# A Reliable Auto-Robust Analysis of Blood Smear Images for Classification of Microcytic Hypochromic Anemia Using Gray Level Matrices and Gabor Feature Bank

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Materials and Methods

#### 3.1. Blood Smear Slide Preparation

#### 3.2. Image Acquisition

#### 3.3. Preprocessing

#### 3.4. Segmentation

#### 3.5. Feature Extraction

#### 3.5.1. Geometric Morphology of Microcytic Hypochromic RBCs

- Area: Area is an important geometrical feature for the detection of microcytes, being small in size compared to other blood cells.
- Circularity: A size-invariant shape descriptor given in Equation (3) which describes a shape to be circular, if the value is closer to 1 and noncircular if the value is closer to 0, where A is Area and P is parameter of a cell.$$Circularity={\displaystyle \frac{4\pi A}{{P}^{2}}}$$
- Rectangularity: It determines the degree of elongation with respect to a rectangle. Equation (4) shows its calculation, where ${A}_{s}$ is area of a shape and ${A}_{r}$ is the area of minimum bounding rectangle.$$Rectangularity={\displaystyle \frac{{A}_{s}}{{A}_{r}}}$$
- Concavity: This property is used to determine how much an object is concave; we applied it on the shapes for identification of the amount of central pallor area occupied in an RBC, given by Equation (5)$$Concavity={\displaystyle \frac{{A}_{c}}{{A}_{H}}}$$
- Convexity: A cell convexity can be determined by Equation (6), which identifies a shape through its boundary convexity.$$Convexity={\displaystyle \frac{{P}_{C}H}{{P}_{C}}}$$

