## 3 Results  
The effectiveness of the proposed models was thoroughly assessed utilizing the dataset from the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) [21]. The LIDC dataset [21] is recognized as a cornerstone for research in lung cancer diagnosis, encompassing 1018 CT scans, each paired with an XML file. During preprocessing, scans exhibiting a slice thickness exceeding 2.5 mm, as well as those lacking slices or exhibiting inconsistent slice spacing were excluded. This filtration process yielded a refined collection of 888 CT scans. The scans retained in this selection showcase nodules with minimum diameters of 3 mm, annotated by four radiologists who provided malignancy scores on a scale from 1 (indicative of likely benignity) to 5 (indicative of likely malignancy). While nodules receiving unanimous scores from all radiologists would be ideal for analysis, adhering to such stringent selection criteria would drastically diminish the dataset's volume. To preserve a comprehensive sample size for analysis, nodules were classified as benign with an average radiologist score of \(\leq\)1.5, and as malignant with an average score of \(\geq\)3.5. Employing this classification strategy, the curated version of the LIDC dataset for our study includes 491 malignant and 331 benign nodules. Three separate experimental setups were devised and examined. The initial experiment was dedicated to differentiating between benign and malignant nodules by feeding raw CT scans into a deep learning framework that incorporates 3D-CNN. The second experiment pursued a similar classification goal, but it utilized magnitude and directional features derived from 3D-LOP extracted from the nodule volumes as inputs for the 3D-CNN architecture. The third experiment amalgamated these methodologies by merging the output probabilities from the preceding two experiments with essential geometric features delineated from the nodules' morphology. This composite information was subsequently analyzed using a softmax classifier to render the ultimate diagnostic verdict. The aim behind integrating geometric characteristics with the probabilities from the initial experiments is to synergize the classification insights based on the nodules' geometric attributes, enhancing the decision-making process beyond simple probabilistic multiplication. Figure 4 clearly illustrates this integration in a detailed diagram. Figure 4: Integration of Initial Outputs from 3D-CNN and 3D-LOP with Geometric Features. In the first experiment, the raw data were input into the CNN model as depicted in Figure 5 for accuracy and Figure 7 for loss. Conversely, Figure 6 presents the accuracy for the second experiment, wherein the CNN model processed a feature vector derived from 3D-LOP with the corresponding loss shown in Figure 8. This incremental advancement highlights the model's capability to effectively learn from the input data. More importantly, the continuous increase in validation accuracy and decrease in validation loss demonstrate the model's ability to generalize well to new, unseen data--a critical aspect of the efficacy of predictive models. This generalization indicates that the identified patterns are not solely characteristic of the training data but also applicable in broader real-world scenarios, thereby validating our model's utility in accurately classifying lung nodules. To evaluate the effectiveness of the proposed 3D-LOP separately, its performance was compared not only with the original LBP but also with several of its variants, specifically Adjustable LBP, Resolved Ambiguity LBP, and the original Local Ternary Pattern (LTP). Figure 8: 3D-LOP model loss evolution over epochs. Figure 7: Raw data 3D-CNN model loss evolution over epochs. As indicated in Table 3, the 3D-LOP outperformed all compared versions of LBP in terms of accuracy. Further analysis revealed that the original 3D-LBP displayed the lowest accuracy and specificity of all evaluated descriptors.