Segmentation of lung nodules in CT images using weighted average based threshold and maximized variance

Lung cancer is a cancerous lung tumor produced by unchecked cell development in the lungs. Tobacco use for an extended period of time is the leading cause of lung cancer. Smokers have a 15–30 times higher probability of developing lung cancer than those who do not smoke. With continued cigarette use, this percentage will only rise. Long-term smokers account for nearly 85% of lung cancer cases. People who have never used nicotine goods account for 10%–15% of all instances. The reasons are a mix of hereditary variables and extended contact with second-hand tobacco or other types of air pollution.^1,2

Cancer is caused by the multistage change of healthy cells into tumor cells. This change steadily advances from a pre-cancerous spot to a dangerous tumor. The tumor is typically found in the airways as pulmonary masses. Pulmonary nodules are tiny lumps in the lungs that vary in size from 3 to 30 mm. These lumps could be innocuous or dangerous tumors.³ On lung computed tomography (CT) images, nodules are a reasonably prevalent abnormality. Certain tiny tumors may be caused by the patient’s medical background. When a tumor is thought to be innocuous, the doctor may recommend a set of CT images to monitor the lesion.⁴ If the tumor is cancerous, the patient is at high risk of developing lung cancer, and the doctor may recommend surgical excision of the lesion.

Recognizing the illness at an early stage improves the chance of recovery by up to 70%. As a result, early diagnosis and therapy of cancer are required to keep mortality rates under control. The goal is to create an automatic computer-aided system that lowers the time and labor required in scanning and helps the clinician successfully identify the illness.⁵ 

Several methods can be used to automatically locate a boundary for the separation of lung tumors in CT images.^6,7 An essential job in medical image analysis is the separation of pulmonary tumors from CT images.⁸ Radiologists can identify lung cancer more precisely and rapidly with the aid of automated lung tumor separation in CT scans. The division of pulmonary nodules includes the automated finding of a cutoff, which is crucial. This cutoff is used to distinguish the tumor’s borders from the pulmonary nodule’s adjacent tissue. The luminance levels of the images in the CT image are usually used to calculate the cutoff. The automated finding of a boundary has been suggested using a number of different techniques. These approaches consist of intensity-based approaches, histogram-based approaches, region-based approaches, and texture-based approaches. Each of these approaches has benefits and restrictions of its own.^9–11 Depending on the sort of image and the intended level of segmentation precision, the right technique must be chosen.

The segmentation of lung nodules in CT images used in this study was done to find an automated criterion that could be applied to recognize the nodules. By separating the nodule from the adjacent tissue, the threshold enables exact measurement and nodule categorization. By examining the CT image to find features such as size, form, density, and substance that set the tumor apart from the adjacent tissue, the cutoff is established. The tumor can be divided and subjected to additional analysis after the cutoff is set. Analyzing the CT image is the first stage in autonomously finding a boundary. Numerous techniques, including histogram analysis, material analysis, and segmentation, can be used to accomplish this. To find the ideal cutoff, histogram analysis examines the pixel luminosity distribution in the image. To identify which regions of the image contain the tumor, a texture analysis examines the structure of the image. The nodule’s border is finally identified and distinguished from the adjacent tissue using segmentation. The tumor can be divided after the best criterion has been found. This is accomplished by adding the cutoff to the CT image and designating the nodule-containing voxels that surpass the threshold.

In Ref. 12, various techniques for segmenting lung nodules have been evaluated. Iterative thresholding and fuzzy region-based level setting techniques are compared in this article. A sample of 52 cases was used, and a true positive percentage of 82.7% was obtained.

In Ref. 13, the authors propose automated pulmonary tumor localization. On the 27 CT images from the LIDC collection, we used the graph cut and snake algorithms and obtained a 100% true positive rate.

In Ref. 14, a Gestalt-based technique has been proposed for detecting pulmonary nodules. The technique begins by segmenting the lung area from the CT image. The highest intensity projection image was then combined with local three-dimensional data from the sagittal, axial, and coronal planes. The precision was 91.29% using 50 images from the ELCAP public database.

In Ref. 15, the authors suggest merging active outlines with adaptive concave hulls for durable lung segmentation. It made use of CT images from Shiraz Medical School’s TABA medical imaging center and ANODE09. It had 95.9% accuracy, a sensitivity of 90.1%, and a precision of 97.6%. The suggested approach detects lung tumors in 50 CT scan images using adaptive thresholding and the watershed segmentation algorithm.

