RETRACTED ARTICLE: Banana disease diagnosis using computer vision and machine learning methods

Abstract

As it is observed that the banana production is plagued by numerous disease conditions and inflicting large loss to the poor farmers. By using modern technology of image processing and soft computing techniques, these may be known at the sooner stage and appropriate precautions may be taken to avoid more injury and thus increase in healthy production. In this research work used identified the banana diseases in sooner stage. Through the pre-processing technique, image is input to urge standardization and soft coring filter is completed to get rid of the noise. Then colour, shape and texture feature are completed for feature extraction, followed by classification techniques. During these classification techniques, two algorithms are used, that’s the Adaptive Neuro-Fuzzy Inference System and case-based reasoning. Then fuzzy logic is used for making the decision. The proposed system analysis was done using the Receiver Operating Characteristics (ROC) curve. The analysis shows Adaptive Neuro-Fuzzy Inference System is best than the case-based reasoning algorithm.

1 Introduction

As per the 2010 Food and Agriculture Organization world agriculture statistics India is that the world’s largest producer of the many recent fruits like banana, mango, guava, papaya, lemon and vegetables like chickpea, okra and milk, major spices like chili pepper, ginger, fibrous crops like jute, staples like millets and aperient seed as claimed by Behera et al. (2020). India is that the second largest producer of wheat and rice, the world’s major food staples.

India is presently the world’s second or third largest producer of many dry fruits, agriculture-based textile raw materials, roots and tuber crops, pulses, farmed fish, eggs, coconut, sugarcane and diverse vegetables. India hierarchic within the world’s five largest turn outs of over eightieth of agricultural produce things, as well as several money crops like occasional and cotton, in 2010. India is one among the world’s five largest producers of eutherian mammal and poultry meat, with one among the quickest growth rates, as of 2011.

Amit et al. (2015) developed a system for remote monitoring of the banana ripening process. The camera was placed on a remote area and the captured banana pictures were sent to the system through microcontroller with GSM module. Collected pictures were fed into the MATLAB software tool, and also the ripening stage of banana was identified based on the RGB values. The accuracy of the projected system was 90%.

Butola et al. (2015) developed a system to supervise the banana ripening stages based on colour feature extraction technique. The high-resolution camera was accustomed to capture the banana image pictures were sent to the system through the Aurdino board and gsm module in a serial manner. Captured image was sent to the MATLAB software tool, to supervise the assorted stages of banana ripening. The accuracy of the proposed system was 93%.

Ochoa et al. (2016) proposed a system to observe the symptoms of black Sigatoka banana disease. The disease was caused by the fungus microsphacrella fijiensis pictures were captured by victimization VIS–NIR camera optical spectrograph this kind of camera is employed to capture the banana leaf pictures on constant speed and camera’s frame rate and to reduce the motion blur and increase the resolution and spatial dimension and to enhance the hyperspectral image quality victimization de-noising technique. The spectral profile extraction was accustomed to extract the black Sigatoka component values. The accuracy of the projected system was 92%.

Karthick et al. (2016) developed hardware to detect and prevent the banana streak virus disease exploitation embedded UNIX board. The image camera was interfaced with the embedded UNIX board, accustomed capture the leaf of the banana plant. The economic intensity algorithm was accustomed to detect the presence of banana streak virus pixel value and healthy pixel value based on the edge value. Recovery methodology was accustomed to send the report back to the farmers supported the output of the economic intensity algorithm. The accuracy of the proposed system was 89% higher than alternative existing methods.

Yossie Cahya Permata (2017) proposed a new carotenoid profile map system exploitation hyperspectral image and to measure the distribution of total carotenoids using the profile map technique. The input image was captured by a hyperspectral camera and group light source. The camera was interfaced with a laptop computer. Partial least square regression methodology was accustomed rework every pixel value of spatial into total carotenoids value 30 samples were employed in this technique, root means sq error price was 0.7934 and the correlation co economical price was 0.94.

Siregar et al. (2017) developed a prediction system to live the banana wet content exploitation visual NIR imaging. The input image was captured with the assistance of a hyperspectral camera and group light. It absolutely was being interfaced with the non-public laptop. Feature extraction was computed exploitation principal element analysis (PCA) to live the wet contents of banana exploitation regression methodology and Partial Least sq. Regression (PLSR). The proposed system used 45 raja banana as an information set the root means square error value of the proposed system was 0.25% and the correlation coefficient was 0.96.

