1 Introduction

Cancer tends to be a sensitive content to our age and majority of peoples globally are fighting due to this disease and still there is no heal. However, acquiring it beneath control by earlier discovery can be a means to elevate the rate of survival. Following cancer amidst the breast and prostate, the lung cancer tends to be most pragmatic cancer amidst both women’s and men’s. Using a death toll of considering 70%, the American Cancer Society hold lung cancer amidst the most antagonistic cancers since 2016 [13]. As a result, the survival probability are maximized up to 49%, if the cancer is determined in the earlier phase whenever it is limited towards lungs and it spreads through lymph [4, 14, 15]. The cancer in lungs has considered as a foremost reason of death amidst world with elevated mortalities. As per cancer statistics in year 2019, the deaths due to lung cancer ranges about142, 670 cases having total 23.51% cancer patients which are projected highly in United States. Squamous Cell Carcinoma (SqCC) and Adenocarcinoma (ADC) are considered as NSCLC types which report for 80 to 85% cases having lung cancer. The survival rate of patient’s 5-year elevates from 19 to 54% if lung cancer can be treated at an earlier phase [16, 17]. Thus, earlier lung cancer treatment is significant to elevate rate of survival [2]. The aim of earlier discovery of lung cancer is needed due to symptoms that occur in sophisticated phases and earlier discovery can treat or make easy diagnosis, and save several lives [1, 18].

The medical images are a fundamental tool to identify and diagnose cancer in former phase. The medical imaging is utilized for earlier cancer discovery, assessment and provides suitable follow-ups [4]. The elucidation of huge medical images manually can be termed as a complicated and may produce error and human bias. The techniques based on model classification helps to categorize the inputted data into various classes as foundation for characteristic features of input. Earlier discovery of lung cancer with recognition of pattern can save the life by evaluating huge count of CT images [1]. The cancer in lungs affected pulmonary nodules amidst lungs and thus for enhancing rate of survival, the nodules must be determined as earlier as possible. Presently, the thoracic CT are devised to detect pulmonary nodules and it aids to envisage thorax tissue in three extents [6, 19]. CT is termed as one of the imaging modality utilized for treating the diseases in lungs [7]. CT is considered as a filtering technique which utilizes attractive domains for capturing the images from films [20]. With the lung CT images, one can detect the pulmonary nodule in an effective manner [21]. Priorly, the image slice of CT is reconstructed in film that elevates the volumetric data. In recent days, the designed CT scanners has prevented huge volumetric data and hence enhanced the detection of cancer. In the biomedical domain, the inspection and treatment of lung CT image by domain experts are receptive procedure that needs time and elevated qualification [9, 22].

The process of diagnosis is handled by using prior technologies and software’s. Hence, the effort of diagnosis and cost are minimized. Hence, one of the general models favored in recent days for diagnosing the lung cancer is deep learning [9, 21]. In general, the most of the techniques are accounted to segment medical images. Imperative issues tackled by classical techniques rely on using manual features for segmenting interesting regions. Moreover, the majority of methods are not able to segment the attached nodules to the lung walls. In recent days, the processing of medical images is done with deep learning-based techniques and has gained huge impacts in the clinical applications. These techniques can suitably learn imperative features from the medical images and as a result it overwhelms the issues of handcrafted features [8, 23]. Most of the researchers have devised the usage of Artificial Intelligence (AI), particularly deep learning to overwhelm the problems and enhance the outcomes. The deep models poses the benefit of being capable to execute end-to end discovery in CAD models by learning through the most crucial features over training and can study features through the experiential data without using hand-engineered features. The Deep Neural Network (DNN), Convolution Neural Network (CNN), and Stacked Auto Encoder (SAE) [24] are termed as a three main deep structures to detect the cancer. The CNN provided better efficacy in contrast to DNN and SAE. The CNN are a kind of multi-layered NN which can differentiate the visual patterns through the pixel images with Inception (GoogleNet), and AlexNet for envisaging the discovery of lung nodule along with its classification [1].

The aim is to design a productive framework for lung cancer detection with AFRO-DBN. The CT image is acquired and undergoes pre-processing with wiener filter for denoising. After that, lung lobe segments are obtained with LadderNet, where network is optimally tuned using devised AFRO. After segmenting lung lobe, the nodule detection is conducted utilizing grid based method. Following to this step, appropriate features like Spider Local Image Feature (SLIF), Shape Local Binary Texture (SLBT), SURF, Histogram of Gradients (HOG), Grey Level Co-occurrence Matrix (GLCM) features and statistical features are extracted. The lung cancer classification is performed using DBN and the hyper parameters of DBN are tuned with devised AFRO.

The main contributions are:

  • Proposed AFRO-based LadderNet for lung lobe segmentation: The segmentation of lung lobe is conducted using AFRO-based LadderNet. Here, the LadderNet undergoes training with AFRO, which is produced by unifying Archimedes Optimization Algorithm (AOA) and Flow Regime Algorithm (FRA).

  • Proposed AFRO-based DBN to identify lung cancer: The discovery of lung cancer is performed with AFRO-based DBN. Here, the DBN undergoes training with AFRO to tune DBN.

The paper is organized as: Section 2 defines the formerly devised lung cancer detection techniques. Section 3 elaborates the proposed model to detect lung cancer. Section 4 illustrates estimation of outcomes with graphs and Section 5 gives conclusion using AFRO-based DBN.

2 Motivations

Various techniques based on the detection of lung cancer are developed and attained promising outcomes. However, the manual examination of huge medical images can be considered as a complicated and is vulnerable to human errors and bias. Thus, motive depends on designing a novel idea for detecting the lung cancer.

