## 3 Results and Discussion
The graphical representation of the true and estimated positions movement of the precious object is given in Figure 21a,b. If the Kalman filter fails to estimate the centroid of the precious object, then an alert signal is given to the museum alarm and computer system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Cover Images**} & \multicolumn{4}{c}{**Time Complexity in ms**} \\ \cline{2-5}  & **Command1 = ’NO’** & **Command2 = ’A1’** & **Command3 = ’A2’** & **Average** \\ \hline Image 1 & 94.7769 & 93.8743 & 95.7877 & 94.8130 \\ Image 2 & 91.0290 & 91.1963 & 90.7975 & 91.0076 \\ Image 3 & 96.1845 & 94.0191 & 96.7095 & 95.6377 \\ Image 4 & 94.5715 & 91.6055 & 93.0815 & 93.0862 \\ \hline \multicolumn{5}{c}{**Mean**} & \multicolumn{2}{c}{**93.6361**} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time complexity analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Cover Image 1** & **Cover Image 2** & **Cover Image 3** & **Cover Image 4** \\ \hline DFT & 94.6 & 95.2 & 94.9 & 95.3 \\ DCT & 93.4 & 93.2 & 93.6 & 94.0 \\ DWT & 95.8 & 96.8 & 95.6 & 95.7 \\ IWT & 96.2 & 97.1 & 96.6 & 97.2 \\ IWT/ARC & 96.8 & 97.3 & 97.6 & 97.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accuracy comparisons of the proposed system for various algorithms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Block Size** & **4 \(\times\) 4** & **8 \(\times\) 8** & **16 \(\times\) 16** \\ \hline Accuracy (\%) & 91.1 & 97.6 & 98.2 \\ Bit Rate (bits/s) & 11,664,000 & 2,916,000 & 729,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy and Bit Rate comparison. Figure 19: ROI for object tracking. Figure 20: Tracking result of six frames. Figure 21: Tracking result of object centroid \(X\) and \(Y\) coordinates (**a**) \(X\) co-ordinate Tracking (**b**) \(Y\) co-ordinate Tracking. The performance of the proposed object tracking algorithm is evaluated in terms of its accuracy in the XY-plane. The actual center position of the object \((x_{act},y_{act})\) is observed visually and noted in terms of cm. The position of the object \((x_{est},y_{est})\) estimated from the image will be in terms of pixels. Hence, a resolution factor \((X_{res},Y_{res})\) correlating the physical dimensions to the pixels of the images is evaluated, as in Equations (14) and (15), for \(X\) and \(Y\)-axis respectively. It can be used to bring down the estimated and actual position of the object to a common domain, which is required to evaluate the error metrics. To normalize the error metrics, the tracking error is evaluated per unit of object dimension A round object of 5 cm diameter is tracked in the proposed work, and the mean tracking error over 'N' frames are evaluated as in Equation (16) for \(X\)-axis and Equation (17) for \(Y\)-axis. Finally, the tracking accuracies of \(X\) and \(Y\) plane are determined using Equations (18) and (19) respectively. The experimental results illustrate a significant tracking accuracy of 95.54% and 98.54% in the \(X\) and \(Y\) coordinates respectively. This demonstrates the performance of the proposed work in terms of providing a reliable tracking mechanism for precious objects, and enhances museum security. \[X_{res}=\frac{\text{Height of the captured image in pixels}}{\text{Physical height of the image in cm}} \tag{14}\]  
\[Y_{res}=\frac{\text{Width of the captured image in pixels}}{\text{Physical width of the image in cm}} \tag{15}\]  
\[E_{x}(\%)=\left(\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{ \sum}}}\left|\left(x(i)_{act}-\frac{x(i)_{est}}{X_{res}}\right)\right|\div D \right)\times 100 \tag{16}\]  
\[E_{y}(\%)=\left(\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}} \left|\left(y(i)_{act}-\frac{y(i)_{est}}{Y_{res}}\right)\right|\div D\right) \times 100 \tag{17}\]  
\[A_{x}(\%)=100-E_{x} \tag{18}\]  
\[A_{y}(\%)=100-E_{y} \tag{19}\]