Saputor et al. (2017) proposed a system to predict the banana fruit quality exploitation hyper spectral imaging based on wavelength choice. The hyperspectral camera was accustomed to collect the input hyperspectral image. Peak and valley detection methodology was accustomed to realize the best band. CARS method was accustomed select the simplest wavelength based on standard deviation value; the PLSR registration method was used to create the training data from the CARS method output value and to select the actual wavelength based on the square relative error value and correlation co-efficient value. The performance of the proposed system was measured exploitation square of the relative error of 0.09 and also the correlation co-efficient was 0.97.

Liao et al. (2018) proposed a system to sight the black Sigatoka malady in banana exploitation Unmanned Aerial Vehicle (UAV). The camera was mounted on the UAV that is employed to capture the shut vary hyperspectral image. It includes the close to an infrared and visual spectrum. The machine learning methodology was employed in the sooner detection of banana black Sigatoka diseases and additionally classify the healthy and unhealthy plant. This proposed system was accustomed to determine the banana Sigatoka malady in its earlier stage and then to scale back the harm of the crop and additionally prevents the spreading of the disease. The accuracy of the proposed system was 92%.

Amara et al. (2017) developed a replacement approach to classifying banana leaf diseases. Image information set might be collected from the banana cultivation field so as to scale back the illumination, totally different resolution, advanced background, cause and size exploitation image process techniques like image size and grayscale conversion methodology. Essential options were extracted exploitation colour feature extraction methodology and texture feature extraction method. LeNet design primarily based typical neural network was accustomed classify the input image information set into totally different banana leaf diseases. The accuracy of the proposed system was 95% higher than the different typical strategies.

Liao et al. (2018) proposed a system to sight the banana diseases exploitation fusion of high-resolution RGB image and shut vary hyperspectral image. The hyperspectral image was captured by the exploitation spectrograph and high-resolution camera. Bilateral filter was accustomed to transfer the felt structure of high-resolution RGB image into low resolution hyper spectral image. The fusion approach was the mix of each hyper spectral image and high-resolution RGB image and additionally determine the pathologic space. The accuracy of the proposed system was 95%.

2 Field survey

Banana is the plant of the Musa, family of the liliopsid family. It’s cultivated primarily for food and additionally used for the assembly of fiber utilized in the textile trade, decorative purpose. The scientific names of banana are Musa acuminate, Musabalbisiana or hybrids of Musa acuminate and musabalbisiana.

On June 2017–April 2018, a survey was conducted among a thousand farmers at numerous districts in Tamilnadu. The most purpose of this survey was accustomed to identifying the issues of banana cultivating farmers. Farmers address the most issues were the detection of diseases in an earlier stage, unaware of recent designation methodology and do not comprehend symptoms of diseases. We tend to had collected the sector survey from the banana cultivating farmers of the subsequent districts as shown in Table 1.

Table 1 Banana varieties

Each district we had collected the random sample from the 100 farmers and sample images as shown Table 2. From this survey we were taken the following diseases for observation.

• Panama wilt

• Leaf spot

• Anthracrose

• Cigar end tip root

• Crown root

• Virus disease

Table 2 Banana field survey sample images

2.1 Panama wilt

Banana panama wilt is a type of soil-borne fungal disease that damages the plant’s body through roots. The primary reason is soil that has been badly damaged. Some of the damaged plant’s symptoms are yellowing of reduced leaves, blades of leaves and petioles. The leaves are hanging around the pseudo and wither (Table 3, Fig. 1).

Table 3 Banana panama wilt images

Fig. 1

Data collection graph for banana panama wilt disease

From this graph, the three districts are affected by panama wilt disease in the banana. (1) Sivangangai, (2) Madurai and (3) Virudunagar can be faced with this disease by about 18 percent of farmers. The following remarks on the Panamawilt banana disease can happen during the rainy season and spread very quickly in water. Remaining district farmers can also experience banana wilt disease from panama around 8 to 3%.

2.2 Leaf spot

Banana leaf spot is one of the banana crop’s severe illnesses. Light yellowish spots on the leaves are the symptom observed at the original point of the illness. In some instances, the color turns to dark brown and finally the gray of the place turn indicating its dead. A lot of places occur sometimes resulting in big sections of the leaf being killed (Table 4, Fig. 2).

Table 4 Banana leaf spot images

Fig. 2

Data collection graph for banana Leaf spot disease

From this graph, the three districts are largely affected by the Banana Lessaf spot disease (1) Tripur, (2) Salem, and (3) Namakkal may face this illness by about 11 percent of farmers. The following remarks on the banana Leafspot disease can be produced during the winter season and distributed very quickly in water and air. Remaining district farmers can also experience banana Leafspot disease by around 9%.

