1. Introduction

2. Background Definitions

3. Materials and Methods

3.4. Image Processing

As seen in Table 2, each GSLM cell shows how many times the corresponding pair occurs in the original matrix for the defined spatial relationship (d = 1.0°).

Table 2. Matrix GLCM.

Table 2. Matrix GLCM.

3.4.1. Feature Extraction

3.4.1.1. A. Feature description:

Features extracted from the GLCM matrix are as follows:

• Constrast: Intensity level of the difference between the gray pixels of the neighboring pixels.

  $$\mathrm{Contrast}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}{(i-j)}^2·P(i,j)$$

  (2)
• where: i, is j, is
  Correlation: Correlation level of gray levels in GLCM matrix

  $$\mathrm{Correlation}={\displaystyle \frac{{\sum }_{i=0}^{N-1}{\sum }_{j=0}^{N-1}(i-{\mu }_i)(j-{\mu }_j)·P(i,j)}{{\sigma }_i{\sigma }_j}}$$

  (3)
• Energy: Measurement of image homogeneity

  $$\mathrm{Energy}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}{\left(P(i,j)\right)}^2$$

  (4)
• Homogeneity: Measurement of the distance of the elements to the diagonal in the GLCM matrix

  $$\mathrm{Homogeneity}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}{\displaystyle \frac{P(i,j)}{1+|i-j|}}$$

  (5)
• Dissimilarity: Difference between the gray levels concerning the neighboring pixels

  $$\mathrm{Dissimilarity}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}|i-j|·P(i,j)$$

  (6)
• ASM: Uniformity or regularity of the texture

  $$\mathrm{ASM}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}P{(i,j)}^2$$

  (7)
• Entropy:Texture randomness

  $$\mathrm{Entropy}=-\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}P(i,j)logP(i,j)$$

  (8)
• Variance: Dispersion of the gray levels around the mean

  $$\mathrm{Variance}=\sum _{i=0}^{N-1}\sum _{j=0}^{N-1}{(i-\mu )}^2·P(i,j)$$

  (9)

B. Types of variables

In the following Table 3, we can observe the variables used in the proposed processing.

3.4.2. Determining the Number of Clusters in K-Mean Using the Elbow Method

The elbow method involves empirically identifying the best partition of objects by iteratively evaluating the inertia values for different numbers of clusters, aggregating the results, and selecting the optimal result [23].

As can be seen in Figure 10, shows us a graph of a curve, what is sought is to find a point of inflection where the decrease in the sum of least squares within the cluster becomes less pronounced. This point suggests that adding more clusters will not improve data compactness.

Then, using the elbow method we can conclude that the appropriate number of clusters for the analyzed data set is probably 3.

3.4.3. Clustering K-Means

This learning procedure can automatically find the number of clusters without any initialization or parameter selection. We first consider an entropy penalty term to adjust the bias and then create a learning scheme to find the number of groups. In Figure 11 is shown the clustering K-means.

$$\begin{array}{cc}\hfill a_k& ={\displaystyle \frac{{\sum }_{i=1}^n{z}_{ik}{x}_{ij}}{{\sum }_{i=1}^n{z}_{ik}}}\hfill \\ \hfill z_{ik}& =\left\{\begin{array}{cc}1\hfill & \mathrm{if}{∥x_i-a_k∥}^2=\underset{1\le k\le c}{min}{∥x_i-a_k∥}^2\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \end{array}$$

(10)

3.4.4. Clustering Gaussian Mixture

Gaussian mixture models (GMMs) are powerful statistical tools for complex data that do not fit a single distribution. distribution. One of the problems with GMMs is that they require the number of components to be specified in advance [32]. The segmentation of the data into groups with the same characteristics will be carried out by clustering an unsupervised algorithm. In this process, 4 clustering groups are achieved. Figure 12 is shown the Clustering. In Table 4 is shows the Cluster description and number of clusters.

In Table 5 is shown the quantity of data per cluster.

3.4.5. Segmentation

The segmentation in image processing is mainly one of the most important stages in the study since the detection of the object in the image must be obtained, and at present, there are several segmentation methods. The method employed in the research is edge detection by employing the large derivative of the derivative in the ratio of change from one pixel to another as can be seen in Equations (11)–(13) and the second derivative as shown in Equations (14) and (15). These equations represent approximations of the second derivative partial of f with respect to y using finite difference.

$$\nabla f(x,y)=\left[{\displaystyle \frac{\partial f(x,y)}{\partial x}},{\displaystyle \frac{\partial f(x,y)}{\partial y}}\right]$$

(11)

$${\displaystyle \frac{\partial f(x,y)}{\partial x}}\approx f(x+1,y)-f(x,y)$$

(12)

$${\displaystyle \frac{\partial f(x,y)}{\partial y}}\approx f(x,y+1)-f(x,y)$$

(13)

$${\displaystyle \frac{{\partial }^{2}f(x,y)}{\partial x^2}}\approx f(x+1,y)-2f(x,y)+f(x-1,y)$$

(14)

$${\displaystyle \frac{{\partial }^{2}f(x,y)}{\partial y^2}}\approx f(x,y+1)-2f(x,y)+f(x,y-1)$$

(15)

The Canny method works by using grayscale images as input and producing as output or edge images. In its application, the Canny method of edge detection consists of the following steps canny edge detection method, namely smoothing or noise filtering, calculation of gradient magnitude or gradient direction, implementation of non-maximal suppression, set the process of Hysteresis Thresholding. Clustering is a multivariate technique that aims to group similar observations into clusters based on the observed values of several variables for each individual in [27]. However, the detected edges are not evident in the images because of this problem, and 2 additional methods are presented to strengthen the calculated edges called dilation and closure. Figure 13 presents the Canny Segmentation.

Bounding Boxes

The bounding box is a box that will enclose the target of the image in this case is the leaf with the pest which will be marked in a box as shown in Figure 14. The capture of the values obtained are the edges of the segmentation when having a sudden change of sharpness in the binary image where it will go through the image row by row looking for a value greater than zero. To finish, the maximum and minimum values of the box are obtained and drawn in the original image.

4. Results and Discussions

5. Conclusions

Abbreviations

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