## 2 Materials and Methods
### Methods
#### 2.2.3 Preliminary Screening  
Preliminary screening is a strategy to remove potential false positives (FPs) from the image. Generally, the automatic detection of nodules produces a relatively high number of non-module lesions, called FPs, because most of the lung structures such as airways, bronchi, and blood vessels possess a grey level that is similar to that of the real nodules. As a negative impact, these structures are usually misclassified as nodules and results in a decline in classification accuracy. Additionally, being prone to FPs can also increase the computational workload. Therefore, it is crucial to reduce FPs before the classification process. In this paper, we initially performed simple thresholding to segment all the structures inside the lungs, such as nodules, airways, blood vessels, and fissures. These structures expose the attenuation ranging from \(-910\) HU to \(-500\) HU [35] on the CT scans. We choose the low-density value of -910 HU as a threshold and segment all the objects higher than that value. This helps to ensure the detection of nodules with ground glass opacities that have very faint intensities. Figure 5: Example of assigning codeword values, based on the F26 chain code. Figure 6: Border reconstruction. (**a**) Under-segmented juxta-pleural nodule, (**b**) inflection points along the boundary voxels, and (**c**) segmented lung after boundary reconstruction. As an illustration, Figure 7 depicts the volumetric structure of the segmented lung regions using the automated seeded region growing and 3D chain-coding methods. Figure 7 describes the initial segmented lung structures using thresholding, and it contains a high number of FPs. To reduce these FPs, we initially applied 3D connected component labeling [36] and analyzed the shape of each labeled object. Generally, nodules are circular, while other lesions, especially vessels and fissures, are tubular in their structure. Based on this fact, we calculated three criteria, namely, surface area, eccentricity, and voxel remove rate (VRR) [13] in order to check the shape of each candidate object. Let \(l\) be a labeled object of a roughly segmented lung structure, and its surface area \(A\) can be calculated by  
\[A\ (l)=\sum l\ (x,y,z), \tag{6}\]  
where \(l\ (x,y,z)\) is a voxel value of \(l\) at the three-dimensional coordinate point \((x,y,z)\). By checking the surface area, we can exclude huge and tiny objects that show a high probability of being non-nodules. We empirically set two threshold values, \(T1=10\) and \(T2=3700\), to eliminate the FPs outside that range. \[FP=l\left\{ \begin{array}{l}if\ A(l)<T1\\ if\ A(l)>T2\end{array} \right. \tag{7}\]  
Figure 7: Preliminary screening. (**a**) Volumetric structure of segmented lungs, (**b**) roughly segmented lung structures, and (**c**) candidate nodules after removing FPs by three criteria. Similarly, we calculated the eccentricity \(Ecc\) to check the roundness of each labeled object. The \(Ecc\) value ranged from 0 (a circular object) to 1 (a tubular object), and we empirically applied the \(Ecc\) threshold as 0.9 to remove the tubular objects. \[Ecc\left(l\right)=\frac{ma\,joraxis\,\left(l\right)}{minoraxis\,\left(l \right)} \tag{8}\]  
\[FP=l\quad if\,\,Ecc(l)>0.9 \tag{9}\]  
Then, another criterion \(VRR\) was also calculated, based on the skeleton structure of the labeled object. Skeletonization gives a topological structure by transforming the labeled object into a set in the interconnected single-voxel centerline. By calculating the \(VRR\), we could exclude the elongated skeletal structures, such as the vessels and bronchioles. \[VRR\,\left(l\right)=1-\frac{A\,\left(l\right)}{A\,\left(ls\right)} \tag{10}\]  
where \(ls\) is the skeleton of \(l\). Then, we empirically set the \(VRR\) threshold as 0.9 to remove the vessels and bronchioles. \[FP=l\quad if\,\,VRR(l)>0.9 \tag{11}\]  
After a preliminary screening using these three criteria, the FPs could be eliminated, as illustrated in Figure 7c.