The geographic information provided by pulmonary tumors is critical for clinical identification. A lung lesion identification and diagnostic system in Ref. 16 comprises two subsystems: the lung nodule segmentation system and the lung nodule diagnosis system. U-Net, a residual learning method, was suggested for the lung tumor segmentation system. This network learns more nuanced characteristics as well as combining high- and low-level lexical knowledge. The loss function fluctuates in this approach. Only when the nodule size is greater than 10 mm do segmenting nodules work well. Given the tiny size and abundant geographic information of lung lesions, the network would add an excessive amount of useless material to the feature map. The diagnostic accuracy for normal and dangerous pulmonary tumors is 87.3%. In this work, it is intended to resample CT data to a higher quality in the future to enhance the network’s classification precision on tiny tumors.

The approach outlined in Ref. 8 employs a number of medical image processing methodologies to detect lung lesions of random shapes or sizes. The approach used in Ref. 8 is based on a thresholding algorithm and a watershed segmentation method to identify tumors. The method was tested on 50 occasions and produced a 96% success rate. In Ref. 17, the authors propose a technique for removing other features from the image, allowing lesion separation. This method calls for segmenting lung lesions based on a previously defined region of concern (ROI). This ROI has to be in a rectangular shape, and it must include the area that surrounds the adjacent lung growth. Furthermore, each CT image is segmented individually, with no information between the segments used. The division is based on background estimation, specifically ROI background estimation. Furthermore, an important assumption is made in order to calculate the ROI background, making the method less reliable. Because lung cancer is the only object split, it is regarded as the only region with significant image focus, and all other images (including the shape and structure that may be related to the tumor) are regarded as image backdrops. The technique¹⁸ is inefficient because it must be modified for different types of cancer. To find clusters of ground glass impermeable material, they suggest using a mixed active contour model. Their model makes use of wavelet energy-based adaptive local energy and a Bayesian probability-based speed function to improve the contrast between the opaque regions of ground glass and the backdrop. This model, however, is only useful for classifying opaque groups of ground glass that have hazy borders and irregular tones. After denoising and improving CT images with windowed Fourier filtering and fuzzy set methods, Mao et al.¹⁹ use the fuzzy c-mean strategy to differentiate lung cancers. Because of the increase in lung cancer cases, the separation of lung tumors in computed tomography (CT) using machine learning has become increasingly essential. Machine learning can be used to identify, divide, and categorize pulmonary tumors in a numerically effective way.

The proposed method uses CT scan images from the LIDC collection, which was obtained from the cancer imaging repository (TCIA) (available at: https://www.cancerimagingarchive.net/). CT scans are obtained as a sequence of 2D images from multiple perspectives for each subject. Each set contains between 50 and hundreds of segments.

The pre-processing phase aims to enhance the clarity of structures in images, which increases the system’s precision in the subsequent processes. The incoming image is converted to gray scale, which includes only luminance information, during the pre-processing. Pixel numbers 0 and 255 are black and white, respectively, with intermediary values matching various hues of gray.

The image processing method improves the images before they are computationally processed. Image processing time can be decreased by improving the image. Some variables, such as distortion, strange colors, noise, and so on, frequently impact image clarity, rendering it unsuitable for further processing. As a result, image analysis requires more pre-processing. Contrast enhancement is a good pre-processing method that improves the luminance levels of the original image.

The values of i, j belong to the image dimensions across the x-axis and y-axis, respectively. In this expression, p(k) is the power distribution level. The ideal intensity level is represented by level in k and i. The quantity intensity splits the distribution into two parts. The highest level of mean $μhi,j$ and the lowest level of mean $μli,j$ is calculated as $μhi,j=Ihi,jHh(i,j)$ and $μli=Ili,jHl(i,j)$⁠. The membership grade $mi$ is measured as the participation number at one of two areas defined by gray level i and gray level t such that $mt,j=11+dt,μhiorμliImax−1$⁠. The $dμhi,μli$ is defined as $i,j=t−μli,t≤it−μhi,t>i$⁠. The distance between any level of intensity can be calculated using the formula d(·). The final pre-processed image with high intensity is restored using $P(i,j)=∑t=0Imax−1mt,j∗(1−mt,j)2$⁠.

A level set model²² is considered capable of segmenting the image and calculating its bias field for the exact localization of the lung border. The proposed model makes use of a function φ(x, y), where x and y are the coordinates with respect to the image. This function establishes a contour that divides the foreground (the area of the lungs) from the background (everything else). Pixels that are located inside the contour, with a φ(x, y) value greater than zero, are classified as lung pixels, while pixels that are located outside the contour, with a φ(x, y) value less than zero, are classified as background pixels. When the value of φ(x, y) is equal to zero, it signifies the true border of the lungs that we must locate. When using a weighted average, the specific approach for automated thresholding is to choose a threshold (τ) that provides the most effective separation between the lung nodules (foreground) and the background tissue. There is a possibility that the algorithm is adjusting to local differences in image intensity since it makes use of a weighted average. When it comes to the suggested model, these two processes are very necessary for the correct identification and segmentation of lung nodules. Through the process of properly extracting the boundaries and isolating them from the background, the model has the potential to enhance the analysis and detection of cancer. The main advantage of this approach is that the exact location of the initial cover has no impact on lung border determination, and two automatic points are used in this study. The contour obtained in each CT scan slice will act as the starting contour in the following slice in this technique because the contour obtained in each slice does not significantly vary from the contour obtained in the preceding slice. The pulmonary tumor border is determined at this point. Before using this technique, the starting numbers must be calculated.