#### 3.5.2. RBC Texture Feature Calculation

- RGB mean and variance of hypochromic microcytic RBCs: The mean values ${\mu}_{r}$, ${\mu}_{g}$, and ${\mu}_{b}$ of pixels of each RBC in R, G, and B, respectively, were calculated in Equation (7).$$\begin{array}{c}\hfill {\mu}_{r}={\displaystyle \frac{1}{N}}\sum _{1}^{N}r(x,y)\\ \hfill {\mu}_{g}={\displaystyle \frac{1}{N}}\sum _{1}^{N}g(x,y)\\ \hfill {\mu}_{b}={\displaystyle \frac{1}{N}}\sum _{1}^{N}b(x,y)\end{array}$$The variances ${\left({\sigma}_{r}\right)}^{2}$, ${\left({\sigma}_{g}\right)}^{2}$, and ${\left({\sigma}_{b}\right)}^{2}$ in the channels R, G, and B, respectively, are calculated in Equation (8)).$$\begin{array}{c}\hfill {\left({\sigma}_{r}\right)}^{2}={\displaystyle \frac{\sum {(X-{\mu}_{r})}^{2}}{N}}\\ \hfill {\left({\sigma}_{g}\right)}^{2}={\displaystyle \frac{\sum {(X-{\mu}_{g})}^{2}}{N}}\\ \hfill {\left({\sigma}_{b}\right)}^{2}={\displaystyle \frac{\sum {(X-{\mu}_{b})}^{2}}{N}}\end{array}$$
- GLCM features of Hypochromic Microcytic RBCs: GLCM is the distribution of cooccurring pixel values defined over an N × N image P at a specific offset, or every P’s element determines the occurrences of a pixel with value of gray level, i, lifted by a certain distance to a pixel with value j. Our next six textural features are GLCM features. The mean of 6 GLCM features were determined for offset values conforming to 0${}^{\circ}$, 45${}^{\circ}$, 90${}^{\circ}$, and 135${}^{\circ}$ consuming 8 gray levels (see Figure 5).Maximum Probability: It measures the strongest response of the cooccurrence matrix. The range of values is [0, 1] as given in Equation (9), where ${P}_{ij}$ is the pixels of gray image.$$P=ma{x}_{ij}\left({P}_{ij}\right)$$Correlation: The degree of correlation of a pixel to its neighbor is determined by the correlation factor of the cooccurrence matrix, ranging from 1 to −1 given by Equation (10). This measure cannot be defined if any of the standard deviation $\sigma $ is 0 for the two existing correlations, perfect positive and perfect negative correlation.$$correlation=\sum _{i,j=1}^{K}{\displaystyle \frac{(i-{m}_{r})(j-{m}_{c}){p}_{\left(ij\right)}}{{\sigma}_{r}{\sigma}_{c}}}$$Pixels intensity contrast: It is a measure of intensity contrast between a pixel and its neighbor over the entire image (calculated in Equation (11)).$$contrast=\sum _{i,j=1}^{k}{(i-j)}^{2}{p}_{ij}$$Energy: It is the measurement of uniformity in the intensities of an image (as given in Equation (12)). Its value is 1, if an image is constant and 0 if the intensities are variable.$$Energy=\sum _{i,j=1}^{k}{\left({P}_{(i,j)}\right)}^{2}$$Homogeneity: It measures the spatial closeness of the distribution of elements in the cooccurrence matrix to the diagonal given by (13). The values range is [0, 1], and the maximum value is attained when the matrix is a diagonal.$$homogeneity=\sum _{i,j=1}^{k}{\displaystyle \frac{{P}_{ij}}{1+|i-j|}}$$Entropy: It measure the degree of variability of the elements of the cooccurrence matrix. Its value is 0 if all intensities of ${P}_{ij}$ are 0 and is maximum when all ${P}_{ij}$ are equal. It may be calculated by (14).$$entropy=-\sum _{i,j=1}^{k}{P}_{ij}lo{g}_{2}{P}_{ij}$$
