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Contribution to the Characterization of the Kidney Ultrasound Image Using Singularity Levels^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Image Analysis Based on Local Information

#### 2.1. The Image of Singularities

#### 2.2. Singularity-Level Run-Length Matrix

- -
- Short-Run Low-Level Singularity Emphasis (SRLLSE) given by ${k}_{i}=-2$ and ${k}_{j}=-2$;
- -
- Short-Run High-Level Singularity Emphasis (SRHLSE) given by ${k}_{i}=2$ and ${k}_{j}=-2$;
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- Long-Run High Singularity Emphasis (LRHSE) given by ${k}_{i}=2$ and ${k}_{j}=2$;
- -
- Long-Run Low Singularity Emphasis (LRLSE) given by ${k}_{i}=-2$ and ${k}_{j}=2$;

- -
- Run-Length Non-Uniformity (RLNU):$$RLNU=\frac{1}{{n}_{\theta}}{\sum}_{j=1}^{{N}_{\theta}}{\left({\sum}_{i=1}^{G}{p}_{\theta}\left(i,j\right)\right)}^{2};$$
- -
- Singularity Level Non-Uniformity (SLNU):$$SLNU=\frac{1}{{n}_{\theta}}{\sum}_{j=1}^{G}{\left({\sum}_{i=1}^{{N}_{\theta}}{p}_{\theta}\left(i,j\right)\right)}^{2};$$
- -
- Runs Percentage (RP):$$RP=\frac{1}{\sum _{i=1}^{G}\sum _{j=1}^{{N}_{\theta}}j{p}_{\theta}\left(i,j\right)}.$$

#### 2.3. First-Order Statistics

## 3. Application for Characterization of Kidney Ultrasound Images

#### Results and Discussion

- Singularity-level run-length matrix methods, compared to the method using the first order statistics, provide a better classification accuracy rate, whereas the best result is obtained using the combined method applied on the ROI representative of the “whole” kidney, and the classification rate reaches 80% obtained with eight features and a test accuracy classification of about 78%.
- The impact of the choice of the number K (K = 6, 7, 8) remains not significant with the mean, on the all the iterative process, of the variation classification accuracy less than 5.8%.
- As a region of interest, the parenchyma remains more representative than the central region. Indeed, for the parenchyma ROI, the best classification accuracy rate, which reaches about 76%, is obtained using the combined method with seven features, while the test classification, using the subset of seven features, is 73.3%.
- The central region remains the least representative with the best classification accuracy obtained using the combined method. Indeed, the classification accuracy rate reached about 62.6%, and test classification is about 60%.