Image thresholding is a basic segmentation technique that divides an image into focuses and background areas. To create a final binary image, this gray scale image analysis method converts pixels with an intensity less than the threshold value to black and pixels with an intensity above the threshold value to white. The threshold is determined by the luminance variations between objects in an image. Setting the cutoff number, on the other hand, can be challenging, and the method makes little use of the location specifics of the tumor. The proposed approach employs a thresholding-based methodology known as weighted average based thresholding. The cutoff value of the intensity of a pixel is determined by first computing the weighted average of its neighboring pixels and then removing a fixed number from this weighted average. The proposed thresholding is a straightforward and efficient method that produces significantly better outcomes after binarization for tumor segmentation as compared to any other thresholding technique.

It is presumed that the image includes two types of pixels: center pixels and background pixels and dots for the backdrop. The optimal range is then calculated by dividing the groups by their total distribution, known as intra-class variation. When the variation between classes is at its highest. The proposed thresholding technique performs iterations for all potential values of the image boundary. Then the measurement for each side of the boundary is compared to see if it has a different amount of dispersion for the pixel values. It can be determined whether the images correspond. The limit of the least intra-class variation and the greatest inter-class variation is decided. The boundary is closely picked by this thresholding number $τ$ with the intra-class variation or difference within the boundary. This is known as the weighted total of variances from two classes (w₀ and w₁) based on the intensity of I_low and I_high. The inter-class variation variance is given by $σ2i,j=woσ2i,j+w1σ2i,j$⁠. Here, w₀ and w₁ are the two weights such that $w0=∑Ilowτ−1Ili,j+∑τ−1IlowIli,j$ and $w1=∑Ihighτ−1Ihi,j+∑τ−1IhIhi,j$⁠. The thresholding method reduces the variations between these two weights by decreasing intra-class variation, which is the same as minimizing the inter-class variation. All that is required is to go through the entire spectrum range, i.e., [1,256], and choose the one that maximizes $σ2i,j$⁠. However, the relationship between intra-class variations and inter-class differences is helpful for quicker computation. The inter-class variability indicates that the sum is steady and unaffected by τ. As a result, reducing intra-class variations is the same as maximizing the inter-class variation variance, which is automatically adapted by the proposed algorithm.

Only the lung image is extracted from the original CT image by segmentation. The divided image is used for the next procedure to identify lung cancer. As a result, the segmentation phase is critical for lung cancer identification. The initial segmentation is done using the weighted average based intensity thresholding approach to include wall connected nodules, and then boundary refinement is used to identify the nodule areas that have the same intensity values as the nodule pixels. The proposed system’s effectiveness is evaluated by using different kinds of classifiers, i.e., linear, k-nearest neighbor (KNN), and support vector machines (SVMs). A KNN based classifier is used if the neighboring element has the highest value, or vice versa. Table I shows the summary of the classier results.