2.1 Literature survey

AR, B., [1] devise a technique, namely Capsule Neural Network (CapsNet) for detecting the lung cancer. Here, the augmentation is employed for enhancing the accuracy and it was also used for determining the training instances. The method did not able to overwhelm the CNN issues with small data. Zhang, G., et al. [2] designed a new technique for classifying the malignant and benign lung nodules using CT. The method utilized squeeze-and-excitation network and aggregated residual transformations (SE-ResNeXt) for detecting the lung cancer. It acquired the benefits of SENet for recalibrating the features and detecting the imaging patterns. The technique needed more memory. Qin, R., et al. [3] designed a deep model which unified the fine—grained features using CT and PET images and it allowed for non-invasive treatment of lung cancer. Here, the multidimensional attention technique was utilized for effectually reducing the feature noise while mining the fine grained features through imaging modalities. However, this technique did not accumulate more labels for segmentation. Polat, H. and Danaei Mehr, H., [4] developed two CNN-based techniques as deep model for diagnosing the lung cancer using CT. To envisage the efficiency, the hybrid 3D-CNN was used, but it did not able to classify different nodules. Lakshmanaprabu, S.K., [5] developed Optimal Deep Neural Network (ODNN) with Linear Discriminate Analysis (LDA) for detecting the lung cancer using CT. Modified Gravitational Search Algorithm (MGSA) with ODNN was applied to classify lung cancer, but it did not consider optimum feature selection with various classifiers. Shanid, M. and Anitha, A., [6] developing an automated lung cancer detection technique with deep model. Here, the lung CT image was used and it was pre-processed and offered to segmentation phase which is executed with active contour. Then, the grid-based model was used for nodules segmentation. Finally, the salp-elephant herding optimization algorithm-based deep belief network (SEOA-DBN) was used to classify lung cancer. The method can handle limited datasets. Shetty, M.V. and Tunga, S., [7] devised Water Cycle Sea Lion Optimization-based Shepard Convolutional Neural Network (ShCNN) for detecting the lung cancer. The median filter was used to filter out noise from images. WSLnO was employed to segment the lung lobes. Then ShCNN provides classification of lung cancer. The method needed huge time to process image. Jalali, Y., et al. [8] developed DNN model for performing an automated lung CT image processing to detect lung cancer. Here, the modified U-Net was app;lied for segmentation and furthermore the Bidirectional Convolutional Long Short-term Memory (BConvLSTM) was employed to classify lung cancer. The technique faced complexities while segmenting huge medical images.

2.2 Challenges

Some of flaws based on lung cancer detection schemes are illustrated below:

  • In [1], a CapsNet technique is developed for detecting the lung cancer. Despite the technique generated elevated accuracy outcomes, it could not enhance the performance metrics with limited count of databases.

  • The 3D SE-ResNeXt technique is devised in [2] and it permitted deep network optimization more effectively for boosting the discriminability of features considering lung nodules. Besides it worked on raw CT images, which failed to differentiate lung nodules for classification.

  • In [4], the hybridized D-DCNN model is developed for detecting the lung cancer. However, it endured more complexities while determining the nodules on complex CT scan images.

  • The Res BCDU-Net model is developed in [8] for detecting the lung cancer. It had few false positives and high scores of dice similarity. However, this method was undesirable for testing the 3D lung CT.

  • In the earlier phase of lung cancer and size of cancer augmentation is low and thus the detection of nodules in less time is complex process. Hence the radiologists failed to discover the lung cancer in earlier stage.

3 Proposed AFRO-DBN to detect lung cancer

Lung cancer is termed as a most severe and life threatening disease worldwide. However, earlier detection and its diagnosis can save the life of peoples. Even though, the images of CT scan is termed as finest imaging modality in medical domain, but it is still complex amidst the doctors to examine and detect the cancer using the CT scan images. Hence, the computer aided treatment can be useful for doctors to detect the cancerous regions more precisely. The aim is to provide a productive framework for lung cancer detection with AFRO-DBN. At first, the input CT image are acquired from specific dataset illustrated in [26] and the first step in image processing applications is pre-processing to make the raw image fit for further processing using wiener filter. After that, lung lobe segmentation is carried out to segment the lung lobe regions using LadderNet [12], where the network classifier are optimally tuned using devised AFRO. After segmenting lung lobe, nodule detection is conducted utilizing grid based method. Following to this step, appropriate features like SLIF, SLBT, SURF, HOG, GLCM and statistical features are extracted. Finally, lung cancer classification are performed using DBN [25] and the hyper parameters of DBN are optimally fine tuned using devised AFRO. Here, the proposed AFRO is achieved by the consolidation of AOA [10] and FRA [11]. Figure 1 explains the structural overview of lung cancer detection model using AFRO-DBN.

Fig. 1
figure 1

Overview of lung cancer detection technique with AFRO-DBN

Full size image

3.1 Congregate data

The processing of images is utilized in the past for diagnosing the lung cancer. The techniques based on machine learning helps in diagnosing and classifying the lung nodules by computing the images of CT generated with different techniques. The aim of earlier discovery of lung cancer is needed due to symptoms that only elevate in advanced phases and earlier discovery can provide diagnosis to save several lives. Here, CT dataset F has z images and it is modelled as,

$$F=\left\{{\rho }_{1},{\rho }_{2},\cdots ,{\rho }_{b},\cdots {\rho }_{z}\right\}$$
(1)

wherein, \({\rho }_{b}\) states bth image and z articulates total count up of CT images.

3.2 Pre-process image with wiener filter

Here, \({\rho }_{b}\) is provided as pre-processing input. The aim of pre-processing is to progress image by suppressing the distortion or by enhancing image features for improved and smoother processing. It involves the variation of size, orientation, and color. The aim of this stage is to elevate the image quality so that one can inspect the image effectually. In addition, it aids to alter the raw data into useful data and aids to impute the missing values and noisy data. Here, the wiener filter [30] is adapted for pre-processing the images. It is utilized for generating an estimated or required or targeted random process. Moreover, this filter is used for removing the additive noise and mean square error and also aids to invert blurring concurrently. It is termed as a linear evaluation of input image. Moreover, this filter minimizes the degradation and noise from an image by comparing it with degraded images. The Wiener filter in a Fourier domain are notated as,

$$\vartheta \left({r}_{1},{r}_{2}\right)=\frac{{B}^{*}({v}_{1},{v}_{2}){C}_{d}\left({v}_{1},{v}_{2}\right)}{{\left|B({v}_{1},{v}_{2})\right|}^{2}{C}_{e}({v}_{1},{v}_{2})+{C}_{f}({v}_{1},{v}_{2})}$$
(2)

wherein, \({C}_{d}({v}_{1},{v}_{2})\) stands for power spectra of input image, \({C}_{f}({v}_{1},{v}_{2})\) signify additive noise and \(B({v}_{1},{v}_{2})\) express blurring filter. The pre-processed image E is then forwarded to lung lobe segmentation phase.

3.3 Segment the lung lobe using AFRO-based LadderNet

The obtained pre-processed image E is offered to segmentation. The CT image with high resolution is utilized for several pulmonary applications. As the function of lungs alters in a region, hence the pulmonary disease is not consistently dispersed in lungs and hence it is beneficial to examine the lungs on lobe-by-lobe manner. It is utilized for analyzing functions of lungs and to make effective plan for surgery. However, the precise segmentation is complex as some patients have fake fissures. Hence, it is imperative for segmenting not only lungs but also lobar fissures. Segmentation is executed with AFRO-based LadderNet. To train LadderNet, AFRO is used and its steps are briefed along with the LadderNet overview.

