## 1 Introduction
### Related Works  
As automated nodule detection has been an active research area since 1980, numerous research papers have been published on this topic. Those papers proposed different algorithms using different datasets with different focuses. Among them, we studied some related research that presented the same objective and processes. As our experiments are based on the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) [28; 29; 30], we reviewed some previous works using the same dataset. An extensive review of nodule detections, working on different datasets, can be referred to [31]. In 2015, [PERSON] and [PERSON] [9] proposed computer-aided lung nodule detection using outer surface extraction. For lung region segmentation, they applied multiple thresholding, which uses two threshold values: maximum and minimum. Afterward, possible nodules were detected using labeling and rule-based methods. From each possible nodule, four different feature groups, including (i) morphological features, (ii) statistical and histogram features, (iii) outer surface statistical and histogram features, and (iv) outer surface textural features, are extracted. Based on these features, false reduction was conducted using a support vector machine (SVM), optimized by the particle swarm algorithm. Their experiments were performed using 200 CT exams of the LIDC-IDRI dataset. Their findings revealed that using outer surface features can provide a higher performance up to 98.03% sensitivity, 87.71% selectivity, 90.12% accuracy, and 2.45 false positives per scan. As a weakness, their work could not detect the nodules that had intensities outside the maximum and minimum threshold range. Moreover, they did not take into account the detection of nodules that were attached to the lung boundary. In addition, [PERSON] et al. [24] also implemented novel nodule detection using multi-view convolutional networks (ConvNets). They initiated suspicious nodule detection by combining three existing candidate detectors, which are designated for solid, sub-solid, and large solid nodules, respectively. Subsequently, multiple streams of 2D ConvNets were created using 2D patches of the detected nodule candidates. ConvNets can learn the discriminative features automatically from the training data in order to perform the false reduction. Their detection is evaluated using three datasets, and the highest performance (sensitivity 90.1% with four false positives per scan) has resulted in the LIDC-IDRI dataset. Even though ConvNets are powerful for feature learning and classification, they demand very high computation costs, especially the graphical processing unit (GPU). Recently, [PERSON] et al. [13] also developed a CAD for nodule detection that applied 3D skeleton features. For lung region segmentation, they used the global optimal active contour model, which can enclose both solitary and boundary attached nodules. Then, the suspicious nodules scattered in the lungs are segmented using thresholding, morphological operations, and labeling methods. Ten features, including the 3D skeleton features, are extracted, and invalid nodule candidates are eliminated, based on prior anatomical knowledge. Finally, the real nodules are segregated by the SVM-based false reduction. Their CAD was also tested on 71 exams of LIDC-IDRI and reported a 89.3% sensitivity, 93.6% accuracy, and 2.1 false positives per subject. Nonetheless, their CAD did not describe the detection of small nodules surrounded by the vessels. Moreover, [PERSON] et al. [25] also presented a lung nodule classification scheme, based on hybrid features. Instead of using a segmentation method to detect suspicious nodules, they created icosahedrons to sample the spherical structures. From these samples, they estimated nodule radii based on threshold values and created a 3D volume of nodule candidates. Then, convolutional neural networks (CNNs)-based statistical features and Fisher vector (FV)-based geometrical features were extracted from the volume candidates.