- Run length matrix features of each RBC: The other textural features are created on the gray-level run length matrix (calculated in Equations (15)–(24). The $l\nabla K$ matrix p, where l is the number of gray levels and k is the maximum run length, is defined for a certain image as the total runs with pixels of gray level i and run length j. Likewise, as in the GLCM, the run length matrices were calculated using 8 gray-levels for 30${}^{\circ}$, 60${}^{\circ}$, 90${}^{\circ}$, and 135${}^{\circ}$.Short Run Emphasis (SRE):$$SRE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{k}{\displaystyle \frac{{}_{{P}_{ij}}}{{j}^{2}}}$$Long Run Emphasis (LRE):$$LRE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{k}\left({p}_{i}j\right){j}^{2}$$Gray-Level Nonuniformity (GLN):$$GLN={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}{\left(\sum _{j=1}^{l}\left({p}_{i}j\right)\right)}^{2}$$Run Length Nonuniformity (RLN):$$RLN={\displaystyle \frac{1}{R}}\sum _{j=1}^{l}{\left(\sum _{i=1}^{k}{p}_{ij}\right)}^{2}$$Low Gray-level Run Emphasis (LGRE):$$LGRE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}{\displaystyle \frac{pij}{{i}^{2}}}$$High Gray-level Run Emphasis (HGRE):$$HGRE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}\left({p}_{ij}\right){i}^{2}$$Short Run Low Gray-level Emphasis (SRLGE):$$SRLGE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}{\displaystyle \frac{{p}_{ij}}{{i}^{2}{j}^{2}}}$$Short Run High Gray-level Emphasis (SRHGE):$$SRHGE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}{\displaystyle \frac{{p}_{\left(ij\right)}{i}^{2}}{{j}^{2}}}$$Long Run Low Gray-level Emphasis (LRLGE):$$LRLGE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}{\displaystyle \frac{{p}_{\left(ij\right){j}^{2}}}{{i}^{2}}}$$Long Run High Gray-level Emphasis (LRHGE):$$LRHGLE={\displaystyle \frac{1}{R}}\sum _{i=1}^{k}\sum _{j=1}^{l}\left({p}_{ij}\right){i}^{2}{j}^{2}$$
- Gabor Feature Extraction: like a human visual processing system, the Gabor filter extracts features at different amplitudes and orientation.$$\begin{array}{c}\hfill \psi (x,y)={\displaystyle \frac{{f}^{2}}{\pi \gamma \eta}}{e}^{-}\left({\displaystyle \frac{{f}^{2}}{{\gamma}^{2}}}{x}^{{}^{\prime}2}\right)+\left({\displaystyle \frac{{f}^{2}}{{\eta}^{2}}}{y}^{{}^{\prime}2}\right){e}^{j2\pi f{x}^{\prime}}\\ \hfill {x}^{\prime}=xcos\theta +ysin\theta \\ \hfill {y}^{\prime}=xsin\theta +ycos\theta \end{array}$$The Gabor filter is the product of a 2D Fourier basis function and origin-centred Gaussian given in Equation (25), where f is the central frequency of the filter, $\gamma $ and $\eta $ are the sharpness or bandwidth measure along the minor and major axes of Gaussian respectively, $\theta $ is the angle of rotation, and ($\eta $/$\gamma $) is the aspect ratio. The analytical form of this function in frequency domain is given in Equation (26) as follow:$$\begin{array}{c}\hfill \psi (u,v)={e}^{-{\displaystyle \frac{{\pi}^{2}}{{f}^{2}}}({\gamma}^{2}{({u}^{\prime}-f)}^{2}+{\eta}^{2}{v}^{{}^{\prime}2})}\\ \hfill {u}^{\prime}=ucos\theta +vsin\theta \\ \hfill {v}^{\prime}=usin\theta +vcos\theta \end{array}$$In the frequency domain given by Equation (27), the function is a single real-valued Gaussian centered at f. A simplified version of a general 2D Gabor filter function in Equations (25) and (26) was formulated by [23], which implements a set of self-similar filters, i.e., Gabor wavelets (rotated and scaled forms of each other, irrespective of the frequency f and orientation $\theta $.Gabor bank or Gabor features were created from responses of Gabor filters in Equations (25) and (26) by using multiple filters on several frequencies ${f}_{m}$ and orientations ${\theta}_{n}$. Frequency in this case corresponds to scale information and is thus drawn from [23]$${f}_{m}={k}^{-m}{f}_{m}ax,m=\{0,\dots ,M-1\}$$

