Multidimensional and fuzzy sample entropy (SampEnMF) for quantifying H&E histological images of colorectal cancer

Classification of Multiple H&E Images via an Ensemble Computational Scheme

In this work, a computational scheme is proposed to identify the main combinations of handcrafted descriptors and deep-learned features capable of classifying histological images stained with hematoxylin and eosin. The handcrafted descriptors were those representatives of multiscale and multidimensional fractal techniques (fractal dimension, lacunarity and percolation) applied to quantify the histological images with the corresponding representations via explainable artificial intelligence (xAI) approaches. The deep-learned features were obtained from different convolutional neural networks (DenseNet-121, EfficientNet-b2, Inception-V3, ResNet-50 and VGG-19). The descriptors were investigated through different associations. The most relevant combinations, defined through a ranking algorithm, were analyzed via a heterogeneous ensemble of classifiers with the support vector machine, naive Bayes, random forest and K-nearest neighbors algorithms. The proposed scheme was applied to histological samples representative of breast cancer, colorectal cancer, oral dysplasia and liver tissue. The best results were accuracy rates of 94.83% to 100%, with the identification of pattern ensembles for classifying multiple histological images. The computational scheme indicated solutions exploring a reduced number of features (a maximum of 25 descriptors) and with better performance values than those observed in the literature. The presented information in this study is useful to complement and improve the development of computer-aided diagnosis focused on histological images.

Bidimensional ensemble entropy: Concepts and application to emphysema lung computerized tomography scans

BACKGROUND AND OBJECTIVE

Bidimensional entropy algorithms provide meaningful quantitative information on image textures. These algorithms have the advantage of relying on well-known one-dimensional entropy measures dedicated to the analysis of time series. However, uni- and bidimensional algorithms require the adjustment of some parameters that influence the obtained results or even findings. To address this, ensemble entropy techniques have recently emerged as a solution for signal analysis, offering greater stability and reduced bias in data patterns during entropy estimation. However, such algorithms have not yet been extended to their two-dimensional forms.

METHODS

We therefore propose six bidimensional algorithms, namely ensemble sample entropy, ensemble permutation entropy, ensemble dispersion entropy, ensemble distribution entropy, and two versions of ensemble fuzzy entropy based on different models or parameters initialization of an entropy algorithm. These new measures are first tested on synthetic images and further applied to a biomedical dataset.

RESULTS

The results suggest that ensemble techniques are able to detect different levels of image dynamics and their degrees of randomness. These methods lead to more stable entropy values (lower coefficients of variations) for the synthetic data. The results also show that these new measures can obtain up to 92.7% accuracy and 88.4% sensitivity when classifying patients with pulmonary emphysema through a k-nearest neighbors algorithm.

CONCLUSIONS

This is a further step towards the potential clinical deployment of bidimensional ensemble approaches to detect different levels of image dynamics and their successful performance on emphysema lung computerized tomography scans. These bidimensional ensemble entropy algorithms have potential to be used in various imaging applications thanks to their ability to distinguish more stable and less biased image patterns compared to their original counterparts.

Pulmonary embolism detection on venous thrombosis ultrasound images with bi-dimensional entropy measures: Preliminary results

BACKGROUND

Venous thromboembolism (VTE) is a common health issue. A clinical expression of VTE is a deep vein thrombosis (DVT) that may lead to pulmonary embolism (PE), a critical illness. When DVT is suspected, an ultrasound exam is performed. However, the characteristics of the clot observed on ultrasound images cannot be linked with the presence of PE. Computed tomography angiography is the gold standard to diagnose PE. Nevertheless, the latter technique is expensive and requires the use of contrast agents.

PURPOSE

In this article, we present an image processing method based on ultrasound images to determine whether PE is associated or not with lower limb DVT. In terms of medical equipment, this new approach (Doppler ultrasound image processing) is inexpensive and quite easy.