  1. a)

    LadderNet overview

The LadderNet [12] is similar to U-Net, but the path count for transmitting the information is limited in case of U-Net. The LadderNet is termed as a multi-branch CNN for performing semantic segmentation which comprises multiple paths to pass the information. The features in various spatial scales are considered as A to E, while the columns are termed as numbers that relies from 1 to 4. Here, the column 1 and 3 indicates encoder branches, and column 2 and 4 indicates decoder branches. The convolution having stride of 2 is used for going from tiny to huge-receptive-field features (like A to B) and utilize transposed convolution having a stride of 2 to reach from huge to huge-receptive-field features (like B to A). The channel counts are doubled from one level to next level (like A to B). The obtained output from LadderNet is signified a A. Figure 2 provides the overview of LadderNet model.

Fig. 2
figure 2

LadderNet overview

Full size image
  1. b)

    Train LadderNet using AFRO

LadderNet is trained with AFRO, and it is generated by the unification of FRA and AOA. The AOA [10] is motivated through the principle of Archimedes which is generated through physics laws. It offers finest performance optimization application with improved convergence speed and effectual exploration–exploitation that consequently aids in addressing the complex problems. It manages potential to adapt a group of solution and prevents local optima trap. It generated best solutions and discovers global best solution rapidly. On the other hand, FRA [11] is motivated from the priorly developed flow regimes and fluid mechanics. It can produce best design and acquires less time to process a task. It can be observed that FRA poses finest efficacy and it can be a candidate solution for addressing the complicated optimization issues. The union of AOA and FRA produces premium solution and steps undergone by AFRO are illustrated below.

  • Step 1) Initialization

Initial and crucial mission is to initiate position of objects, and it can be articulated by,

$${H}_{s}={L}_{s}+rand\times \left({O}_{s}-{L}_{s}\right); s=\mathrm{1,2},\cdots ,R$$
(3)

Here, \({H}_{s}\) refers to sth object considering the objects population R, \({O}_{s}\) indicate upper bound and \({L}_{s}\) stands for lower bound and rand enumerate random number amid 0 and 1.

Hence build density and volume with each object provided by,

$${G}_{s}=rand$$
(4)
$${K}_{s}=rand$$
(5)

where, ramd express D-dimensional vector randomly generated amid 0 and 1.

Thereafter, commence acceleration of sth object and it is stated by,

$${M}_{s}={L}_{s}+rand\times \left({O}_{s}-{L}_{s}\right)$$
(6)

Enumerate starting population and pick object with better value of fitness. Allocate \({\varepsilon }_{best},{G}_{best},{K}_{best}\) and \({M}_{best}\).

  • Step 2) Produce fitness with error

Fitness is derived for getting premium solution in order to deal with optimization issues and it is notified by,

$${\rm E}=\frac{1}{\vartheta }{\sum_{{\rm N}=1}^{\vartheta }\left[{\Pi }_{\rm N}^{*}-\Pi \right]}^{2}$$
(7)

Thus, \(\vartheta\) delineates total instances attained, \(\Pi\) is generated outcome from LadderNet, and \({\Pi }_{\rm N}^{*}\) states predicted result.

  • Step 3) Update volume and density

The object density \(s\) for iteration \(\Delta + 1\) is provided by,

$${G}_{s}^{\Delta +1}={G}_{s}^{\Delta }+rand\times \left({G}_{best}-{G}_{s}^{\Delta }\right)$$
(8)

where, \({G}_{best}\) states density linked with finest object.

The object volume s considering iteration \(\Delta +1\) is provided by,

$${K}_{s}^{\Delta +1}={K}_{s}^{\Delta }+rand\times \left({K}_{best}-{K}_{s}^{\Delta }\right)$$
(9)

where, \({K}_{best}\) stands for volume linked with finest object.

  • Step 4) Enumerate density factor and transfer operator

In beginning stage, the collision amongst objects happens and after specific time, the object attempts to acquire state of equilibrium. It is implemented using transfer operator and is stated by,

$$I={\text{exp}}\left(\frac{\Delta -{\Delta }_{{\text{max}}}}{{\Delta }_{{\text{max}}}}\right)$$
(10)

where, \(\Delta\) stands for present iteration and \({\Delta }_{{\text{max}}}\) delineate elevated iteration.

The density decreasing factor aids to establish local and global search and it reduces with respect to time and is stated by,

$${w}^{\Delta +1}={\text{exp}}\left(\frac{{\Delta }_{{\text{max}}}-\Delta }{{\Delta }_{{\text{max}}}}\right)-\left(\frac{\Delta }{{\Delta }_{{\text{max}}}}\right)$$
(11)

  • Step 5) Estimate three phases

Here, three phases, named exploration, exploitation and acceleration normalization is performed and each phase is illustrated herewith.

  1. a)

    Exploration phase

Considering \(I\le 0.5\), the collision amongst objects happens and pick arbitrary material \({\ell}\) and acceleration update using object for iteration \(\Delta +1\) is modelled by,

$${M}_{s}^{\Delta +1}=\frac{{G}_{{\ell}}+{K}_{{\ell}}+{K}_{{\ell}}}{{G}_{s}^{\Delta +1}\times {K}_{s}^{\Delta +1}}$$
(12)

where, \({G}_{s}^{\Delta +1},{K}_{s}^{\Delta +1}\) and \({M}_{s}^{\Delta +1}\) density, volume and acceleration considering object s using iteration \(\Delta +1\), and \({G}_{{\ell}},{K}_{{\ell}}\) and \({M}_{{\ell}}\) density, volume and acceleration of random material \({\ell}\).

  1. b)

    Exploitation phase

Considering \(I>0.5\), the there exists no collision amid objects and acceleration update with iteration \(\varpi +1\) is stated by,

$${M}_{s}^{\Delta +1}=\frac{{G}_{best}+{K}_{best}+{K}_{best}}{{G}_{s}^{\Delta +1}\times {K}_{s}^{\Delta +1}}$$
(13)

Here, \({M}_{best}\) denote acceleration linked to finest object.

  1. c)

    Normalize acceleration

Normalization of acceleration is accomplished to produce alteration in percentage and is notified by,

$${M}_{s-norm}^{\Delta +1}=\tau \times \frac{{M}_{s}^{\Delta +1}-{\text{min}}\left(M\right)}{{\text{max}}\left(M\right)-{\text{min}}\left(M\right)}+\kappa a$$
(14)

Here, \(\tau\) and \(\kappa\) represents range of normalization and it is fixed to 0.9 and 0.1.