#### 3.6. ADASYN Sampling

#### 3.7. Features Reduction

## 4. Classification

## 5. Results

#### 5.1. Dataset

#### 5.2. Qualitative Results

#### 5.3. Quantitative Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) A normal blood smear image and (

**b**) microcytic hypochromic, (

**c**) normocytic hypochromic, (

**d**) macrocytic hypochromic, and (

**e**) microcytic hyperchromic anemia.

**Figure 3.**Output images after the preprocessing step: (

**a**) original RGB image, (

**b**) red channel, (

**c**) green channel, (

**d**) blue channel, (

**e**) enhanced green channel, and (

**f**) quantized image leaving behind RBCs.

**Figure 4.**(

**a**) Binarized original image of a sample blood smear, (

**b**) binarized image of a sample blood smear quantized, and (

**c**) exclusive OR of (

**a**,

**b**).

**Figure 5.**(

**a**) Orientation of angles overlayed on a sample red blood cell (RBC) and (

**b**) scanning through 0${}^{\circ}$, 45${}^{\circ}$, 90${}^{\circ}$, and 135${}^{\circ}$.

**Figure 6.**(

**a**) Original image of hyperchromic macrocytic RBC, (

**b**) gray level image of hyperchromic macrocytic RBC, (

**c**) Gabor filter bank of hyperchromic macrocytic RBC, (

**d**) original image of hypochromic microcytic RBC, (

**e**) gray level image of hypochromic microcytic RBC, (

**f**) Gabor filter bank features of hypochromic microcytic RBC, (

**g**) original image of hyperchromic microcytic RBC, (

**h**) gray level image of hyperchromic microcytic RBC, and (

**i**) a hyperchromic microcytic RBC with its Gabor filter bank features.

**Figure 8.**(

**a**,

**d**,

**g**) Original RGB images of a sample blood smear, (

**b**,

**e**,

**h**) removal of white blood cells (WBCs) from the blood smear images, and (

**c**,

**f**,

**i**) enhanced gray-scale images of RBCs in blood smears.

**Figure 9.**Classes of cells among RBCs (

**a**,

**b**) microcytic hypochromic cells, (

**c**) microcytic narmochromic cells, (

**d**) macrocytic hyperchromic cells (

**e**,

**f**) microcytic hyperchromic cells (

**g**) macrocytic Hyperchromic cells, and (

**h**,

**j**) codocytes or taget cells.

**Figure 10.**Graphs showing the results of four types of texture features, (

**a**) GLRLM (

**b**) GLCM (

**c**) GMSE (

**d**) GMA.

Cell Type | Original | Synthetic | Total |
---|---|---|---|

Microcyte | 157 | 197 | 354 |

Normocytes | 270 | 57 | 327 |

Macrocytes | 101 | 211 | 312 |

Hypochromic | 157 | 150 | 340 |

Narmochromic | 380 | 0 | 380 |

Cell No. | Contrast | Correlation | Energy | Homogeneity |
---|---|---|---|---|

Cell1 | 85.40 | 406.62 | 123.52 | 105.8 |

Cell2 | 80.02758 | −112.132 | 136.3636 | 108.52 |

Cell3 | 116.9 | 394.59 | 100 | 93.68 |

Cell4 | 96.18 | 94.716 | 117.85 | 100.0 |

Cell5 | 121.1 | −79.49 | 80 | 92.77 |

Cell6 | 106.2 | −148.7 | 80 | 98.03 |

Cell7 | 86.6 | −201.2 | 120 | 104.07 |

Cell8 | 88.12 | 88.12 | 120 | 104 |

Cell9 | 106.1 | 97.47 | 100 | 98 |

Cell10 | 100 | 100 | 100 | 100 |

Cell No. | SRE | LRE | GLN | RLN | RP | LGRE | HGRE | SRLGE | SRHGE | LRLGE | LRHGE |
---|---|---|---|---|---|---|---|---|---|---|---|

Cell1 | 0.56 | 44.24 | 116.35 | 113.27 | 8.74 | 2.09 | 50.11 | 0.22 | 12.46 | 24.79 | 209.57 |

Cell2 | 0.7 | 40.25 | 126.78 | 108.01 | 8.69 | 2.26 | 39.37 | 0.29 | 14.12 | 25.91 | 127.59 |

Cell3 | 0.43 | 44.88 | 135.02 | 139.61 | 8.47 | 2.02 | 51.45 | 0.18 | 10.59 | 24.89 | 268.0 |

Cell4 | 0.5 | 65.18 | 137.38 | 115.35 | 12.93 | 2.62 | 48.2 | 0.23 | 7.83 | 45.05 | 134.07 |

Cell5 | 88.24 | 106.62 | 94.77 | 106.14 | 102.68 | 93.53 | 110.29 | 80.23 | 86.07 | 96.51 | 118.61 |

Cell6 | 115.4 | 100.85 | 94.51 | 98.77 | 103.26 | 92.73 | 99.82 | 120.77 | 73.02 | 88.5 | 120.18 |

Cell7 | 0.39 | 61.57 | 132.04 | 111.73 | 11.22 | 2.6 | 43.64 | 0.19 | 7.9 | 42.7 | 130.44 |

Cell8 | 1.25 | 89.76 | 103.12 | 103.36 | 29.92 | 7.01 | 81.33 | 0.59 | 19.3 | 70.39 | 130.52 |

Cell9 | 0.33 | 47.64 | 309.2 | 216.5 | 11.1 | 2.44 | 28.86 | 0.15 | 6.02 | 32.81 | 254.73 |

Cell10 | 0.37 | 45.41 | 355.65 | 206.29 | 10.46 | 2.56 | 28.17 | 0.18 | 5.99 | 31.69 | 325.68 |

Cell No. | MSE1 | MSE2 | MSE3 | MSE4 | MSE5 | MSE6 | MSE7 | MSE8 | MSE9 | MSE10 | MSE11 | MSE12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cell1 | 376 | 263 | 165.7 | 155.2 | 414.9 | 301.7 | 216.3 | 204.5 | 424.4 | 313.3 | 226.3 | 197 |

Cell2 | 258 | 350 | 274.6 | 316.8 | 436.3 | 380.9 | 264.9 | 306.7 | 439.7 | 382.9 | 273.3 | 299 |

Cell3 | 269 | 403 | 419.8 | 554.9 | 328.8 | 457.5 | 386.6 | 493.4 | 314.5 | 440.3 | 377.1 | 462 |

Cell4 | 234 | 205 | 207.9 | 153.3 | 177.8 | 157.8 | 186.5 | 174.7 | 173.5 | 153 | 200.3 | 172 |

Cell5 | 62 | 96 | 121.3 | 164.9 | 72.1 | 110.4 | 157.8 | 173.6 | 73.3 | 109.7 | 155.8 | 167 |

Cell6 | 45 | 70 | 91.5 | 113.5 | 40.8 | 70.5 | 93.3 | 104.4 | 41.5 | 72.4 | 102 | 105 |