2.3 Anthracnose

The fungus colletotrichummusae causes banana anthracnose. It is a very hazardous disease because it can spread readily through the wind, water, and other agents. The outcome of this illness is blacking in the fruit and shrinking the fruit. This damages the manufacturing as a whole (Table 5, Fig. 3).

Table 5 Banana anthracnose images

Fig. 3

Data collection graph for banana anthracnose disease

The most important information from this chart are as follows. The four counties have a major impact on the banana anthracnose illness (1) Coimbatore, (2) Tripur, (3) Salem, (4) Namakkal may experience this illness for about 15% of farmers. The following remarks can be produced about the anthracnose banana disease that happens during the sunny season and is spreading very quickly in air and water. Remaining district farmers around 7% farmers can also face this problem.

2.4 Cigar end tip root

Banana cigar end root is a disease that has lately emerged. Verticillium theobromae influences the roots and this influences the fruit’s fingers, the finger turns to ash gray and the get lost, they are dismissed on the market, resulting in the farmer’s loss (Table 6, Fig. 4).

Table 6 Banana cigar end tip root images

Fig. 4

Data collection graph for banana Cigar end tip root disease

From this chart, the root illness of the banana end cigar has a major impact on the four constituencies (1) Sivangangai, (2) Virudunagar, (3) Theni, (4) Dindugal may experience this illness for about 12% of farmers. The following remarks can be produced on the root disease of the banana cigar end tip during the autumn season and its spread very quickly in the air.

2.5 Crown rot

The fruit is also affected by banana crown rot disease. The skin’s blackening ultimately infects the pulp and therefore the rots of the fruit. The crown is first impacted leading to fruit disease (Table 7, Fig. 5).

Table 7 Banana crown rot disease images

Fig. 5

Data collection graph for banana crown root disease

From this graph, the five districts are mainly affected by root disease in the banana crown. (1) Madurai, (2) Virudunagar, (3) Theni, (4) Dindugal, (5) Coimbatore can be faced with this disease by around 15% of farmers. The following remarks can be produced on the root disease of the banana crown occurring during the rainy season and spreading it very quickly in air and water.

2.6 Virus disease

Stretching the leaves in yellow and even in black owing to necrotic in some instances. Due to bugs, infected materials and also saccharicoccus sacchari, the disease is primarily present in these crops. The culture of shoot tips can not withstand this assault. Banana virus disease also impacts the fruit, stem, and leaf. Banana streak virus affects the blackening of the stem and leaves. Young vein leaves impacted by the mosaic disease of the banana brack. Cucumber Mosaic Virus can affect banana flowers (Table 8, Fig. 6).

Table 8 Banana virus disease images

Fig. 6

Data collection graph for banana virus disease

From this graph, the three districts are significantly affected by the banana virus disease (1) Tripur, (2) Salem, (3) Namakkal may experience this disease by about 26% of farmers. During the rainy season, the following remarks can be produced about the banana virus disease and its spread very quickly in water. Remaining farmers in the district can also experience banana virus by about 2–5%.

3 Methodology

Using image processing and Adaptive Neuro Fuzzy Inference System (ANFIS), rice, banana and sugarcane diseases are diagnosed in this research work. Input images from the agricultural field have been collected, pre-processing method has been used to remove noise owing to environmental circumstances. Extraction of the feature was used to obtain data from the pre-processed output picture from the diseased region. Fuzzy Inference System Artificial Neural Network has been used to diagnose rice, banana, and sugarcane diseases. The Operating Characteristic Receiver (ROC) curve was used to assess the efficiency of the suggested scheme (Fig. 7).

Fig. 7

Block diagram for computer aided diagnosis of agricultural diseases

In this research work the following modules are used as shown in Fig. (4.1).

• 1. Input image

• 2. Preprocessing

• 3. Feature extraction

• 4. CBR, ANFIS

• 5. ROC curve

• 6. Result analysis

3.1 Input image

The picture is generally stored in matrix format; each matrix element is called as a pixel. It is categorized into two kinds to capture the input picture using a digital camera.

• 1. Testing image

• 2. Training image

Training pictures are gathered from Coimbatore University of Agriculture at Tamilnadu, Madurai, and multiple institutes of rice studies in India. Testing pictures from rice-growing farming areas are gathered. We use 1000 pictures for input picture in this research work. For training data set, 700 pictures are used and 300 pictures are used to test information. Blast, brown spot, bacterial leaf blight, sheath rot, leaf scald and stem root input picture as shown in the Table 9.