METHODS

With the aim to help medical doctors in detecting PE, we herein propose to process ultrasound images of patients with DVT. After a first step based on histogram equalization, the analysis procedure is based on the use of bi-dimensional entropy measures. Two different algorithms are tested: the bi-dimensional dispersion entropy (D i s p E n 2 D $DispEn_{2D}$ ) mesure and the bi-dimensional fuzzy entropy (F u z E n 2 D $FuzEn_{2D}$ ) mesure. Thirty-two patients (12 women and 20 men, 67.63 ± 16.19 years old), split into two groups (16 with and 16 without PE), compose our database of around 1490 ultrasound images (split into seven different sizes from 32× 32 px to 128 × 128 px). p-values, computed with the Mann-Whitney test, are used to determine if entropy values of the two groups are statistically significantly different. Receiver operating characteristic (ROC) curves are plotted and analyzed for the most significant cases to define if entropy values are able to discriminate the two groups.

RESULTS

p-values show that there are statistical differences betweenF u z E n 2 D $FuzEn_{2D}$  of patients with PE and patients without PE for 112× 112 px and 128× 128 px images. Area under the ROC curve (AUC) is higher than 0.7 (threshold for a fair test) for 112× 112 and 128× 128 images. The best value of AUC (0.72) is obtained for 112× 112 px images.

CONCLUSIONS

Bi-dimensional entropy measures applied to ultrasound images seem to offer encouraging perspectives for PE detection: our first experiment, on a small dataset, shows thatF u z E n 2 D $FuzEn_{2D}$  on 112× 112 px images is able to detect PE. The next step of our work will consist in testing this approach on a larger dataset and in integratingF u z E n 2 D $FuzEn_{2D}$  in a machine learning algorithm. Furthermore, this study could also contribute to PE risk prediction for patients with VTE.

Colored Texture Analysis Fuzzy Entropy Methods with a Dermoscopic Application

Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for gray scale images. However, to the best of our knowledge, there are no well-established entropy methods that deal with colored images yet. Therefore, we propose the recent colored bidimensional fuzzy entropy measure, FuzEnC2D, and introduce its new multi-channel approaches, FuzEnV2D and FuzEnM2D, for the analysis of colored images. We investigate their sensitivity to parameters and ability to identify images with different irregularity degrees, and therefore different textures. Moreover, we study their behavior with colored Brodatz images in different color spaces. After verifying the results with test images, we employ the three methods for analyzing dermoscopic images of malignant melanoma and benign melanocytic nevi. FuzEnC2D, FuzEnV2D, and FuzEnM2D illustrate a good differentiation ability between the two-similar in appearance-pigmented skin lesions. The results outperform those of a well-known texture analysis measure. Our work provides the first entropy measure studying colored images using both single and multi-channel approaches.

EntropyHub: An open-source toolkit for entropic time series analysis

An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropy, as it relates to information theory and dynamical systems theory, can be estimated in many ways, with newly developed methods being continuously introduced in the scientific literature. Despite the growing interest in entropic time series and image analysis, there is a shortage of validated, open-source software tools that enable researchers to apply these methods. To date, packages for performing entropy analysis are often run using graphical user interfaces, lack the necessary supporting documentation, or do not include functions for more advanced entropy methods, such as cross-entropy, multiscale cross-entropy or bidimensional entropy. In light of this, this paper introduces EntropyHub, an open-source toolkit for performing entropic time series analysis in MATLAB, Python and Julia. EntropyHub (version 0.1) provides an extensive range of more than forty functions for estimating cross-, multiscale, multiscale cross-, and bidimensional entropy, each including a number of keyword arguments that allows the user to specify multiple parameters in the entropy calculation. Instructions for installation, descriptions of function syntax, and examples of use are fully detailed in the supporting documentation, available on the EntropyHub website- www.EntropyHub.xyz. Compatible with Windows, Mac and Linux operating systems, EntropyHub is hosted on GitHub, as well as the native package repository for MATLAB, Python and Julia, respectively. The goal of EntropyHub is to integrate the many established entropy methods into one complete resource, providing tools that make advanced entropic time series analysis straightforward and reproducible.