  • Step 6) Position update

Considering \(I\le 0.5\), then sth object position for subsequent iteration \(\Delta +1\) is modelled by,

$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times \left({\tau }_{rand}-{\tau }_{s}^{\Delta }\right)$$
(15)

Here, \({J}_{1}\) express constant equal to 2.

$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}$$
(16)

From FRO [11], the update expression is modelled by,

$${\tau }_{c+1}^{s}={\tau }_{c}^{s}+\chi Levy\times \left({k}_{c}-{\tau }_{c}^{s}\right)\times \frac{0.37}{\sqrt[5]{\alpha }}$$
(17)

Assume \({\tau }_{c+1}^{s}={\tau }_{c}^{s}\), \({\tau }_{c}^{s}={\tau }_{s}^{\Delta }\) and \({k}_{c}={k}_{s}\),

$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }+\chi Levy\times \left({k}_{s}-{\tau }_{s}^{\Delta }\right)\times \frac{0.37}{\sqrt[5]{\alpha }}$$
(18)
$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }+\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}-\chi Levy\times {\tau }_{s}^{\Delta }\times \frac{0.37}{\sqrt[5]{\alpha }}$$
(19)
$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)+\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}$$
(20)
$${\tau }_{s}^{\Delta +1}={\tau }_{s}^{\Delta }\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)+\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}$$
(21)
$${\tau }_{s}^{\Delta }=\frac{{\tau }_{s}^{\Delta +1}-\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}$$
(22)

Substitute expression (22) in expression (16),

$${\tau }_{s}^{\Delta +1}=\left[\frac{{\tau }_{s}^{\Delta +1}-\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}$$
(23)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}=\frac{{\tau }_{s}^{\Delta +1}\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)\\ +{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(24)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}-\frac{{\tau }_{s}^{\Delta +1}\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}=-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)\\ +{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(25)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}\left[1-\frac{\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]=-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)\\ +{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(26)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}\left[\frac{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}-1+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]=-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\\ \left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(27)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}\left[\frac{\left(-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]=-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\\ \left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(28)
$$\begin{array}{c}{\tau }_{s}^{\Delta +1}=\left[\frac{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}{\left(-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)}\right]-\left[\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}}{\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right)}\right]\\ \left(1-{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\right)+{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}\end{array}$$
(29)

The final AFRO update is notified by,

$${\tau }_{s}^{\Delta +1}=\frac{\chi Levy\times {k}_{s}\times \frac{0.37}{\sqrt[5]{\alpha }}\left({J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w-1\right)+\left(1-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}\right){J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times {\tau }_{rand}}{{J}_{1}\times rand\times {M}_{s-norm}^{\Delta +1}\times w-\chi Levy\times \frac{0.37}{\sqrt[5]{\alpha }}}$$
(30)

Considering I > 0.5, then update of object position is stated by,

$${\tau }_{s}^{\Delta +1}={\tau }_{best}^{\Delta }+P\times {J}_{2}\times rand\times {M}_{s-norm}^{\Delta +1}\times w\times \left(\varpi \times {\tau }_{best}-{\tau }_{s}^{\Delta }\right)$$
(31)

where, \({J}_{2}\) denote constant equal to 6, \(\varpi\) varies with time and P signify flag.

The parameter \(\tau\) is stated by,

$$\varpi ={J}_{3}\times I$$
(32)

The flag to alter direction of motion is notated as,

$$P=\left\{\begin{array}{c}+1,\;If\;Y\leq0.5\\-1,\;If\;Y>0.5\end{array}\right.$$
(33)

Here, parameter Y is manipulated by,

$$Y=2\times rand-J_4$$
(34)

  • Step 7) Estimate premium solution

Specify each object with fitness and provide best solution generated till now.

  • Step 8) Termination

The above steps are repeated until elevated iteration is acquired. Table 1 illustrates pseudo code of AFRO.

Table 1 Pseudo code of AFRO
Full size table

3.4 Identification of nodule with grid-based technique

Once lung lobes A are segmented, the nodule detection from the lung lobes is performed by employing grid-based technique. It effectively discovered whether nodule region is impacted or not. Thus, grid-based technique is employed on segmented lung for dividing the segmented regions to different blocks termed as grids. For making evaluation simple and to lessen time of computation, it is needed to split segmented image into different blocks. Hence, the nodule area is detected through segmented image and is denoted by N.

3.5 Extraction of features

The identified nodules N are provided to mine feature. The extraction of effective features aids in transforming the raw data into beneficial features which are operated by preserving data through the original data. It offers enhanced outcomes and aids to acquire improved efficiency. Here, the texture, statistical and GLCM features are being extracted to detect the lung cancer.

  • Texture features

Some of the texture features are defined below.

  1. a)

    HoG

HOG [32] is modeled by dividing a frame area into tiny cells of spatial image, which is known as a block. By employing each cell, the acknowledgment of a local 1-D histogram of gradient alterations through the cell pixels is computed. Thus, gradients are discovered for horizontal and vertical movements. The Q signified gradient magnitudes and \(\phi\) represents directions computed as,

$$Q=\sqrt{{Q}_{\psi }^{2}+{Q}_{\upsilon }^{2}}$$
(35)
$$\phi ={{\text{tan}}}^{-1}\left(\frac{{Q}_{\psi }}{{Q}_{\upsilon }}\right)$$
(36)

Thus, the feature image produced by adapting HOG is signified by \({\eta }_{1}\).

  1. b)

    SLIF

SLIF [34] is adapted to solve problems which happen at certain time to match image. This feature is enumerated by extracting image details using feature point. The SLIF process is described below,

  • SLIF’s orb web sampling pattern

The orb web model is represented as,

$${V}^{q}=\left\{{W}_{x,y}^{q}\left|x=\mathrm{1,2},...,X;y=\mathrm{1,2},...,Y\right.\right\}$$
(37)

Here, \({W}_{x,y}^{q}\) stands for position of web node. Furthermore, it is essential to transmit orb web structure position to match features. The location of each node \({\left(x,y\right)}^{q}\) in shifted orb web structure \({V}^{q}\) is provided as,

$${W}_{x,y}^{q}=\left({p}_{q}+\frac{y\cdot {\text{cos}}\left(\frac{2\pi x}{X}\right)}{Y},{a}_{q}+\frac{y\cdot {\text{cos}}\left(\frac{2\pi x}{X}\right)}{Y}\right)$$
(38)

Here, \({p}_{q}\) and \({a}_{q}\) enumerate coordinates of horizontal and vertical image using qth point. The orb web sampling structure is defined by,

$${W}_{x,y}^{q}=\left({p}_{q}+\frac{\mathfrak{I}\cdot {\varpi }_{q}\cdot y\cdot {\text{cos}}\left(\frac{2\pi x}{X}\right)}{Y},{a}_{q}+\frac{\mathfrak{I}\cdot {\varpi }_{q}\cdot y\cdot {\text{cos}}\left(\frac{2\pi x}{X}\right)}{Y}\right)$$
(39)

where, \({\varpi }_{q}\) stands for feature scale considering key-point, and \(\mathfrak{I}\) stands for positive scalar factor.