Table 9 Input images of banana diseases

3.2 Preprocessing

To extract the noise from the input picture, pre-processing is used. Standardization technique and smooth coring filter technique are used in this research. Use the following Eq. (1) to convert the RGB picture into a gray scale picture (Fig. 8).

Fig. 8

Soft coring filter

$$I\left(x,y,z\right)=\frac{(Gx+Gy+Gz)}{3}$$

(1)

Soft technique of coring filtering is a non-linear technique of filtering. It is used to extract from the normalized picture the unwanted data. Using the Gaussian high pass filter, the visually representative is obtained based on the function of the high pass filter kernel that can be performed in the frequency domain. Gaussian high-pass filter uses sliding windowing method to quickly convert Fourier into two-dimensional convolutions. The standardized output picture is carried to the high-pass filter and the high-pass filter output is added with the α) (smooth coring feature as shown in Fig. 8). Table shows the yield (10)

$$P\left(x,y\right)=Ih\left(x,y\right)+\alpha \left(I\left(x,y\right)\right)$$

(2)

where $P\left(x,y\right)- Preprocessed output image$, $Ih\left(x,y\right) is the Highpass fiter output image$

$$Ih\left(x,y\right)=I\left(x,y\right)-Z\left({e}^{jwx},{e}^{jwy}\right)$$

(3)

where $Z({e}^{jwx},{e}^{jwy})$ is the high pass filter co-efficient, $\alpha (I\left(x,y\right))$ is the soft coring function

$$\alpha \left(I\left(x,y\right)\right)=m .I\left(x,y\right)(1-{e}^{\left|\frac{I\left(x,y\right)}{\tau }\right|}$$

(4)

where m, τ is the random variables ranges between 0 and 1.

To remove the noise from the input picture, the Gaussian high pass filter is used. For the input image line and edge data, the soft coring kernel function is used. Soft coring filtering method is used for two-dimensional pictures and in comparison with median filtering technique, data loss is much lower. Two step pre-processing technique adds to enhancing image quality, decreasing processing time, componensing illumination, decreasing shaded background and maintaining contrast and brightness of the picture (Table 10).

Table 10 Pre processing output of banana disease

3.3 Feature extraction

Image stores pixel values, some characteristics are shown in each pixel value. Colour, texture and shape are some general characteristics of the picture.

3.4 Colour feature extraction

The feature is obtained using the pre-processed image’s colour, shape and texture characteristics. Segment by threshold technique is used to obtain the colour characteristic. Table 11 shows the threshold value for each illness.

Table 11 Threshold value for banana diseases

Colour feature is extracted by using the following Eq. (5)

$$\begin{aligned}E\left(x,y\right)=\left\{\begin{array}{ll}o & if\; P\left(x,y\right)<T1\\ 1 & if\; T1\le P(x,y)\le T2\\ 0 & if\; P\left(x,y\right)>T2\end{array}\right.\end{aligned}$$

(5)

where T1 is the lower threshold value, T2 is the upper threshold value.

Feature extraction output image is shown Table 12.

Table 12 Colour feature extraction output of banana diseases

3.5 Shape features extraction

Extraction of the shape function is used to obtain the single object from more objects in the picture. This technique is used to obtain the object’s specific shape from the drawing of the image (Table 13).

• Identifiability

• Translation, rotation and scale invariance

• Affine invariance

• Noise resistance

• Occulation, invariance

• Statistically independent

• Reliability

Table 13 Shape feature extraction output of banana diseases

In this research work, we used the technique of carrying edge detection for the extraction of shape features. This technique is used to detect a broad variety of edges of objects in an image.

• 1. Smoothing

• 2. Finding gradients

• 3. Non maximum suppression

• 4. Double thresholding

• 5. Edge tracking by hysteresis

Step 1 Smoothing

The input picture is drawn from a digital camera and includes some noise owing to sunlight leading to picture blurring. Gaussian filter can be used in smoothing technique to remove the noise and the noise can be removed.

$$Is=I*Gf$$

(6)

To find out the smoothed image using the Eq. (6) where Is is the smoothed filter output, I is the input image, Gf is the kernel function of Gaussian filter

The kernel function of the Gaussian filter is calculated using Eq. (7) with standard deviation σ = 1.4

$$Gf= \frac{1}{59}\left[\begin{array}{ccccc}2& 4& 5& 4& 2\\ 4& 9& 12& 9& 4\\ 5& 12& 15& 12& 5\\ 4& 9& 12& 9& 4\\ 2& 4& 5& 4& 2\end{array}\right]$$