Cell7 | 120 | 115 | 149.8 | 136 | 79.1 | 140 | 201.2 | 149.7 | 70.6 | 102.6 | 147.2 | 156 |

Cell8 | 50 | 101 | 138.6 | 120 | 51.8 | 101 | 149.7 | 146 | 54.2 | 113.4 | 163.6 | 131 |

Cell9 | 701 | 682 | 737.9 | 862.7 | 669 | 592 | 692 | 784 | 70 | 653.5 | 685.5 | 820 |

Cell10 | 730 | 695 | 700 | 850 | 670 | 590 | 701 | 770 | 715 | 1373.9 | 1396.1 | 1397 |

Cell No. | MA1 | MA2 | MA3 | MA4 | MA5 | MA6 | MA7 | MA8 | MA9 | MA10 | MA11 | MA12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cell1 | 2 | 5 | 11 | 20 | 2 | 6 | 13 | 21 | 2 | 6 | 13 | 21 |

Cell2 | 1 | 5 | 12 | 23 | 1 | 5 | 12 | 21 | 1 | 5 | 12 | 22 |

Cell3 | 1 | 4 | 11 | 23 | 1 | 4 | 11 | 21 | 1 | 4 | 10 | 21 |

Cell4 | 2 | 5 | 16 | 24 | 2 | 5 | 16 | 24 | 1 | 5 | 16 | 24 |

Cell5 | 1 | 4 | 13 | 25 | 1 | 5 | 15 | 26 | 1 | 5 | 15 | 26 |

Cell6 | 1 | 4 | 11 | 21 | 1 | 4 | 12 | 21 | 1 | 4 | 12 | 21 |

Cell7 | 1 | 4 | 13 | 22 | 1 | 5 | 16 | 23 | 1 | 4 | 13 | 23 |

Cell8 | 1 | 4 | 14 | 22 | 1 | 5 | 16 | 25 | 1 | 5 | 16 | 24 |

Cell9 | 1 | 4 | 12 | 18 | 1 | 4 | 12 | 17 | 1 | 4 | 11 | 17 |

Cell10 | 1 | 4 | 12 | 16 | 1 | 4 | 12 | 16 | 1 | 4 | 12 | 16 |

**Table 6.**Performance evaluation of each classification algorithm with statistical measurement tools.

Statistical | K-means Clustering (%) | Logistic Regression (%) | Naive Bayes (%) | Proposed Classifier (%) |
---|---|---|---|---|

Precision | 81.1 | 86.4 | 87.1 | 92.3 |

Accuracy | 80.7 | 86.2 | 88.3 | 93.2 |

Recall | 80.3 | 83.2 | 84.3 | 95.4 |

F1-Score | 79.8 | 82.1 | 84.1 | 94.1 |

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## Share and Cite

**MDPI and ACS Style**

Azam, B.; Ur Rahman, S.; Irfan, M.; Awais, M.; Alshehri, O.M.; Saif, A.; Nahari, M.H.; Mahnashi, M.H.
A Reliable Auto-Robust Analysis of Blood Smear Images for Classification of Microcytic Hypochromic Anemia Using Gray Level Matrices and Gabor Feature Bank. *Entropy* **2020**, *22*, 1040.
https://doi.org/10.3390/e22091040

**AMA Style**

Azam B, Ur Rahman S, Irfan M, Awais M, Alshehri OM, Saif A, Nahari MH, Mahnashi MH.
A Reliable Auto-Robust Analysis of Blood Smear Images for Classification of Microcytic Hypochromic Anemia Using Gray Level Matrices and Gabor Feature Bank. *Entropy*. 2020; 22(9):1040.
https://doi.org/10.3390/e22091040

**Chicago/Turabian Style**

Azam, Bakht, Sami Ur Rahman, Muhammad Irfan, Muhammad Awais, Osama Mohammed Alshehri, Ahmed Saif, Mohammed Hassan Nahari, and Mater H. Mahnashi.
2020. "A Reliable Auto-Robust Analysis of Blood Smear Images for Classification of Microcytic Hypochromic Anemia Using Gray Level Matrices and Gabor Feature Bank" *Entropy* 22, no. 9: 1040.
https://doi.org/10.3390/e22091040