Development of the abnormal tissues in the spinal column or spinal cord [1] is a spinal tumor. These abnormal tissues are grown uncontrollably, influencing and controlling normal cell growth. The spinal tumor [2] has two subtitles primary and secondary tumors. The spinal cord originated abnormal cells are primary and cancer spreading from another region to the spine is a secondary or metastatic tumor. The tumors are identified in two ways: region (sacrum, lumbar, thoracic, and cervical) and locations (Intradural-extramedullary,Intramedullary, and Extradural) [3]. The intradural tumors have occurred in the thin region of the spinal cord, around 40% [4]. The intramedullary tumor cells are developed inside the cord obtained from ependymal cells, and 5% in frequency of occurrence [5]. Then, extradural is located outside of the dura, and 55% [6] is the frequency of occurrence. These abnormal tissues encompass the nerve roots. In addition to this, bone metastasis is one of the general bony spinal which experience almost 30% to 70% of patients [7]. The bone spine is vertebral hemangiomas are benign lesions that have rare symptoms like pain. Lower or middle back pain is the most common spinal tumor symptom [8]. The back pain not only occurred by injuries; it also happened physical and stress activities. The main spread from the back to the legs, hips, arms, and feet aggravates over time. Additionally, a spine tumor has several symptoms: muscle weakness, sensation loss, stiff back, neurological symptoms, walking difficulties, sensitivity loss, paralysis, and scoliosis [9].

Once the patient suffers from these symptoms, a medical examination must require to diagnose spinal tumors. The radiological tests [10] include computed tomography (CT scan), X-ray, Magnetic Resonance Imaging (MRI), and Bone Scan. These radiological experiments investigated the inner details that help to identify the tumor types. However, a biopsy [11] needs to diagnosis the unclear findings to maximize the treatment procedures. During the treatment, abnormal tissues or neoplasms are classified by examining spinal canal involvement, soft tissues, and bony. Then, abdomen and lung scanning are suggested to confirm the spine tumors. The manual medical examination consumes more time as well as failure to identify the exact affected area. Therefore, various medical analysis is performed to create an automated computer-aided system for detecting the spine tumor [12]. The computerized system utilizes radiological images to achieve clinical examination using image processing and machine learning techniques. The automated system utilizes the MRI images [13] to detect the spine tumor because the MRI images can identify the tumor position, size, and type with minimum effort. It can discriminate the normal small tissues and tissue density changes and mutations linked with tumors. The main reason for choosing an MRI image is, it does not have any ionizing radiation. The captured MRI images are investigated by segmentation techniques [14] that predict the spine modalities, which helps identify the tumor issues accurately.

The image segmentation process identifies the affected region by minimizing the manual delineation time consumption. The segmenting process locates the density changed tissues by contouring the MRI images. This process identifies the irregular boundaries and tissue interest variation from images effectively. Although, the exact tumor detection is a complex task while overlapping between the normal and abnormal tissues. Then most of the tissues are heterogeneous in tumor size, shape, appearance, and position, so the abnormal tissues [15] affect average tissue growth. The MRI high-resolution images are needs high computational resources and memory to segment the affected region. Different types of methods were introduced to overcome the spinal MRI image segmentation process. The segmentation process decomposes the images into 2D slices processed sequentially while training the MRI image features. The second method decomposes the images into patches that effectively process the volumetric data. However, the traditional techniques are facing difficulties while investigating image topological changes like splitting and merging issues. This causes slow convergence and optimal local problems, which reduces the overall tumor detection accuracy.

Several researchers utilize advanced techniques that include integrating machine learning and swarm intelligent techniques to resolve the convergence issues. The swarm techniques optimize the system’s performance by updating the network parameters, and the global solution is obtained during the updating process. However, the region interest intensity should be identified to improve the recognition accuracy. For this, an intense training set is needed to enhance the system performance with minimum difficulties. Thus the primary intention of this study is to improve the tumor segmentation accuracy with minimum complexity. In this paper, the super-pixel analytics Numerical characteristics Disintegration Model (SNCDM) approach is utilized. The SNCDM approach segments the region based on the super-pixels that minimize the variance between the identified pixels. The vertebral super-pixel is examined that extracts the spinal features based on the super-pixel using the optimized convolution neural networks. This process reduces the maximum inaccurate segmentation problem (MIS) successfully. The effectiveness of the system is evaluated using MATLAB tool with respective performance metrics.