(7)

Step 2 Finding gradients

If the gradients of the smoothed picture have a high magnitude, the objects edges of the picture should be labeled. In this technique we discover corners of objects based on the intensity of the grayscale off the picture modifications most, then the gradients of the picture are determined. Using sobel-operator, the gradient value of each pixel is determined. To find the approximate gradient in X and Y direction as shown in Eqs. (8) and (9)

$$FGX=\left[\begin{array}{ccc}-1& 0& 1\\ -2& 0& 2\\ -1& 0& 1\end{array}\right]$$

(8)

$$FGY=\left[\begin{array}{ccc}1& 2& 1\\ 0& 0& 0\\ -1& -2& -1\end{array}\right]$$

(9)

The gradient magnitude value can be calculated using Euclidean distance measurement as shown in Eq. (10).

$$\left|G\right|=\sqrt{{GX}^{2}+{GY}^{2}}$$

(10)

The gradient magnitude can be determined using Manhattan distance measurement as shown in Eq. (11)

$$\left|G\right|=\left|GX\right|+\left|GY\right|$$

(11)

where GX is the gradients in X-direction, GY is the gradients in Y-direction

The direction of the edges of object can be determined using the Eq. (12)

$${\theta }_{g}=arctan\left(\frac{\left|GY\right|}{\left|GX\right|}\right)$$

(12)

Step 3 Non maximum suppression

Local maximum image values can be used to create an object’s edge. This step is used to convert the object’s blurred edges into the object’s sharp edges. It will be considered in the gradient as the local maximum and the remaining gradient values will be detected.

• 1. Round the direction of the gradient ${\theta }_{g}$ to the closest 45°, using eight link the neighbourhood.

• 2. Compare edge power using gradient magnitude value of present pixels with gradient magnitude values of positive and negative gradient direction. If the gradient direction is increased, compare with present pixels to boost and decrease direction.

• 3. If the present pixel value’s gradient magnitude value is big, maintain the edge resistance value, and otherwise delete (remove) the pixel value.

Step 4 Double thresholding

Thresholding technique can determine the remaining prospective edges of the item. Some object edges may be missed due, for example, to noise or colour variation owing to rough surfaces. The canny edge detection technique is testing, dual thresholding technique. It has two limit value, one of which is greater and the other of which is smaller. If the edge pixel value is greater than the threshold value marked as a powerful edge pixel value. If the edge pixel values are smaller than (weaker than) the reduced threshold value is withdrawn (deleted), if the edge pixel values between the two threshold values are labelled as a soft edge in an image object. The image’s strong edges are depicted by white colour and the image’s fragile edges are represented by gray colour.

Step 5 Edge tracking by hysteresis

The final edges are calculated by removing all the edges not connected to the strong edges. All the strong edges are considered to be the final edges of an object and the weak edges are those connected to the strong edges, can be considered as the final edges of an object, the remaining weak edges can be suppressed. Edge training can be implemented using Binary Large OBject (BLOB) analysis.

3.6 Texture feature extraction

Texture is described as the picture description based on pixel scale, regularity and directionality-texture is depicted by the intensities of the neighbouring pixel values to disregard the present pixel value type. The extraction of texture features is used to classify the picture implementation, and segmentation of the picture implementation, ground inspection, orientation of the surface and shape. To extract the texture feature the following four methods are used:

• 1. Statistical methods

• 2. Structural methods

• 3. Model based methods

• 4. Transform based methods

3.7 Co-occurrences matrix based features

The second order gray level probability distribution of an picture can be evaluated in pairs at a moment using the gray level values of pixels. The following occurrence matrix characteristics can be evaluated.

• 1. Inertia (contrast)

• 2. Energy

• 3. Entropy

3.8 Contrast

The element difference moment of order 2 is called as comparison. If maximum values appear in the main diagonal of the matrix of co-occurrence, it has comparatively minimum values.

$$Contrast=\sum_{g1}\sum_{g2}{\left(g1-g2\right)}^{2 }{C}_{g1 g2}$$

(13)

where g1 is the grey level value of pixel location at (x, y), g2 is the grey level value of pixel location at (x, Dx, y, Dy), Dx, Dy is the displacement vector of x and y, C is the co-occurrence matrix

3.9 Energy

The calculation of the energy value using the following Eq. (14)

$$ENERGY=\sum_{g1}\sum_{g2}{{C}_{g1 g2}}^{2}$$

(14)

If all values in the matrix of co-occurrence are equal then the maximum energy value.

