# Enhanced Localisation and Handwritten Digit Recognition Using ConvCARU
## 4 Experimental Results and Discussion
### Performance Comparison  
Meanwhile, a carefully selected set of evaluation metrics was used to measure both the visual fidelity of the predicted frames and the computational efficiency of the models. Several quantitative metrics are recommended for evaluating the accuracy and visual similarity of reconstructed or compressed media compared to a reference. In this context, the structural similarity index (SSIM) and the peak signal-to-noise ratio (PSNR) are key indicators of visual quality, with higher values denoting improved reconstruction. \[\text{SSIM}(x,y)=\frac{(2\mu_{x}\mu_{y}+C_{1})(2\sigma_{xy}+C_{2})}{(\mu_{x}^{ 2}+\mu_{y}^{2}+C_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2})} \tag{13}\]  
where  
* \(\mu_{x}\) and \(\mu_{y}\) are the mean values of images \(x\) and \(y\),
* \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variances,
* \(\sigma_{xy}\) is the covariance,
* \(C_{1}\) and \(C_{2}\) are small constants to avoid division by zero. \[\text{PSNR}=10\log_{10}\!\left(\frac{MAX_{I}^{2}}{MSE}\right) \tag{14}\]  
where  
* \(MAX_{I}\) is the maximum possible pixel value,
* \(MSE\) is the Mean Squared Error. In turn, the mean squared error (MSE) quantifies the deviation between pixels in images. This deviation is minimised in high-quality outputs, making lower MSE valuespreferable. In video analysis, the Frechet video distance (FVD) is a deep learning-based perceptual metric where lower scores correspond to enhanced temporal coherence and realism. \[\text{MSE}=\frac{1}{N}\sum_{i=1}^{N}(x_{i}-y_{i})^{2} \tag{15}\]  
where  
* \(x_{i}\) and \(y_{i}\) are pixel values of the original and compressed images,
* \(N\) is the number of pixels. \[\text{FVD}=\|\mu_{r}-\mu_{g}\|^{2}+\textit{Tr}(\Sigma_{r}+\Sigma_{g}-2(\Sigma_ {r}\Sigma_{g})^{1/2}) \tag{16}\]  
where  
* \(\mu_{r}\) and \(\mu_{g}\) are the mean feature vectors of real and generated videos,
* \(\Sigma_{r}\) and \(\Sigma_{g}\) are the covariance matrices,
* \(\textit{Tr}()\) denotes the trace operation. To provide a detailed evaluation of the effectiveness of the proposed model, extensive experiments were conducted to compare its performance with that of the current state-of-the-art (SOTA) approaches in video prediction. As presented in Table 1, the results demonstrate improvements in all considered metrics. The proposed model achieves an SSIM value of 0.901, which is very close to the value of 0.902 reported by DMVFN. This highlights the model's ability to maintain structural integrity in predicted frames. However, the model demonstrates higher overall image fidelity, achieving a PSNR of 29.31 dB and surpassing the 29.11 dB achieved by DMVFN. Although DMVFN achieves a lower MSE (0.039 vs. 0.041), our model offers superior video prediction quality, as evidenced by its significantly lower FVD score of 155.5. Although it requires 13.66% more computational time than DMVFN, this is justified by the improvements in PSNR and FVD, which are two critical metrics for maintaining visual consistency and realism in generated frames. Furthermore, the refined architecture improves the modelling of temporal dependencies, enabling more precise prediction of object trajectories and transformations. The feature decoupling mechanism strengthens spatial representation, preserving essential structural elements throughout the prediction process. Meanwhile, the optimised gating strategy mitigates information degradation to ensure superior temporal consistency across generated sequences. Overall, these results highlight the effectiveness of our approach in achieving a balance between predictive performance and computational efficiency. Further discussion of these aspects will clarify the advantages of our methodology and its potential to advance the field of video prediction.