Then the rest of the paper is organized as follows; Section 2 discusses the various researchers’ analyses about spinal tumor detection—Section 3 analyzes the SNCDM method-based spinal tumor detection framework. Section 4 evaluates the effectiveness of the system discussed, and the conclusion is summarized in Section 5.

Alafri 2019 [16] recommended deep neural networks to detect lumbar spinal stenosis from MRI images. The method investigates the boundary of the spine images according to the lumbar spine characteristics. The method uses the network layers that classifies the changes in MRI image. The method maintains the system’s consistency, quality, and confidence while segmenting the affected region. In addition, the Jaccard metric shows that the deep learning approach has highly differentiated the normal and abnormal tissues in MRI images.

Liu, et al., 2019 [17] apply convolution neural network technique to identify and detect the lumbar in MRI images. The method uses the convolute layers that speed up the computation process and store the memory. The method derives the S1 shapes from the spine image, and L1-L5 features are extracted from the round region. The discussed system attains 98.9% of accuracy while detecting Lumbar.

In MRI image analysis, Alam et al., 2019 [18] introduced fuzzy c-means clustering to detect brain tumors. Initially, the image grey level intensity value is estimated, which helps to identify the cluster center. Then fuzzy membership values are computed to group the similar pixel, and this computation is updated according to the membership values. The clustered details are investigated to extract entropy, energy, contrast, homogeneity, dissimilarity, correlation, and entropy value. According to these features, the affected tumor region was detected with minimum time.

Chmelik et al., 2018 [19] detected spinal lesions from 3D CT data by applying the deep convolutional network. Here, convolution networks are utilized to extract the automatic features without depending on the patient’s activities. The extracted features are processed by a random forest approach that classifies the lesion region. Then medial axis transform is applied to improve the overall segmentation approach.

Anter et al., 2019 [20] applying neutrosophic fuzzy c-means and adaptive watershed algorithm to segment the tumor region from CT liver image. The CT images are processed by median filter and histogram equalization approach to eliminate noise and improve the quality of the image. Then, a clustering algorithm is applied to differentiate the image regions. Here, morphological and adaptive threshold values are utilized to determine the segmenting strategies. This process ensures 95% of accuracy and minimum time while segmenting the tumor-affected region.

Punarselvam et al., 2019 [21] analyzed MRI spine images for detecting tumors by applying the soft computing and finite element approaches. The gathered MRI images are continuously analysed to detect the boundary lines. The region boundaries are predicted using different methods like Roberts, Prewitt, Sobel, and canny edges. The predicted edges are smoothened by noise removal techniques that help to improve the overall spine tumor detection accuracy. In addition to this, the method investigating the L4 and L5 lumbar predicts changes in spinal structure effectively.

Jena et al., 2020 [22] recommend a canny, morphological, and Sobel (CMS) edge detection approach to predict image edges. The method uses mathematical operators to identify the edges in the color and greyscale images. The extracted edges are more powerful to derive the affected region. The obtained results are compared with Laplacian of Gaussian, Roberts, Sobel, and Prewitt detection approaches.

Reza et al., 2019 [23] segmenting tumor region from spine MRI images using cascaded convolution neural networks. This paper uses the auto context model that uses the learners to identify the tumor voxel and fine-tuning procedure applied to classify the tumor region. The method predicts the correlation between the features with maximum accuracy and minimum deviations. According to the various researcher’s analyses, the MRI image segmentation is performed by applying different image processing and machine learning techniques. However, the existing approaches consume more time and create a segmentation problem. Therefore, in this paper, Super-pixel analytics Numerical characteristics Disintegration Model (SNCDM) is utilized to improve the overall segmentation accuracy. The detailed working process of this study is illustrated in Section 3.