3.10 Entropy

Entropy is used to calculate the gray-level picture data. The following Eq. (15) is used to calculate the entropy value,

$$ENTROPY=-\sum_{g1}\sum_{g2}{C}_{g1g2}{log}_{2}{C}_{g1g2}$$

(15)

The effect of texture extraction method is shown in Table 14.

Table 14 Texture feature extraction output of banana diseases

3.11 Case based reasoning

Case based reasoning (CBR) is a method of prediction used in apps for disease diagnosis. CBR is distinct from the Perceptron algorithm, the information from the current database will be taken. The information from the databases of the previous year are used as the forecast operation input information. Case-based reasoning is an uncontrolled technique of teaching. The case-based reasoning is categorized as being as normal and abnormal in two groups. The abnormal class is further categorized as initial, very small, small, medium, high, very high, six classes. Since the threshold values of each class are taken from the current input database, as shown in Table 15, the output information is anticipated to be very accurate (Table 16).

Table 15 Threshold value for banana panama wilt, leaf spot and crown rot diseases

Table 16 Threshold value for banana anthracnose, cigar-end tip rot and virus disease

Fuzzy logic is one of the many-valued logic techniques based on classification, where the classification outputs are provided in degrees of reality. The truth value ranges from 0 to 1. In crisp logic, the findings are either binary values 1 or 0. Fuzzy logic provides outcomes based on truth values of 0, 0.25, 0.5 and 1. If the rule is used for an abnormal class.

• If the abnormal class > 60 then it is suggested to remove the agricultural plant from agricultural field.

• If the abnormal class > 20–40 then suggested to treat the agricultural plant with natural fertilizers.

Output of CBR for banana disease is shown in Fig. 9

Fig. 9

CBR output for banana disease

3.12 Adaptive Neuro Fuzzy Inference System (ANFIS)

ANFIS is a monitored technique of teaching. It is a mixture of the technique of neural network and fuzzy logic. In this study job we use the neural network feed forward as a neural network technique and the fuzzy logic method takagi-sugeno fuzzy model. Figure 10 shows the architecture of ANFIS. Six rules are used in the blurred model of takagi-sugeno. ANFIS is used to fix issues associated with illness detection. Identification of the illness is conducted by a mixture of the least square technique and the gradient process of back propagation with a hybrid learning rule. ANFIS network consists of nodes with each layer’s requirements. The rules of ANFIS IF/THEN can build a network realization. ANFIS network neurons perform the same function in each layer of neurons. Table 4.27–4.29 shows the output of the ANFIS system

Fig. 10

ANFIS Architecture

Rule 1 = If a is A1, b is B1, c is C1, d is D1, e is E1 and f is F1 then

$${\text{O}}/{\text{P1}} = {\text{ p1a}} + {\text{q1a}} + {\text{r1a}} + {\text{s1a}} + {\text{t1a}} + {\text{u1a}} + {\text{v1}}$$

(16)

Rule 2 = If a is A2, b is B2, c is C2, d is D2, e is E2 and f is F2 then

$${\text{O}}/{\text{P2}} = {\text{ p2b}} + {\text{q2b}} + {\text{r2b}} + {\text{s2b}} + {\text{t2b}} + {\text{u2b}} + {\text{v2}}$$

(17)

Rule 3 = If a is A3, b is B3, c is C3, d is D3, e is E3 and f is F3 then

$${\text{O}}/{\text{P3}} = {\text{ p3c}} + {\text{q3c}} + {\text{r3c}} + {\text{s3c}} + {\text{t3c}} + {\text{u3c}} + {\text{v3}}$$

(18)

Rule 4 = If a is A4, b is B4, c is C4, d is D4, e is E4 and f is F4 then

$${\text{O}}/{\text{P4}} = {\text{ p4d}} + {\text{q4d}} + {\text{r4d}} + {\text{s4d}} + {\text{t4d}} + {\text{u4d}} + {\text{v4}}$$

(19)

Rule 5 = If a is A5, b is B5, c is C5, d is D5, e is E5 and f is F5 then

$${\text{O}}/{\text{P5}} = {\text{ p5e}} + {\text{q5e}} + {\text{r5e}} + {\text{s5e}} + {\text{t5e}} + {\text{u5e}} + {\text{v5}}$$

(20)

Rule 6 = If a is A6, b is B6, c is C6, d is D6, e is E6 and f is F6 then

$${\text{O}}/{\text{P6}} = {\text{ p6f}} + {\text{q6f}} + {\text{r6f}} + {\text{s6f}} + {\text{t6f}} + {\text{u6f}} + {\text{v6}}$$