- Increasing the size of the database so that it contains other classes of images corresponding to different pathologies while carrying out image acquisitions in the most standard conditions;
- Setting the parameters that most influence the reproducibility of the texture features;
- Combining the multifractal with other texture classification approach to improve the results;
- Applying this approach for the characterization of texture images of other human organs such as the liver;
- Improving a selecting puncture for considering all the kidney images.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sharma, K.; Virmani, J. Haralick’s Texture Descriptors for Classification of Renal Ultrasound Images. In Hybrid Intelligent Techniques for Pattern Analysis and Understanding; Chapman and Hall: London, UK, 2017. [Google Scholar] [CrossRef]
- Akkasaligar, P.T.; Biradar, S. Classification of Ultrasound Images of Kidney. IJCA Proc. Int. Conf. Inf. Commun. Technol.
**2014**, 3, 24–28. [Google Scholar] - Ahmad, R.; Mohanty, B.K. Chronic Kidney Disease Stage Identification Using Texture Analysis of Ultrasound Images. Biomed. Signal Process. Control
**2021**, 69, 102695. [Google Scholar] [CrossRef] - Iqbal, F.; Pallewatte, A.S.; Wansapura, J.P. Texture Analysis of Ultrasound Images of Chronic Kidney Disease. In Proceedings of the Seventeenth International Conference on Advances in ICT for Emerging Regions (ICTer), Colombo, Sri Lanka, 6–9 September 2017; pp. 299–303. [Google Scholar] [CrossRef]
- Garelnabi, M.; Abdullah, I.; Bakry, A.H.A.; Abdulla, E.A.; Adam, M. Characterization of Kidney Infection in Ultrasound B-mode Images Using Texture Analysis. Int. J. Sci. Res.
**2016**, 5, 2319–7064. [Google Scholar] [CrossRef] - Vehel, J.L.; Mignot, P.; Berrior, J.-P. Texture and Multifractals: New Tools for Image Analysis; Technical Report 1706; Institut National de Recherche en Informatique et en Automatique: Le Chesnay-Rocquencourt, France, 1992. [Google Scholar]
- Ranjan, U.S.; Narayana, A. Classification of Objects in SAR Images Using Scaling Feature, ICVGIP, 16–18 December; Space Applications Centre Ahmedaba: Ahmedabad, India, 2002. [Google Scholar]
- Saucier, A.; Richer, J.; Muller, J. Assessing the scope of the multifractal approach to textural characterization with statistical reconstructions of images. Phys. A Stat. Mech. Its Appl.
**2002**, 311, 231–259. [Google Scholar] [CrossRef] - Chaudhuri, B.; Sarkar, N. Texture segmentation using fractal dimension. IEEE Trans. Pattern Anal. Mach. Intell.
**1995**, 17, 72–77. [Google Scholar] [CrossRef] - Xu, Y.; Ji, H.; Fermüller, C. Viewpoint Invariant Texture Description Using Fractal Analysis. Int. J. Comput. Vis.
**2009**, 83, 85–100. [Google Scholar] [CrossRef] - Florindo, J.B.; Bruno, O.M.; Landini, G. Multifractal Texture Analysis Using a Dilation-Based Hölder Exponent. In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), Berlin, Germany, 11–14 March 2015; pp. 505–511. [Google Scholar] [CrossRef]
- Sailhac, P.; Seyler, F. Texture Characterization of ERS-1 Images by Regional Multifractal Analysis; Springer: Berlin, Germany, 1997; pp. 32–41. [Google Scholar] [CrossRef]
- Stanczyk, P.; Sharpe, P. Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum. Fractals
**1999**, 67–79. [Google Scholar] [CrossRef] - Véhel, J.L.; Vojak, R. Multifractal Analysis of Choquet Capacities: Preliminary Results; Rapport de Recherche de INRIA; INRIA: Le Chesnay-Rocquencourt, France, 1995. [Google Scholar]
- Muzzolini, R. A Volumetric Approach to Segmentation and Texture Characterization of Ultrasound Images. Ph.D. Thesis, Université de Saskatchewan, Saskatoon, SA, Canada, 1 April 1997. [Google Scholar]

**Table 1.**

**(1)**Classification accuracy rates of the three regions (

**P**:

**P**arechyma,

**C**:

**C**entral,

**W**: “

**W**hole” kidney), with K = 6, 7, 8.

**(2)**The number of texture features used to obtain the best classification accuracy rate.

**(3)**Results of the test classification.

(1) (P, C, W) K = 6 | (1) (P, C, W) K = 7 | (1) (P, C, W) K = 8 | (2) Number of Features (P, C, W) | (3) Test Classification Accuracy Rate (P, C, W) | |
---|---|---|---|---|---|

First order statistics | (50.6%, 37.3%, 64.5%) | (52%, 38.6%, 73.3%) | (49.3%, 34.6%, 73.3%) | (3, 2, 4) | (60%, 41.3%, 72%) |

Singularity-level Run-length matrix | (72%, 60%, 76%) | (70.6%, 54.6%, 73.3%) | (69.3%, 58.6%, 76%) | (6, 3, 6) | (72%, 58.6%, 74.6%) |

Combined method | (76%, 62.6%, 80%) | (73.3%, 54.6%, 78.6%) | (73.3%, 60%, 74.6%) | (7, 5, 8) | (73.3%, 60%, 78%) |

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**MDPI and ACS Style**

Alaoui, M.T.; Korchiyne, R.
Contribution to the Characterization of the Kidney Ultrasound Image Using Singularity Levels. *Comput. Sci. Math. Forum* **2023**, *6*, 12.
https://doi.org/10.3390/cmsf2023006012

**AMA Style**

Alaoui MT, Korchiyne R.
Contribution to the Characterization of the Kidney Ultrasound Image Using Singularity Levels. *Computer Sciences & Mathematics Forum*. 2023; 6(1):12.
https://doi.org/10.3390/cmsf2023006012

**Chicago/Turabian Style**

Alaoui, Mustapha Tahiri, and Redouan Korchiyne.
2023. "Contribution to the Characterization of the Kidney Ultrasound Image Using Singularity Levels" *Computer Sciences & Mathematics Forum* 6, no. 1: 12.
https://doi.org/10.3390/cmsf2023006012