# Method-Induced Errors in Fractal Analysis of Lung Microscopic Images Segmented with the Use of HistAENN (Histogram-Based Autoencoder Neural Network)

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*Appl. Sci.*

**2018**,

*8*(12), 2356; https://doi.org/10.3390/app8122356 (registering DOI)

## Abstract

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## Featured Application

**Considered technique allows the segmentation of histological images by means of semisupervised learning using Histogram-based Autoencoder Neural Networks.**

**Data analysis applying fractal estimators is proposed for the evaluation of the method-induced errors of autopsy lung images.**

## Abstract

## 1. Introduction

- This work assumes hierarchical design using autoencoder neural network (the first hierarchy level) and the fractal-based estimator for complex structure analysis (the second hierarchy level) of segmented images and shows how to select or preselect algorithms in the second hierarchy level algorithm using small data sets and the semisupervised training principle. The choice of the best algorithm can be automated. Manual segmentation of entire images, required for supervised learning for creating training pairs, is not required in this case. It is the main contribution of this paper.
- This paper demonstrates a different approach to the design of image segmentation algorithms, because in majority of papers’ single results of neural networks are provided. There are numerous reasons why single results are provided, such as learning time, but it leads to false final conclusions about the architecture of the neural network. Neural network should be learned multiple times, because such empirical verification leads to different non-optimal networks, and the distribution for most quality parameters is achieved. Single learning gives a single value of neural network quality parameters, so the comparison of two different neural network architectures leads to significant errors.
- This paper addresses the problem of lung autopsy microscopic image analysis that is completely different from examination of regular histological slides of lung tissue. The issue of result variability due to the selection of image segmentation, and image analysis algorithms are discussed. The outcome has good potential for further designing of classification algorithms, which is essential not only for researchers and software developers but also for the forensic pathologist community. Moreover, methods described and discussed in this paper are appropriate for different types of digital images.
- The segmentation algorithm with the use of machine learning approach and comparison of results for two fractal-based algorithms—2D box-counting and fractals related lacunarity—are discussed in this paper. Binary images from the classification algorithm should be achieved, but the inherited properties of histological slides do not allow the discovery of an exact solution. The segmentation algorithm introduces errors and could be considered as noise. Segmented images are processed by fractal algorithms and input data including noise influence on the final variability of estimated fractal descriptors. Low variability of the system is especially important for semisupervised learning, because this type of learning is preferred for the processing of large images with some control of this process by specialists (patomorphologists or cytomorphologists.
- Method-induced errors could be estimated using the Monte Carlo approach. This work uses 100 HistAENNs trained for every image for the determination of algorithm influence on results. Overlapping tables could be achieved and analyzed for the determination of variability. The selection of a possibly more acceptable algorithm (e.g., fractal) and the selection of parameters for particular algorithm could be attained. The analysis of variability which may be applied for data sets with very raw manual segmentation is most important. Moreover, providing the expected classification results for the selection of segmentation and fractal analysis algorithms is not necessary.
- This paper shows the viability of the designing of segmentation algorithms with the use of neural networks if the appropriate rotational invariance algorithm is applied. It is possible by the application of the Sliding Window Local Histogram (SWLH) to achieve desired invariance. The training of such rotational invariance inside much deeper and larger CNN (Convolutional Neural Network [6,7,8]) is feasible, but SWLH that is a part of HistAENN simplifies training. SWLH reduces the size of the neural network as well as training time, so Monte Carlo tests are possible with a few days of processing.

## 2. Related Works

## 3. Data

## 4. Methods

#### 4.1. Variability of Estimators

#### 4.2. Manual Segmentation Techniques in Semisupervised Learning

- The inner part of region labeling is straightforward for the user but leads to numerous problems. Separation between two regions could be significant and both distributions do not overlap (Figure 3a). There are numerous possible discriminants which could be achieved during the training of a classifier using typical neural network training algorithms. Optimal discriminant is between both distributions and it is usually not achieved.
- The near-to-edge selection uses previously mentioned properties of distributions to achieve better discrimination. Both selections in this method overlap and both distributions overlap too. This means that the distance between them is much smaller compared to the first method (Figure 3a), but full overlapping is not achieved as in the distribution shown in Figure 3b. The application of typical neural network training algorithms leads to positioning of the discriminant between both overlapped distributions. There is no gap between them, thus an optimal or very close to optimal solution is achieved.