(21)

where A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, B5, B6, C1, C2, C3, C4, C5, C6, D1, D2, D3, D4, D5, D6, E1, E2, E3, E4, E5, E6, F1, F2, F3, F4, F5, F6 is the membership function. p1, q1, r1, s1, t1, u1, v1, p2, q2, r2, s2, t2, u2, v2, p3, q3, r3, s3, t3, u3, v3, p4, q4, r4, s4, t4, u4, v4, p5, q5, r5, s5, t5, u5, v5, p6, q6, r6, s6, t6, u6, v6 is the linear parameters.

3.13 Layer 1

We use the Gaussian membership function Eq. (22) with a generalized bell-shaped membership function Eq. (23) in this research work.

$$\mu Ai\left(a\right)=exp\left[\frac{-{\left(a-zi\right)}^{2}}{{\left(2ai\right)}^{2}}\right]$$

(22)

$$\mu Bi\left(b\right)=exp\left[\frac{-{\left(b-zi\right)}^{2}}{{\left(2bi\right)}^{2}}\right]$$

(23)

$$\mu Ci\left(c\right)=exp\left[\frac{-{\left(c-zi\right)}^{2}}{{\left(2ci\right)}^{2}}\right]$$

(24)

$$\mu Di\left(d\right)=exp\left[\frac{-{\left(d-zi\right)}^{2}}{{\left(2di\right)}^{2}}\right]$$

(25)

$$\mu Ei\left(e\right)=exp\left[\frac{-{\left(e-zi\right)}^{2}}{{\left(2ei\right)}^{2}}\right]$$

(26)

$$\mu Fi\left(f\right)=exp\left[\frac{-{\left(f-zi\right)}^{2}}{{\left(2fi\right)}^{2}}\right]$$

(27)

$$layer1 \, ouput (i)= \mu Ai\left(a\right), \quad i=1,2,3,4,5,6$$

(28)

$$layer1 \, ouput (i)= \mu Bi\left(b\right), \quad i=1,2,3,4,5,6$$

(29)

$$layer1 \, ouput (i)= \mu Ci\left(c\right), \quad i=1,2,3,4,5,6$$

(30)

$$layer1\, ouput (i)= \mu Di\left(d\right), \quad i=1,2,3,4,5,6$$

(31)

$$layer1\, ouput (i)= \mu Ei\left(e\right), \quad i=1,2,3,4,5,6$$

(32)

$$layer1 \, ouput (i)= \mu Fi\left(f\right), \quad i=1,2,3,4,5,6$$

(33)

$\mu Ai\left(a\right)$ is the degree of fuzzy set membership function, Ai- Bi is the fuzzy set

3.14 Layer 2

Each node is adaptive in this layer, it is labelled as π. This layer’s output is the first layer’s multiplying outcome as shown in Fig. 9 of ANFIS architecture. Using OR logic, the target value is calculated in this research.

$$layer2\; output \left(i\right)=FS\left(i\right)= \mu Ai\left(a\right)*\mu Bi\left(b\right)* \mu Ci\left(c\right)*\mu Di\left(d\right)*\mu Ei\left(e\right)*\mu Fi\left(f\right) \quad i=1,2,3,4,5,6$$

(34)

where FS (i) is the firing strength of the each node.

3.15 Layer 3

Each node is adaptive in this layer, it is labelled as N. This layer’s yield is the proportion of each node’s firing power to the sum of all the firing power of the nodes.

$$layer3 \,output\left(i\right)=\overline{FS(i)}= \frac{FS(i)}{\sum FS(i)}$$

(35)

3.16 Layer 4

Each node is adaptive in this layer. This layer’s yield is calculated using the Eq. (36)

$$layer4 \,ouput \left(i\right)= \overline{-}{FS\left(i\right)} K\left(i\right)= \stackrel{-}{FS\left(i\right)} (pia+qib+ric+sid+tie+uif+vi)$$

(36)

where $\overline{FS\left(i\right)}\, is \,the \,Output\, of\, layer 3$, $K\left(i\right)=pia+qib+ric+sid+tie+uif+vi\, is \,the\, parameter\, of\, the\, node.$

3.17 Layer 5

There is a single node in this layer, it is non-adaptive and it is displayed as a single node. The output of this layer is the summation of the prior output layer values, calculated using the following Eq. (37) (Fig. 11)

Fig. 11

ANFIS output for banana disease

$$layer5 output \left(i\right)= \sum_{i}\stackrel{-}{FS\left(i\right)} K(i)$$

(37)

$$=\frac{\sum_{i}FS\left(i\right)K(i) }{\sum_{i}Fs(i)}$$

3.18 ROC curve

Receiver operating characteristics (ROC) curve is a graph representing the system output of the classifier for distinct threshold value in order to plot the graph between sensitivity and specificity. Sensitivity is also referred to as true positive rate (tpr), detection and recall of probability. Also called specificity as false positive rate (fpr), likelihood of false alarm and falling out.