The unification of details considering each keypoints orientation into orb web is modelled as,

$${Q}_{x,y}^{q}=\left({p}_{q}+\frac{\mathfrak{I}\cdot {\varpi }_{q}\cdot y\cdot {\text{cos}}\left(\frac{2\pi x}{X}+{\varphi }_{j}\right)}{Y},{a}_{q}+\frac{\mathfrak{I}\cdot {\varpi }_{q}\cdot y\cdot {\text{cos}}\left(\frac{2\pi x}{X}+{\varphi }_{q}\right)}{Y}\right)$$
(40)

where, \({\varphi }_{q}\) defines orientation of key point.

  • Assignation of web weights: To avert aliasing impact, the data of pixel intensity considering each node position \({\mathfrak{R}}_{\beta ,\chi }^{e}\).

$${\rm H}_{x,y}^{q}=V\left({\mathfrak{R}}_{x,y}^{q}\right)\times {\rm T}_{z}^{q}\left(\phi \right)$$
(41)

Here,

$${\rm T}_{z}^{q}\left(\phi \right)={\rm B}_{z}^{q}\left(\phi \right)+{\rm M}_{z}^{q}\left(\phi \right)$$
(42)

Here, \(V\left({\mathfrak{R}}_{x,y}^{q}\right)\) symbolize data of pixel intensity extracted through image V at particular web node position \({\mathfrak{R}}_{x,y}^{q}\), \({\rm B}_{z}^{q}\left(\phi \right)\) denote Gaussian kernel, and \({\rm M}_{z}^{q}\left(\phi \right)\) symbolize linear kernel, and kernels size is modelled as,

$${S}_{k}=\frac{{\rm P}\cdot {\phi }_{q}\cdot y}{2\cdot X}$$
(43)

where, P express feature scale, and \(\phi\) denote standard deviation which is equal to 0.5.

  1. c)

    Orientation allocation

It is utilized for determining angle of orientation for each determined interest point in certain image. The 2-D directional influence vector for each web node is provided as,

$${\overrightarrow{J}}_{x,y}^{q}=\left[{\nabla }_{x,y}^{q}\cdot {\text{cos}}\left(\frac{2\pi x}{X}\right),{\Upsilon}_{o,z}^{j}\cdot {\text{sin}}\left(\frac{2\pi x}{X}\right)\right]$$
(44)

where, \({\nabla }_{x,y}^{q}\) delineates web weight associated to web node. Thereafter, the vectorial sum is computed by,

$${\overrightarrow{J}}^{q}=\sum_{x=1}^{X}\sum_{y=1}^{Y}{\overrightarrow{J}}_{x,y}^{q}$$
(45)

  • iv) SLIF’s descriptor structure

At last, the built feature vector \(\varpi\) considering interest point is provided by,

$${\varpi }_{j}=\left[{s}_{\mathrm{1,1}}^{q},{s}_{\mathrm{2,1}}^{q},...,{s}_{X,1}^{q},{s}_{\mathrm{1,1}}^{q},{s}_{\mathrm{2,1}}^{q},...,{s}_{X,2}^{q},...,{s}_{1,Y}^{q},{s}_{2,Y}^{q},...,{s}_{XY}^{q}\right]$$
(46)

Here, values of \({s}_{x,y}^{q}\) express 8 bit binary array. The pair of web weight values \({\rm H}_{x,y}\) and \({\rm H}_{x+p,y+q}\) is modelled by,

$$s_{x+p,y+q}^q=\left\{\begin{array}{lc}1&if\;\mathrm H_{x,y}^q>\mathrm H_{x+p,y+q}^q\\0&otherwise\end{array}\right.$$
(47)

The SLIF feature is notified by \({\eta }_{2}\).

  1. d)

    SLBT

In modeling the texture, the projects of SLBT [33] depicts shape-free patches and the LBP feature histogram with eigen face space are considered. Hence, SLBT mine shape modeling's disparity of global shape, modeling of texture and local shape and variation of texture more efficiently, and thus SLBT is notated by \({\eta }_{3}\).

  1. e)

    SURF

SURF [27, 28] indicates a local feature descriptor, and is widely employed to handle functions, like categorization, detection of object and 3D reconstruction. The identifier discovers finest points spotted in an image, whereas descriptor illustrates interesting features. It is expressed by,

$${\mathfrak R}_2\left(\aleph,\gamma\right)=\left\{\begin{array}{lc}{\mathrm A}_\beta\left(\aleph,\gamma\right)&D_\beta\left(\aleph,\gamma\right)\\{\mathrm A}_\varpi\left(\aleph,\gamma\right)&D_\varpi\left(\aleph,\gamma\right)\end{array}\right.$$
(48)

Here, \({D}_{\beta }\left(\aleph ,\gamma \right),{D}_{\varpi }\left(\aleph ,\gamma \right)\) signify Gaussian second order derivative convolution. The SURF feature result is notated by \({\eta }_{4}\).

  • Statistical features

It is extensively used statistical notion in data science. It is adapted as an initial stats model which one can adapt while exposing a database and includes features like mean, variance and so on. It is easy to grasp and implement in code. It is used to manage computational tasks considering definite aspect.

  1. a)

    Mean

It is known as arithmetic addition of a value set. It is also described as all pixels intensity average to total pixel count and formulated by,

$${\eta }_{5}=\sum_{u=0}^{T-1}u*Z(u)$$
(49)

wherein, \(Z(u)\) states uth occurrence probability, total grey level count is modelled as T, image grey level is denoted as \(\varepsilon (o,\partial )\), total gray level is represented by u, and mean is signified as \({\eta }_{5}\)

  1. b)

    Variance

It is known as dispersion metric. It expresses average squared distance amongst mean and each image pixel and is notated by,

$${\eta }_{6}={\sum_{u=0}^{T-1}(u-{\eta }_{5})}^{2}*Z(u)$$
(50)

Here, \({\eta }_{5}\) designate mean value, and \({\eta }_{6}\) states variance.