The SNCDM framework-based spinal tumor prediction process is illustrated in Fig. 1. This system aims to overcome the maximum inaccurate segmentation problem (MIS) by segmenting the relevant region from an MRI image. The images are investigated via super pixels because it helps to identify the pixel characteristics during the segmentation. The super pixel identifies the relationship between the pixels, ensuring the changes in region intensity, position, and size. The successive identification of the affected region solves the maximum error classification while classifying the spinal tumor. The SNCDM framework is illustrated in Fig. 1.

The captured spinal cord images are analyzed by elliptical Fourier descriptors used to get the vertebral shape. This process does not consider the aliasing issues in different resolution images but produces continuous descriptors. The captured spinal cord image d(t) is defined as a vector function that has position points (p1…p2)∀pc which are presented in the two orthonormal axes. Then, the spinal region has axial coordinates (xc,….yc,….zc) and the spinal cord is represented in the mathematical form in Eq. (1)(1) d(t)=dy(t)Vy+dx(t)Vx

The dy(t) and dx(t) values are estimated according to the Fourier descriptor derivation concerning the bx0,by0 defined in Eq. (2). Here Vy=[10]T and Vx=[01]T . The coordinate values are calculated as follows

(2) by0(t)=by02+∑l=1l=∞⁡(bylcos⁡(lωt)+aylsin⁡(lωt))bx0(t)=bx02+∑l=1l=∞⁡(bxlcos⁡(lωt)+axlsin⁡(lωt))}

The descriptor coefficients are derived from the trigonometry computation of angular frequency ( ω) and harmonic number ( l) . These coefficients in both directions help identify the spinal tumor-affected region by solving the maximum error-rate classification problem. Here, the Fourier descriptor coefficients byl , bxl , ayl and axl are computed using Eq. (3)(3) byl=2n∑j=1n⁡yjcos⁡(lωj)ayl=2n∑j=1n⁡yjsin⁡(lωj)bxl=2n∑j=1n⁡xjcos⁡(lωj)axl=2n∑j=1n⁡xjsin⁡(lωj)}

The coefficients byl , bxl , ayl and axl computed from the sampling points n both axial position xj and yj of the j shape model. These sampling points are more used to identify the shape of the spinal cord concerning the (p1…p2)∀pc points. Considering these mathematical computations, the spinal cord region-related descriptors are estimated and simplified as Eq. (4).(4) ((p1…p2)∀pc)=[dy(t)dx(t)]=12[by0bx0]+∑l=1l=∞⁡[bylaylbxlaxl][cos⁡(lωt)sin(lωt)]

From the investigated regions in d(t) , L1-L5 lumbar region is more beneficial to identify the tumor-related spot. The computed (p1…p2)∀pc in discrete cosine components helps to compute the sharp ROC model with maximum frequency. The computed tumor-related coefficients axial points are estimated in Eq. (5).(5) [dy(t)dx(t)]=∑l=1l=∞⁡[bylaylbxlaxl][cos⁡(lωt)sin(lωt)]

The derived coefficients are more valuable to identify the super-pixel (SP) in the spinal image. The SP computation helps to get the features from the images by considering the image boundaries, shapes, and location characteristics. This process converts the images into a sequential representation which helps to identify the exact tumor affected region. Here, the d(t) images are divided into grid cells (small images). The spinal MRI images have a height (H) and width (W) denoted as I=H∗W . Then the I is divided into small images with a size of h∗w . Initially, every grid cell has super pixels (seed) that are more useful for identifying the tumor-affected region. Each pixel in the image (u,v);u=(axl,bxl)andv=(ayl,byl) is mapped with the super pixel SP=(i,j) . The mathematical form of mapping is defined as gs(SP)=gi,j(u,v) . If the mapping process gs(SP)=gi,j(u,v) returns one as value, then the pixel belonging to super-pixel else not. According to the super-pixel, the remaining pixels are grouped that are segmented for further analysis. To reduce the computation complexity, here, SP matching process performed in defined small grids ℵSP . For every computation, almost 9 grid cells are utilized to perform the mapping process. This grid cell-based mapping minimizes the maximum inaccurate segmentation problem (MIS). Therefore, the mapping is written as G∈ZH∗W∗|ℵSP| .