Receiver operating features (ROC) curve is a model for diagnosing example grouping between distinct classes. The output of the diagnosis is the ongoing (true) output. The classifier may be categorized by threshold value with distinct limits between distinct classes. The binary classification scheme has two classes, one is labelled as positive (P) and the other as an unusual class of cells and is labelled as adverse (N). There are four possible results for the binary classification

• 1. True Positive (TP)

• 2. False Positive (FP)

• 3. True Negative (TN)

• 4. False Negative (FN)

The ROC curve is developed by plotting the sensitivity cumulative distribution function in the y-axis and the specificity function in the x-axis cumulative distribution. Using Eqs. (38) and (39) to evaluate sensitivity and specificity values based on real positive and negative values. Based on the following criteria, calculate the true positive and negative values as shown in Table 17.

Table 17 True Positive and Negative values

$$Senstivity=\frac{TP}{(TP+FN)}$$

(38)

$$Specificity=\frac{TN}{TN+FP}$$

(39)

where TP is the True Positive, TN is the True Negative, FN is the False Negative, FP is the False Positive.

Analysis of the ROC curve is a better instrument for selecting optimization model, class allocation, disease diagnosis and decision making. ROC curve is used in a variety of applications such as biometrics, machine learning, natural hazard forecasting, radiology, performance model evaluation and medicine. Based on the diagonal splits in the ROC region, ROC curve assessment is used to diagnose banana illnesses. The ROC curve above the diagonal reflects the disease-affected picture and the ROC curve below the diagonal represents the disease-free picture. The output of the ROC curve depends primarily on the threshold value; we need to select the suitable threshold value to enhance the efficiency of the ROC curve evaluation. Figure 12 shows the ROC curve. If the curve in the plot is above the slope line of 45°, this implies that the system output is nice and outstanding or the system output is bad or worse.

Fig. 12

ROC curve for banana disease

3.19 Result analysis

The accuracy value is calculated using the following Eq. (40) for the suggested scheme.

$$Accuracy= \frac{TP+TN}{TP+TN+FP+FN}$$

(40)

where TP is the True Positive, TN is the True Negative, FN is the False Negative, FP is the False Positive

The suggested system’s accuracy value is contrasted with other current systems’ accuracy rate. Tables 18, 19, 20, 21, 22 and 23 shows the comparison table and Figs. 13, 14, 15, 16, 17 and 18 shows the chart.

Table 18 Result comparison for banana panama wilt disease diagnosis

Table 19 Result comparison for banana leaf spot disease diagnosis

Table 20 Result comparison for banana anthracnose disease diagnosis

Table 21 Result comparison for banana cigar-end tip rot disease diagnosis

Table 22 Result comparison for banana crown rot disease diagnosis

Table 23 Result comparison for banana virus disease diagnosis

Fig. 13

Result comparison for banana panama wilt disease diagnosis

Fig. 14

Result comparison for banana leaf spot disease diagnosis

Fig. 15

Result comparison for banana anthracnose disease diagnosis

Fig. 16

Result comparison for banana cigar-end tip rot disease diagnosis

Fig. 17

Result comparison for banana crown rot disease diagnosis

Fig. 18

Result comparison for banana virus disease diagnosis

Compared to MDC, KNN, SVM, and CBR, we inferred from the outcome evaluation graph that the ANFIS technique provides better accuracy, sensitivity, specificity and precision results.

4 Conclusion

Using computer vision and machine learning methods, banana plant diseases are diagnosed. Images from the paddy field were gathered input and the noise was removed using the technique of smooth coring filtering. Computer-assisted detection using segmentation is performed using threshold technique to locate the preprocessed image’s diseased place. Computer-aided diagnosis utilizes ANFIS to classify the diseased cells as original, very tiny, tiny, medium, high and very high classes. Based on the above classification value, the Fuzzy logic technique was used to create the choice. The ROC curve was used to assess the efficiency of the scheme. The system’s suggested accuracy is 97.5%.