#### 4.3. Architecture of HistAENN and Two-Step Learning

#### 4.4. HistAENNseg—Image Segmentation Software

#### 4.5. Fractal-Based Analysis of Microscopic Lung Images

## 5. Results

## 6. Discussion

#### 6.1. All-in-One and Hierarchical Segmentations

- All-in-One approach, where a single machine learning algorithm is used for overall image processing. Such an approach could also be used for the final classification purposes, so the input is the image and the output is the recognized class.
- Hierarchical approach, with well-defined processing stages where some of them could be machine learning-based and others could be typical image processing algorithms, such as filters.

#### 6.2. Selection of Learning Principles

- Supervised learning requires input and output image pairs. The input image from each pair is available directly, but the desired output image should be manually segmented. Large slide images and their large data set lead to extremely high costs of design. The advantage is the possibility of designing a fully automatic CADx system.
- Unsupervised learning requires input images only, so the problem of manual segmentation of desired output images is avoided. This approach is based on automatic clustering. The number of classes could be arbitrarily selected or could be estimated automatically [76,77]. Unsupervised learning could be applied for well separated classes directly, but in most cases requires manual fitting of algorithms for a particular data set. This additional effort depends on the image content.
- Semisupervised learning is a promising solution for cost reduction of manual segmentation. This process assumes labeling of very small parts of images that belong to the specific classes. Semisupervised learning could be used for CADx system development or as a CADx working principle. In the latter case, semisupervised learning is used by patomorphologists during the analysis of a particular image. Obtained results are checked and corrected iteratively (Human in The Loop) for segmentation improving to the desired level. A very significant advantage of this learning principle is the possibility of an image segmentation system design without access to all possible image variants.

#### 6.3. Invariant Image Representation and Neural Networks

- Invariant transformations guaranteed by machine learning,
- Invariant transformations guaranteed by preprocessing algorithms.

#### 6.4. Selection of Fractal Descriptors for Image Analysis

## 7. Final Conclusions and Further Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Examples of lung autopsy images ((

**a**) emphysema, (

**b**) edema, (

**c**) autolysis, (

**d**) blood cells in alveoli and congestion).

**Figure 3.**Examples of manual labeling, achieved distribution and possible regions discriminations ((

**a**) inner regions labeling, (

**b**) regions edge labeling, (

**c**) near-to-edge labeling).

**Figure 4.**Scheme of HistAENN architecture for both training phases (RELU—REctified Linear Unit Layer, FC—Full Connection Layer) ((

**a**) autoencoder phase, (

**b**) classifier phase).

**Figure 6.**Exemplary results for box-counting analysis for single image (standard deviations are shown as a vertical line in left figures; raw distributions are shown in right figures).

**Figure 7.**Exemplary results for lacunarity analysis for single image (standard deviations are shown as a vertical line in left figures; raw distributions are shown in right figures).

**Figure 8.**Examples of overlapping: (

**a**) box-counting (Case 1), (

**b**) box-counting (Case 2), (

**c**) lacunarity case (Case 3), (

**d**) lacunarity (Case 4). Black is for overlapping.

Case | Type | Scales List | ${\mathit{Q}}_{\%}$ |
---|---|---|---|

1 | box-counting | $-2.5649,-1.9459,0$ | $7.24$ |

2 | box-counting | $-2.9444,-2.5649,-1.9459$ | $14.10$ |

3 | lacunarity | $0.8451,1.1361,1.3010$ | $67.72$ |

4 | lacunarity | $0,0.8451,1.1461$ | $73.30$ |

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**MDPI and ACS Style**

Oszutowska-Mazurek, D.; Mazurek, P.; Parafiniuk, M.; Stachowicz, A.
Method-Induced Errors in Fractal Analysis of Lung Microscopic Images Segmented with the Use of HistAENN (Histogram-Based Autoencoder Neural Network). *Appl. Sci.* **2018**, *8*, 2356.
https://doi.org/10.3390/app8122356

**AMA Style**

Oszutowska-Mazurek D, Mazurek P, Parafiniuk M, Stachowicz A.
Method-Induced Errors in Fractal Analysis of Lung Microscopic Images Segmented with the Use of HistAENN (Histogram-Based Autoencoder Neural Network). *Applied Sciences*. 2018; 8(12):2356.
https://doi.org/10.3390/app8122356

**Chicago/Turabian Style**

Oszutowska-Mazurek, Dorota, Przemyslaw Mazurek, Miroslaw Parafiniuk, and Agnieszka Stachowicz.
2018. "Method-Induced Errors in Fractal Analysis of Lung Microscopic Images Segmented with the Use of HistAENN (Histogram-Based Autoencoder Neural Network)" *Applied Sciences* 8, no. 12: 2356.
https://doi.org/10.3390/app8122356