## 3 Results  
The proposed model was trained using 360 paired bi-plane fluoroscopic images obtained during mock procedures in the catheterization lab at New York Presbyterian Hospital. These images depict the maneuvering of a VersiSight Pro ICE catheter (Philips) in both AP and LAO90 planes. As was described previously, the data was partitioned into three subsets, with 70% (252 images) allocated as the training set, 20% (72 images) as the validation set, and 10% (36 images) as the testing set. The training and validation sets were utilized during the model training phase, while the testing set was reserved for evaluating the model's performance at the conclusion of the training phase. To ensure a representative distribution of the ICE catheter's movement in both the training and testing datasets and prevent overfitting, the data was randomly shuffled prior to being divided into the training and testing sets.  
The standard process of system identification consists of three stages: data creation (feature extraction), model determination, and validation [27]. The first two stages are described in Section 2. In this section, the focus is on the validation stage, where the model is tested on a portion of the dataset that it has not seen before. The results, as depicted in Figure 6, indicate that the proposed model closely follows the output with high accuracy. To quantitatively assess the performance of the method, three metrics are selected: Normalized Mean Square Error (NMSE), Mean Absolute Error (MAE), and Standard Deviation of Absolute Error (SDAE). In Figure 7a,b, the values of NMSE, MAE, and SDAE are depicted for three sample groups: Training and Validation samples, Blind test samples, and all samples (Training, Validation, and Blind test). As displayed, the NMSE values are of the order of \(\sim\)\(3\times 10^{-3}\), indicating a low error and a high level of fitting. The MAE values are of the order of \(\sim\)4.5 degrees of error in the prediction of the roll angle, corresponding to \(\sim\)1.25% error on average (\(\sim\)4.5/360 degree), which is considered acceptable for practical purposes. Finally, the SDAE values show a standard deviation of less than five degrees, implying that the model is capable of predicting the roll angle of the ICE catheter with a deviation of approximately 1.39% or 5/360 degree, which is  
Figure 5: (**a**) Euclidean distance (D) of the black width (between points \(q_{1}\) and \(q_{2}\)) of the ICE catheter tip on the AP plane. (**b**) Distance “D” and the extracted Roll angle of the ICE catheter as the ground truth data for the ML model.  
also acceptable for surgeons. In Figure 7c-e, the absolute error histograms of the model are displayed for the same three sample groups. All three histograms exhibit a normal distribution centered around zero, indicating that the majority of errors are less than five degrees, which is acceptable for catheterization procedures. To demonstrate the linear correlation between the predicted and actual outputs of the model, a line was fitted over the data for each of the three sample groups in Figure 7f-h. The R-squared values for all three groups are approximately 0.99, indicating a high degree of accuracy in replicating the actual output by the proposed model.  
Figure 6: Actual Prediction of Blind test dataset using the proposed LF/HF ML model.  
Figure 7: Error criteria for three sample groups: Training and Validation samples, Blind test samples, and all samples (Training, Validation, and Blind test). (**a**) Normalized Mean Square Error (NMSE), (**b**) Mean Absolute Error (MAE), and Standard Deviation of Absolute Error (SDAE), (**c–e**) Error histograms, (**f–h**) Linear correlation and R-squared.