The proposed method has been experimented with on LIDC collection, which was obtained from the cancer imaging repository (TCIA) (available at: https://www.cancerimagingarchive.net/).²³ The proposed technique is based on the availability of images in the library, which is verified for 315 images. The system includes image processing functions such as pre-processing, thresholding, and segmentation. The segmentation technique isolates the lung tumors from the rest of the lung area with 98.96% accuracy. It allows for the most accurate detection of tumors while also avoiding over-segmentation. The width and structure of the tumor will be critical for the subsequent evaluation. Finally, the drawbacks of these methods are primarily determined by the thresholding value, which requires further improvement for better classification. Figures 1–5 show the qualitative results in images 1–5, respectively. In Figs. 1–5, row 1 denotes the input image, row 2 denotes the lung nodule before maximizing $στ2i,j$⁠, and row 3 denotes the lung nodule after maximizing $στ2i,j$⁠). Based on each image chosen, the confusion matrix parameters were approximated based on the results. A confusion matrix is a particular tabular arrangement that provides for the visualization of an algorithm’s performance. Three performance measures were computed based on the confusion matrix: accuracy, sensitivity (true positive rate), and precision. (true negative rate). Accuracy is the ratio of accurately diagnosed tumor samples to healthy tissue samples. The accuracy of the k-nearest neighbors (KNNs) approach depends on the number of surrounding data points, k. Support vector machines’ kernel functions are crucial to their performance. Linear classifiers work well on unbiased datasets. The sensitivity measure shows the percentage of actual tumors that were positive. The sensitivity of support vector machines (SVMs) makes them ideal for cancer diagnosis. Linear classifiers such as KNN may overlook cancers due to their low sensitivity. Support vector machines and linear classifiers detect normal tissues well. Since the KNN is imprecise, it may misidentify malignant tumors as benign. Support vector machines and linear classifiers may detect cancer, according to much research. KNN’s inadequate accuracy may cause cancer misdiagnosis in healthy tissues. Typically, SVMs get the best F1-score. This holds true when there is a high degree of similarity between the tumor and healthy samples. The F1-scores of linear and KNN classifiers could be low on some datasets. It is necessary to modify the hyperparameters of the support vector machine (SVM) and k-nearest neighbor (KNN) with respect to the k value, regularization, and kernel function. This enhances efficiency. Compared to KNNs and SVMs, linear classifiers produce more straightforward judgments. One reason for this is the simplicity of linear classifiers. A majority of malignancies may be detected using support vector machines. Using a linear classifier will allow you to better comprehend and assess the outcomes. The confusion matrix before maximizing $στ2i,j$ in Fig. 6 and the confusion matrix after maximizing $στ2i,j$ in Fig. 7. A confusion matrix illustrates the number of properly and erroneously identified samples per class. The confusion matrix may have moderate to high accuracy before optimization, although the model’s class classifications may be inconsistent. If the model excels with positive data but suffers with negative ones, it may have a high false negative rate. The model may miss many positive samples due to weak confusion matrix sensitivity. As seen by the confusion matrix, a low-specificity model misidentifies many negative data points. Optimizing for maximum accuracy may improve the model’s performance in the underperforming class. The model’s accuracy and confusion matrix may improve, but its performance in the original class may decrease. During optimization, we may assess if increasing model sensitivity increases positive detection and false negative reduction. Tumor detection jobs where missed positives are disastrous may need this. However, increasing sensitivity may cause false positives. As optimization improves specificity, the model may be more careful about selecting positive samples. This may reduce expensive false positives but decrease sensitivity and miss real positives. Optimizing the F1-score may include balancing recall and accuracy. Balancing the confusion matrix may increase genuine positive and negative performance. The number of images for training, testing, and validation values is summarized in Table II. A larger training set helps the model grasp complex connections and generalize to new data. The validation set helps you reduce hyperparameter overfitting while still receiving decent training set results. A new test set may improve the model’s generalizability assessment.

The numerical results of the proposed method with a KNN classifier are shown in Table III. It has been observed that good results are obtained after maximization. Table IV summarizes the comparison results with state-of-the-art methods.^8,16–19

The threshold level to differentiate between the clusters and the backdrop was automatically determined by the threshold’s automated placement. The image is divided into two regions: one with the clusters and the other with the backdrop, after the cutoff has been established by examining the luminance values of the image. In comparison to human methods, the automated placement of a cutoff significantly increases segmentation accuracy because it does away with the need for biased judgments and the potential for user prejudice. This method enables more accurate detection of the nodules and is particularly helpful when the tumor difference is minimal. Once the criteria have been established, division can start. Then, using a mix of structural procedures such as disintegration and elongation, the clusters can be precisely located and delineated. The size, form, and other features of the discovered clusters can then be examined in more detail. In computed tomography (CT) images, the proposed technique has been used to separate lung tumors. The technology is able to precisely separate the nodules from the adjacent lung tissue after autonomously locating a benchmark to define the nodules’ limits. The technology can distinguish normal lesions from cancerous tumors. The clusters are segmented and classified by the algorithm using a KNN classifier. The segmentation process will be improved even further by the system using autonomous learning techniques such as grouping algorithms. Finally, the system’s efficiency and precision have been assessed using the dataset.

This research received no external funding.

The authors have no conflicts to disclose.

Conceptualization, L.M. methodology, T.Z.; software, Y.L.; validation, E.W.; formal analysis, L.M.; investigation, T.Z.; resources, Y.L.; data curation, E.W.. All authors have read and agreed to the published version of the manuscript.

Liang Ma: Conceptualization (equal); Formal analysis (equal). Tong Zhang: Investigation (equal); Methodology (equal). Yankun Liu: Resources (equal); Software (equal). Enguo Wang: Data curation (equal); Validation (equal).

The data used to support the findings of this study are included within the article.