# Effect of Camera Choice on Image-Classification Inference
## 4 Results and Discussion
### Quantitative Effect of Camera Choice
Formally, [PERSON]'s Kappa \(\kappa\) is defined as follows:  
\[\kappa=\frac{p_{o}-p_{e}}{1-p_{e}} \tag{3}\]  
where  
* \(p_{e}\) is the theoretical probability of agreement by random chance and is calculated using the observed data as follows: \[p_{e}=\frac{1}{N^{2}}{\sum_{c}}n_{ci}n_{cj}\] (4) where
* \(c\) is the index of the categories or classes that can be chosen (ranges from 1 to 1000 in this case, given that the ImageNet-1k dataset contains 1000 classes);
* \(n_{ci}\) is the observed number of times that the classifier predicted category \(c\) (out of \(N\) images) for images captured by one camera in the camera pairing;
* \(n_{cj}\) is the observed number of times that the classifier predicted category \(c\) (out of \(N\) images) for images captured by the other camera in the camera pairing. Table 3 illustrates the raw observed agreement proportion \(p_{o}\) and [PERSON]'s Kappa \(\kappa\) as a function of scenario and camera pairing. It is clear that [PERSON]'s Kappa \(\kappa\) is always significantly smaller than the raw agreement proportion \(p_{o}\). Although the model is trained on the ImageNet-1k database and can therefore make predictions on 1000 classes, it is usually classifying the images in this study as cups or mugs, and even when it makes different classifications, only a small percentage of the 1000 image classes are represented in the inference results. For this reason, \(p_{e}\) tends to be relatively large, so [PERSON]'s Kappa \(\kappa\) is smaller than \(p_{o}\). Table 3 demonstrates clearly that the best agreement in model predictions for different camera pairs is achieved in Scenario 1, while the worst agreement in model predictions occurs in Scenario 3. This is to be expected because Scenario 1 is the least cluttered scenario and so we would expect that differences between comparable images acquired by different cameras would have less bearing in the top model prediction. It is also clear that the agreement in top model predictions for the Logitech C920e/Microsoft LifeCam pairing is significantly better than the other two camera pairings in Scenarios 2 and 3 (although not in Scenario 1). This quantitatively demonstrates that the chosen camera model can have a significant effect on the model inference output. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Scenario 1**} & \multicolumn{2}{c}{**Scenario 2**} & \multicolumn{2}{c}{**Scenario 3**} \\ \cline{2-7}
**Camera** & **Raw Agreement** & **Cohen’s Kappa** & **Raw Agreement** & **Cohen’s Kappa** & **Raw Agreement** & **Cohen’s Kappa** \\
**Pairing** & **Proportion**\(p_{o}\) & \(\kappa\) & **Proportion**\(p_{o}\) & \(\kappa\) & **Proportion**\(p_{o}\) & \(\kappa\) \\ \hline Angetube 962A/ & 0.86 & 0.56 & 0.52 & 0.44 & 0.37 & 0.25 \\ Logitech C920e & 0.81 & 0.50 & 0.43 & 0.35 & 0.37 & 0.28 \\ Logitech C920e/ & 0.82 & 0.49 & 0.59 & 0.50 & 0.51 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Top prediction agreement statistics for camera pairings and scenarios. Although somewhat arbitrary, there is an interpretation attached to certain ranges of Cohen's Kappa \(\kappa\)[46], as illustrated in Table 4. From this table, the agreement between the top model predictions for comparable images taken with different cameras is moderate in Scenario 1 but generally only fair in Scenario 3. Again, this demonstrates the complex relationship between model, camera, and scenario for image-classification inference.