  1. c)

    Standard derivation

It is known as square root of variance and is notified as \({\eta }_{7}\).

  1. d)

    Kurtosis

It is known as relative flatness or distribution peakedness with respect to normal distribution and notated as,

$${\eta }_{8}={\hslash }^{-4}\left[\sum_{u=0}^{T-1}{(u-\hslash )}^{4}*Z(u)\right]$$
(51)

Here, kurtosis is notated as \({\eta }_{8}\).

  1. e)

    Skewness

It expresses asymmetry metric of a data or distribution concerning mean. The skewness value are either positive or negative and is notated by,

$${\eta }_{9}={\hslash }^{-3}\left[\sum_{u-0}^{T-1}{(u-\hslash )}^{3}*Z(u)\right]$$
(52)

Thus, skewness is notified as \({\eta }_{9}\).

  • GLCM features

GLCM feature operates based on co-occurrence event with adjacent gray level and count of image. It is computed using square matrix based on regions of interest with various gray levels. Thus, five GLCM features are mined and are described as follows.

  1. a)

    Energy

The energy [31] describes degree of pixel using repetitions pairs. It refers evaluation of disorder with texture using an image. When pixels are correlated, then value of energy seems to be high. The energy feature is formulated by,

$${\eta }_{10}={\sum }_{g,h}U{\left(g,h\right)}^{2}$$
(53)

where, g, h signify coefficients and elements coordinates.

  1. b)

    Entropy

Entropy [31] evaluates degree of uniformity amongst pixel in an image and randomness is used to exemplify image. It is formulated by,

$${\eta }_{11}=\sum_{g=0}^{{\aleph }_{\kappa }-1}\sum_{h=0}^{{\aleph }_{\kappa }-1}U\left(g,h\right){\text{log}}\left(U\left(g,h\right)\right)$$
(54)

Here, \(\aleph\) imply total gray levels count.

  1. c)

    Dissimilarity

Dissimilarity [31] evaluates distance amongst pairs of object with interesting areas. It evaluates difference amidst mean of gray levels with distribution of image. It is notated by,

$${\eta }_{12}={\sum }_{g}{\sum }_{h}\left|g-h\right|U\left(g,h\right)$$
(55)
  1. d)

    Autocorrelation

Autocorrelation [31] defines roughness evaluation and fitness depicts image as texture feature. It is associated using dimension of texture primal and texture fitness. It exposes peaks and valleys. The Autocorrelation considering image E(B,X) is defined as,

$${\eta }_{13}=\aleph \left({\rm B},{\rm X}\right)=\frac{{\sum }_{\delta =0}^{\aleph }{\sum }_{{\rm H}=0}^{\aleph }{\rm I}\left({\rm E},{\rm H}\right){\rm I}\left({\rm E}+{\rm B},{\rm H}+{\rm X}\right)}{{\sum }_{{\rm E}=0}^{{\aleph }_{\kappa -1}}{\sum }_{{\rm H}=0}^{{\aleph }_{\kappa -1}}{I}^{2}\left({\rm E},{\rm H}\right)}$$
(56)

The produced feature vector is notated as,

$$\eta =\left\{{\eta }_{1},{\eta }_{2},\cdots ,{\eta }_{13}\right\}$$
(57)

3.6 Detection of lung cancer using AFRO-based DBN

Thus, feature vector \(\eta\) is provided to lung cancer detection phase. The CT is utilized for determining pulmonary nodules as it aids to detect thorax tissue. The lung cancer cause elevated incidence and high rate of deaths and hence it is essential to mechanize tumor identification. The discovery of pulmonary module outcomes in earlier lung cancer detection and thus enhances the rate of survival. With lung CT images, the lung cancer detection is considered and it is performed using AFRO-based DBN. The DBN overview and AFRO steps are illustrated below.

  1. a)

    DBN overview

DBN [25, 29] indicates a component of deep model. Here, DBN is effectual and is used for various tools. It is pre-trained using unsupervised samples that aid to execute improved efficacy under various attacks. In addition, it helps to solve unsupervised samples and reduces dimensionality of features. Thus, each DBN layer is constructed using restricted Boltzmann machine (RBM) and trained concurrently. The outcome of prior layer's are utilized as successive input layer. Figure 3 endows DBN preview, such that x1 indicate input layer, and x2, x3 symbolize hidden layers and y1, y2, y3 explores output layer.

Fig. 3
figure 3

DBN overview

Full size image

The layers of network are adapted as logistic regression (LR). During pre-training, the layers are trained of RBM are used one after other. While performing DBN training, weight update is executed with AFRO:

RBM contains i visible cells and j hidden cells, \({p}_{o}\) express oth visible unit, \({U}_{t}\) states tth hidden unit. The update of weight are executed as,

$${l}_{m}(o+1)={l}_{m}(o)+S\frac{\mu {\text{log}}(\partial (\varphi ))}{\mu {l}_{m}}$$
(58)

where, \(\partial (\varphi )\) signify probability of visible vector, and is provided by,

$$\partial (\varphi )=\frac{1}{\xi }\sum {e}^{-\iota ({\rm T},{\rm O})}$$
(59)

where, \(\xi\) signify partition function and \(\iota ({\rm T},{\rm O})\) states energy function. The sensible joint distribution of input value K and hidden layer \(U(v)\) is modelled as,

$$\partial \left(K,{U}_{1},\dots ,{U}_{W}\right)=\left(\prod_{q=0}^{W-2}\partial \left({U}_{q}/{U}_{q+1}\right)\right).\partial \left({U}_{W-1},{U}_{W}\right)$$
(60)

Here, \({\rm K}={Y}_{0},\)  \(\partial ({U}_{q+1}|{U}_{q})\) symbolize conditional visible units with q layer. \(\nabla ({U}_{W-1},{U}_{W})\) states visible-hidden joint division. The input data produced with first layer is featured as second layer's data. Two ways exist, \(\partial ({U}_{1}=1|{U}_{0})\) or \(\partial ({U}_{1}|{U}_{0})\) and is chosen to be dynamic averagely.

  1. b)

    Train DBN with AFRO

The DBN training is executed with AFRO, but the fitness considered here is mean square error which is formulated as,

(61)

Thus, ƛ delineates total instances attained, v is generated outcome from LadderNet, and \({\nu }_{\varsigma }^{*}\) states predicted result.

4 Results and discussion

Ability of AFRO-based DBN is inspected using various types of measures with training data values and K-fold values in its x-axis.

4.1 Experimental set-up

AFRO-based DBN is implemented in Python.