In the image, the (SP) they are computed using the encoder-decoder network design. Here, convolution networks use the input images and give the high-level feature maps are output. The derived feature maps are more helpful in identifying the tumor-affected region performed in the encoder phase. After that, the decoder utilizes the de-convolution layer functionalities to up sample the features from the encoder layer. The max-pooling ReLU activation process is performed during this process to get the output from the feature vector. The last layer uses the softmax activation function to obtain the SP value from the collection of image pixels. This encoder-decoder convolution networks based SP analysis reduces the loss functions and increases the flexibilities. The identified SP value should be preserved because the remaining pixels are grouped according to SP . For every SP , it has a location vector ISP and property vector USP ; then the center SP value is written as CSP=(USP,ISP) . These values are computed using Eq. (6).(6) USP=∑SP:∈ℵP⁡f(P).qsP(P)∑SP:∈ℵP⁡qs(P)ISP=∑P:SP∈ℵP⁡P.qsP(P)∑P:SP∈ℵP⁡qsP(P)}

The super-pixel SP characteristics are computed from the P surrounding pixels ℵP and predicting probability qsP(P) of P associated with SP . The Eq. (6) computation is carried out for the entire pixel involved in the spinal image. For pixels in images have property values that have been reconstructed as,(7) f′(P)=∑SP∈ℵP⁡USP.qsP(P)P′=∑SP∈ℵP⁡ISP.qsP(P)}

According to this computation, the loss function (Eq. (8)) is computed from the property of interest and super-pixel spatially compact.(8) LF=∑P⁡dist(f(P),f′(P))+mS‖P−P‖2′

The loss function ( LF) computed from the distance of pixel properties f(P) Weight balancing of two-term m and super-sampling interval S. The super-pixel extraction process is illustrated in Fig. 2.

With the help of the computed super-pixel, vertebral features are extracted to identify the affected region precisely. For each super-pixel, a set of features are extracted that helps to quantify the pixel orientation, position, and shape. Initially, orientation and position-related features are extracted concerning the super-pixel. The super-pixel centroid value (Cx,Cy) is calculated respective to the image dimension in xj and yj the said Lumbar MRI region is obtained by assigning in the supine position during the scanning time axis. Then, the orientation of the SP should be computed in ӿ axis of the ellipse. The calculated orientation and centroid information identify the availability of the medical images. These two values are analyzed the super-pixels form the recorded vertebral. The orientation and position feature extraction process is illustrated in Fig. 3.

After that, complexity features such as fractal and shape information is retrieved from the MRI spinal image. Generally, the MRI images are obtained from a specific orientation and frame, which helps derive the complexity features with minimum cost. Here, fractal features (Pr2A) are derived in three ways such as superpixel boundaries are measurement is challenging one; therefore, it has been calculated by taking the ratio between the square of the perimeter (Pr2) And area (A) of superpixel. The calculated fractal features are varied from standard spinal image and abnormal spinal image. The standard MRI image fractal value is square, which is varied in odd images. Then shape features like solidity and extent features are extracted from the MRI image. Solidity (SP−AAc) is computed between the ratio of superpixel area (SP-A) and convex hull area (Ac) . The computed solidity values are convex that have the value of 1 else 0. The Extent feature (SP−AAb) value is also calculated by taking the ratio between super-pixel areas bounding box areas ( Ab) . The extent value must be high due to the square shape characteristics of the super-pixel. According to the super-pixel characteristics and feature vectors, tumor affected region is identified effectively. This process identifies the vertebral changes in MRI images. The complexity feature extraction process is illustrated in Fig. 4.

