unparalleled quality and trustworthiness, laying a solid foundation for a future deep-learning-based model. Some of the mathematical deductions for the equations are presented here (as shown in Algorithm 1), as follows:  
```
Data Acquisition \(V\leftarrow\)\(capture\_video\)\((DVR)\) Data Preprocessing : \(V_{c}\leftarrow\)\(denoise(V)\) \(F\leftarrow\)\(extract\_frames(V_{c})\) \(F_{cal}\leftarrow\)\(calibration\)\((F)\) \(F\_{aug}\leftarrow\)\(data\_augmentation(F\_cal)\) ModelTraining : #Initialize the deep learning model parameters: \(\theta\leftarrow\)\(model\_init()\) \(X_{train}\)\(X_{bal}\leftarrow\)\(data\_split(F_{cal})\) \(\varepsilon\gets 10\) best_val_loss \(\leftarrow\)\(\infty\) no_improvement_count \(\leftarrow\)\(0\)
```  
**Algorithm 1** Algorithmic representation of the proposed conceptual framework. ```
\(for\;i\;\leftarrow\;1\;to\;\epsilon:\)  if(no_improvement_count > N): # Early stopping break for\((x,\;y)\) in \(X_{train}\) do \(\overset{\sim}{Y}\;\leftarrow\;\theta(x)\;\#\;Forward\;pass\) \(\overset{\sim}{Y}\_norm=batch\_norm(\overset{\sim}{Y})\;\#\;Batch\; normalization\) \(\overset{\sim}{Y}\_dropout=dropout(\overset{\sim}{Y}\_norm,\;dropout\_rate)\;\#\;Dropout\) \(L\;\leftarrow\;loss\) \(\overset{\sim}{\left(\overset{\sim}{Y}\_Y\right)}\) #\(\;Performing\;Regularization\) \(L_{reg}=L+\lambda\bullet\parallel\theta\parallel_{2}{}^{2}\) \(\
abla L_{reg}\;\leftarrow\;\
abla loss(L_{reg})\) #Optimizing the algorithm \(p_{opt}=\beta_{1}\;*\;p+(1-\beta_{1})\;*\;\
abla L_{reg}\) \(q_{opt}=\beta_{2}\;*\;q+(1-\beta_{2})\;*\;(\
abla L_{reg})^{2}\) \(p_{opt_{Cor}}=\frac{p_{opt}}{(1-\beta_{2})}\) #\(\;Process\;of\;background\) \(\
abla\theta\;\leftarrow\;\eta\;*\;\frac{P_{opt_{Cor}}}{\left(\sqrt{\pi}a_{ opt_{Cor}}+\epsilon\right)}\) \(\theta\;\leftarrow\;\theta-\
abla\theta\;\#\;adaptive\;gradient\; descent\) #\(\;Learning\;Rate\;Scheduling\) if\((i\;\%\;M==0):\) \(\eta=\eta\;*\;decay\_{rate}\) #\(\;Performance\;Evaluation:\) \(for\;(x,\;y)\;in\;V\)do \(\overset{\sim}{Y}\;\leftarrow\;\theta(x)\;(Forward\;pass\;of\;the\; model)\) \(M\;\leftarrow\;evaluation\_metrics(\overset{\sim}{Y},\;y)\)
```  
**Algorithm 1**\(Cont.\)  
In the data acquisition step, we capture the video data \(X\) and apply denoising to obtain denoised video data \(X\prime\). We then extract frames from the denoised data \(X^{\prime}\) to obtain the set of frames \(F\) and perform camera parameter calibration to obtain calibrated frames \(F\prime\).