4.2 Dataset description

The analysis is performed with LIDC-IDRI dataset [26]. It comprises lung cancer screening and of CT scans with annotated lesions. It is accessible through web and used for training, development and evaluation of lung cancer and its diagnosis. It contains 1018 cases wherein each subject involves image through a clinical thoracic CT scan.

4.3 Experimental results

Figure 4 represents the experimental outcomes of the proposed method. Here, the CT image is acquired from LIDC-IDRI dataset and undergoes pre-processing with wiener filter for denoising. After that, lung lobe segments are obtained with LadderNet, where network is optimally tuned using devised AFRO. After segmenting lung lobe, the nodule detection is conducted utilizing grid based method. Following to this step, appropriate features like Spider Local Image Feature (SLIF), Shape Local Binary Texture (SLBT), SURF, Histogram of Gradients (HOG), Grey Level Co-occurrence Matrix (GLCM) features and statistical features are extracted. The lung cancer classification is performed using DBN and the hyper parameters of DBN are tuned with devised AFRO. Here, the Input image of lungs is displayed in Fig. 4a). The pre-processed image using Wiener filter is exposed in Fig. 4b). The segmented image with LadderNet is exposed in Fig. 4c). The Nodule image with grid based scheme is displayed in Fig. 4d). The HoG image is exposed in Fig. 4e). The SIFT image is explicated in Fig. 4f). The SURF image is displayed in Fig. 4g).

Fig. 4
figure 4

Experimental outcomes of a Input image b pre-processed image c Segmented image d Nodule image e HoG image f SIFT image g SURF image

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4.4 Evaluation measures

The fitness of AFRO-based DBN is evaluated by examining it with former schemes and are explicated below,

  1. a)

    Precision

It represents propinquity of various data happening amongst each other to detect lung cancer disease and it is formulated as,

$$pn=\frac{{\Delta }_{u}}{{\Delta }_{u}+{\Pi }_{u}}$$
(62)

Here, \({\Delta }_{u}\) endow true positive, \({\Pi }_{u}\) represent false positive.

  1. b)

    F-measure

It describes harmonic mean of recall and precision and is notated as,

$$\mathfrak{I}m=2*\frac{pn*\zeta }{pn+\zeta }$$
(63)

Here, pn and \(\zeta\) states precision and recall.

  1. c)

    Accuracy:

It describes how close available group of observation exist to its true value and is manipulated as,

$$Ay=\frac{{\Delta }_{n}+{\Delta }_{u}}{{\Delta }_{u}+{\Delta }_{n}+{\Pi }_{n}+{\Pi }_{u}}$$
(64)

wherein, \({\Delta }_{u}\) states true positive, \({\Delta }_{n}\) articulates true negative, \({\Pi }_{u}\) delegate false positive, and \({\Pi }_{n}\) delineates false negative.

4.5 Performance analysis

4.5.1 Analysis by varying iterations

Figure 5 elaborates AFRO-based DBN performance evaluation using different metrics. The accuracy graphs are explained in Fig. 5a). With 90% data of training, the accuracy measured for AFRO-based DBN with iteration 20 is 0.877, 40 is 0.898, 60 is 0.908, 80 is 0.926, and 100 is 0.947. The F-measure graphs are illustrated in Fig. 5b). Considering 90% data of training, the highest F-measure of 0.917 is measured for AFRO-based DBN with iteration = 100 while F-measure for iteration 20, 40, 60, 80 are 0.848, 0.866, 0.877, 0.888. The precision graphs are examined in Fig. 5c). The utmost precision of 0.926 for AFRO-based DBN with iteration 100 and 0.869 for iteration 20, 0.888 for iteration 40, 0.904 for iteration 60, 0.860 for iteration 80 are computed with 90% data of training.

Fig. 5
figure 5

AFRO-based DBN performance evaluation varying iterations using a Accuracy b F-measure c Precision

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4.5.2 Analysis by varying population size

Figure 6 elaborates AFRO-based DBN performance evaluation using different metrics. The accuracy graphs are explained in Fig. 6a). With 90% data of training, the accuracy measured for AFRO-based DBN with population size 5 is 0.927, 10 is 0.931, 15 is 0.936, and 20 is 0.947. The F-measure graphs are illustrated in Fig. 6b). Considering 90% data of training, the highest F-measure of 0.917 is measured for AFRO-based DBN with population size = 20 while F-measure for population size 5, 10, 15, are 0.899, 0.907, 0.911. The precision graphs are examined in Fig. 6c). The utmost precision of 0.926 for AFRO-based DBN with population size 20 and 0.909 for population size 5, 0.914 for population size 10, 0.915 for population size 15, are computed with 90% data of training.

Fig. 6
figure 6

AFRO-based DBN performance evaluation varying population size using a Accuracy b F-measure c Precision

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4.6 Algorithm methods

The algorithms utilized for evaluation are Coot + DBN [29, 35], CSA + DBN [29, 36], FRA + DBN [11, 29], AOA + DBN [10, 29], and AFRO + DBN.

4.7 Algorithmic analysis

Figure 7 discovers algorithm estimate with size of population. The accuracy graphs are illustrated in Fig. 7a). When population size = 20, the accuracy measured for Coot + DBN is 0.890, CSA + DBN is 0.895, FRA + DBN is 0.907, AOA + DBN is 0.927, and AFRO + DBN is 0.947. The performance improvement of the proposed method is 6.01%, and 5.49% higher than the existing methods, such as Coot + DBN, and CSA + DBN. The F-measure graphs are examined in Fig. 7b). Using population size = 20, the chief F-measure of 0.917 is measured for AFRO + DBN while F-measure of Coot + DBN, CSA + DBN, FRA + DBN, AOA + DBN are 0.875, 0.886, 0.890, 0.897. The performance improvement of the proposed method is 2.94%, and 2.18% higher than the existing methods, such as FRA + DBN, and AOA + DBN. The precision graphs are explained in Fig. 7c). When size of population tends to 20, the equivalent precision noted is 0.874 for Coot + DBN, 0.875 for CSA + DBN, 0.887 for FRA + DBN, 0.898 for AOA + DBN, and 0.926 for AFRO + DBN. The performance improvement of the proposed method is 5.61%, and 5.50% higher than the existing methods, such as Coot + DBN, and CSA + DBN.

Fig. 7
figure 7

Algorithm estimation graphs using a Accuracy b F-measure c Precision

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4.8 Comparative methods

The strategies considered for estimation are CNN [1], SE-ResNeXt [2], 3D-CNN [4], WSLnO-based ShCNN [7], and AFRO-based DBN.