The maximum error-rate classification problem is reduced by applying the effective training process. Consider, the training set has a set of images I={I1,J2,……Ji……JT} . The training images are T training set of MRI images and pre-selected super-pixel SSPij . The superpixel selection procedure selects the vertebral parameter represented as P={P1,P2,….Pj,….PN} . With the help of these parameter settings, a training label set Kij is created for image Ji According to Eq. (9).(9) {SPijk|k∈1,….Kij}=S(Ji,Pj)

For the entire super-pixel relative training process illustrated with respective parameter settings Pj represented as Eq. (10).(10) Sj={SPijk∀k∈1,….Kij;i∈1,…..T}

The successful computation of these training parameters generate S value and the collective training response shown in Eq. (11)(11) S={{s}1,{s}2,….{s}j,….{s}N}

From the derived S={{s}1,{s}2,….{s}j,….{s}}N superpixel, different features (F) are extracted using the training parameter settings Pj . The derived features for superpixel with g dimensionality are defined in Eq. (12).(12) Fj=F(SPijk)∀k∈1,….Kij;i∈1,…..T

Then the collective response of the feature set for the entire super-pixel is denoted as,(13) F={F}1,{F}2,….{{F}j,….{F}N}

The extracted features F are overlapped with the super-pixel, if it has high overlap, then the region is affected, and the value is labeled as 1 else 0. Then labeling Lj for every feature Fj Is represented as Eq. (14).(14) L={{L}1,{L}2,….{L}j,….{L}}N

The derived features and labels are fed into the convolution network that uses the softmax activation function to classify the tumor-affected region effectively. According to the above process, training is performed with minimum computation complexity. The training process requires network parameter updating, which is done by applying the genetic bee optimization algorithm—the network parameter updating working according to the genetic and bee algorithm characteristics. The algorithm uses the onlooker, employee, and scout bees that choose the optimized parameters. The parameters are selected in a specific population space (PS) and the limited number of parameters to select the network parameters. In every layer, the network computes the optimized parameter to compute the output value. The solution is derived using Eq. (15).(15) u=ui,jmin+rand[0,1](ui,jmax−ui,jmin)

Here, a solution is to get from minimum ( ui,jmin) and maximum ( ui,jmax) boundary values with decision variable j and index i. The selected parameter, the objective function, is applied to get the network parameter values. The chosen values are processed by the employee bee that is performed similarly to the food searching behaviour. The estimated values are higher; it has been selected in memory for a further network updating procedure. Then the searching process is increased to the next level to updating searching process.(16) vi,j=ui,j+θi,j(ui,j−uk,j)

The selected solution probability value is computed to identify the best parameter, using Eq. (17).(17) pi=fiti∑j=1PS⁡fitj

This updating process reduces the binary optimization problem and the selected criteria defined in Eq. (18).(18) Ui:i=1,2,….. SN; uij={0ifG(0,1)≤0.51ifG(0,1)>0.5

The choice principles are defined based on the uniformly distributed values of G(0,1) . Thus the practical computation of each pixel, super-pixel, and image complexity features are more helpful to identify the normal and abnormal regions from captured spinal MRI images. The discussed system effectiveness was evaluated using experimental results and discussion.

The effectiveness of introduced Super-pixel analytics Numerical characteristics Disintegration Model (SNCDM) based tumor region segmentation is discussed in this section. This work uses the Lumbar Spine MRI Dataset information to apply the introduced SNCDM framework.

Thus the paper analyzing the Super-pixel analytics Numerical characteristics Disintegration Model (SNCDM) based spinal tumor segmentation process. In this work uses the Lumbar Spine MRI Dataset information which are processed by applying the introduced machine learning approach. The gathered images are investigated in both axis to obtain the Fourier descriptors. The derived descriptors further examined to obtain the super-pixels which match with other pixels presented in the image. Then, different features such as complexity and shape related information extracted to classify the tumor relevant pixels successfully. The segmentation performance improved because of effective training process with respective labels. Then the efficiency of the system evaluated using experimental results in which system attains high recognition accuracy and minimum error rate. In future, the effectiveness of the system improved by applying the optimized segmentation techniques.