4.9 Comparative analysis

The methods evaluation with training data and K-fold are illustrated below.

  1. a)

    Training data valuation

Figure 8 explains technique evaluation with training data in its x-axis. The accuracy estimate is explained in Fig. 8a). Assuming training data = 90, the accuracy measured for CNN is 0.865, SE-ResNeXt is 0.887, 3D-CNN is 0.898, WSLnO-based ShCNN is 0.909, and AFRO-based DBN is 0.947. The performance improvement of the proposed method is 8.65%, and 6.33% higher than the existing methods, such as CNN, and SE-ResNeXt. The F-measure graphs are illustrated in Fig. 8b). With training data = 90, the F-measure noted is 0.826 for CNN, 0.837 for SE-ResNeXt, 0.848 for 3D-CNN, 0.877 for WSLnO-based ShCNN, and 0.917 for AFRO-based DBN. The performance improvement of the proposed method is 7.52%, and 4.36% higher than the existing methods, such as 3D-CNN, and WSLnO-based ShCNN. The precision graphs are examined in Fig. 8c). By means of training data = 90, the supreme precision of 0.926 is obtained for AFRO-based DBN while precision noted by CNN, SE-ResNeXt, 3D-CNN, WSLnO-based ShCNN are 0.848, 0.865, 0.887, 0.899. The performance improvement of the proposed method is 8.42%, and 6.58% higher than the existing methods, such as CNN, and SE-ResNeXt.

  1. b)

    K-fold estimate

Fig. 8
figure 8

Training data estimation graphs using a Accuracy b F-measure c Precision

Full size image

Figure 9 explains technique assessment with different kinds of metrics. The accuracy graphs are illustrated in Fig. 9a). When K-fold tends to be 8, the accuracy noted for CNN is 0.876, SE-ResNeXt is 0.898, 3D-CNN is 0.909, WSLnO-based ShCNN is 0.916, and AFRO-based DBN is 0.958. The performance improvement of the proposed method is 5.11%, and 4.38% higher than the existing methods, such as 3D-CNN, and WSLnO-based ShCNN. The F-measure graphs are depicted in Fig. 9b). Assuming K-fold = 8, the highest F-measure of 0.926 is noted for AFRO-based DBN while F-measure of CNN, SE-ResNeXt, 3D-CNN, WSLnO-based ShCNN are 0.837, 0.847, 0.858, 0.887. The performance improvement of the proposed method is 9.61%, and 8.53% higher than the existing methods, such as CNN, and SE-ResNeXt. The precision graphs are portrayed in Fig. 9c). The precision of 0.854 for CNN, 0.877 for SE-ResNeXt, 0.898 for 3D-CNN, 0.908 for WSLnO-based ShCNN, and 0.936 for AFRO-based DBN is observed when K-fold = 8. The performance improvement of the proposed method is 4.05%, and 2.99% higher than the existing methods, such as 3D-CNN, and WSLnO-based ShCNN.

Fig. 9
figure 9

K-fold estimation graphs using a Accuracy b F-measure c Precision

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4.10 Segmentation accuracy evaluation

Figure 10 produces segmentation accuracy estimation graph. Using 60% training data, the subsequent segmentation accuracy noted by PSP-Net + AFRO is 0.848, K-Net + AFRO is 0.865, PSI-Net + AFRO is 0.877, Segnet + AFRO is 0.887, and LadderNet- AFRO is 0.908.

Fig. 10
figure 10

Segmentation accuracy estimation graph

Full size image

The performance improvement of the proposed method is 6.60%, and 4.73% higher than the existing methods, such as, PSP-Net + AFRO, and K-Net + AFRO. The subsequent segmentation accuracy of 0.948 for LadderNet- AFRO while segmentation accuracy of PSP-Net + AFRO, K-Net + AFRO, PSI-Net + AFRO, Segnet + AFRO are 0.877, 0.898, 0.908, 0.916 assuming 90% training data. The performance improvement of the proposed method is 4.21%, and 3.37% higher than the existing methods, such as, PSI-Net + AFRO, and Segnet + AFRO.

4.11 Comparative discussion

The comparative evaluation using different algorithms and schemes are illustrated below.

  1. a)

    Algorithm evaluation

Table 2 discusses the comparative evaluation with different measures. The highest accuracy of 94.7% is noted by AFRO + DBN, while accuracy of remaining methods are 89%, 89.5%, 90.7%, and 92.7%. The augmented precision of 91.7% is noted by AFRO + DBN, while precision of remaining methods are 87.5%, 88.6%, 89%, and 89.7%. The F-measure of 92.6% is computed by AFRO + DBN while the F-measure of remaining methods are 87.4%, 87.5%, 88.7%, and 89.8%.

Table 2 Comparative evaluation
Full size table
  1. b)

    Technique evaluation

Table 3 discusses the comparative evaluation using various metrics. With training data, the supreme accuracy of 94.7%, precision of 91.7% and F-measure of 92.6% is computed by AFRO + DBN. In terms of K-fold, the highest accuracy of 95.8%, precision of 92.6% and F-measure of 93.6% is enumerated by AFRO + DBN.

Table 3 Comparative analysis
Full size table

5 Conclusion

Lung cancer is known as a serious disorder and can take the life of peoples thereby increasing the mortality rates worldwide. Thus, timely treatment and diagnosis can help to save the life of many patients. Despite, CT scan is finest imaging model in medical domain, it is complex for doctors to understand and detect the cancer through CT. Thus, the treatment can be useful for doctors to discover the cancerous cells precisely. The aim is to design a productive framework for lung cancer detection with AFRO-DBN. Initially, CT image undergoes image processing to make the raw image fit for further processing using wiener filter. After that, segmentation of lung lobe is implemented to segment the lung lobe regions using LadderNet, and tuned with AFRO. After lung lobe segmentation, the nodule detection is conducted utilizing grid based method. Following to this step, appropriate features are extracted. Then lung cancer is classified which is implemented with DBN and training of DBN is optimally fine tuned using devised AFRO. The AFRO-DBN outperformed with accuracy of 95.8%, F-measure of 92.6% and precision of 93.6%. The developed method gets accuracy of 95.8%, which helps to diagnose the lung cancer accurately and also, it helps in the reduction of mortality rates. Moreover, the developed method is useful in various applications, such as healthcare and medical applications so on. Future works include consideration of image augmentation to prevent overfitting. When a model learns the training data too well and is unable to generalize to new data, overfitting occurs. Image augmentation gives the new data to learn, which helps prevent overfitting.