Texture Analysis and its Applications in Biomedical Imaging: A Survey

Texture analysis describes a variety of image analysis techniques that quantify the variation in intensity and pattern. This paper provides an overview of several texture analysis approaches addressing the rationale supporting them, their advantages, drawbacks, and applications. This surveys emphasis is in collecting and categorising over five decades of active research on texture analysis. Brief descriptions of different approaches are presented along with application examples. From a broad range of texture analysis applications, this surveys final focus is on biomedical image analysis. An up-to-date list of biological tissues and organs in which disorders produce texture changes that may be used to spot disease onset and progression is provided. Finally, the role of texture analysis methods as biomarkers of disease is summarised.

The novel approach of temporal dependency complexity analysis of heart rate variability in obstructive sleep apnea

Obstructive sleep apnea (OSA) is a serious sleep disorder, which leads to changes in autonomic nerve function and increases the risk of cardiovascular disease. Heart rate variability (HRV) has been widely used as a non-invasive method for assessing the autonomic nervous system (ANS). We proposed the two-dimensional sample entropy of the coarse-grained Gramian angular summation field image (CgSampEn_2D) index. It is a new index for HRV analysis based on the temporal dependency complexity. In this study, we used 60 electrocardiogram (ECG) records from the Apnea-ECG database of PhysioNet (20 healthy records and 40 OSA records). These records were divided into 5-min segments. Compared with the classical indices low-to-high frequency power ratio (LF/HF) and sample entropy (SampEn), CgSampEn_2D utilizes the correlation information between different time intervals in the RR sequences and preserves the temporal dependency of the RR sequences, which improves the OSA detection performance significantly. The OSA screening accuracy of CgSampEn_2D (93.3%) is higher than that of LF/HF (80.0%) and SampEn (73.3%). Additionally, CgSampEn_2D has a significant association with the apnea-hypopnea index (AHI) (R = -0.740, p = 0). CgSampEn_2D reflects the complexity of the OSA autonomic nerve more comprehensively and provides a novel idea for the screening of OSA disease.

Comparison of texture-based classification and deep learning for plantar soft tissue histology segmentation

Histomorphological measurements can be used to identify microstructural changes related to disease pathomechanics, in particular, plantar soft tissue changes with diabetes. However, these measurements are time-consuming and susceptible to sampling and human measurement error. We investigated two approaches to automate segmentation of plantar soft tissue stained with modified Hart's stain for elastin with the eventual goal of subsequent morphological analysis. The first approach used multiple texture- and color-based features with tile-wise classification. The second approach used a convolutional neural network modified from the U-Net architecture with fewer channel dimensions and additional downsampling steps. A hybrid color and texture feature, Fourier reduced histogram of uniform improved opponent color local binary patterns (f-IOCLBP), yielded the best feature-based segmentation, but still performed 3.6% worse on average than the modified U-Net. The texture-based method was sensitive to changes in illumination and stain intensity, and segmentation errors were often in large regions of single tissues or at tissue boundaries. The U-Net was able to segment small, few-pixel tissue boundaries, and errors were often trivial to clean up with post-processing. A U-Net approach outperforms hand-crafted features for segmentation of plantar soft tissue stained with modified Hart's stain for elastin.

Developing a clinical decision support system based on the fuzzy logic and decision tree to predict colorectal cancer

Background: Colorectal Cancer (CRC) is the most prevalent digestive system- related cancer and has become one of the deadliest diseases worldwide. Given the poor prognosis of CRC, it is of great importance to make a more accurate prediction of this disease. Early CRC detection using computational technologies can significantly improve the overall survival possibility of patients. Hence this study was aimed to develop a fuzzy logic-based clinical decision support system (FL-based CDSS) for the detection of CRC patients. Methods: This study was conducted in 2020 using the data related to CRC and non-CRC patients, which included the 1162 cases in the Masoud internal clinic, Tehran, Iran. The chi-square method was used to determine the most important risk factors in predicting CRC. Furthermore, the C4.5 decision tree was used to extract the rules. Finally, the FL-based CDSS was designed in a MATLAB environment and its performance was evaluated by a confusion matrix. Results: Eleven features were selected as the most important factors. After fuzzification of the qualitative variables and evaluation of the decision support system (DSS) using the confusion matrix, the accuracy, specificity, and sensitivity of the system was yielded 0.96, 0.97, and 0.96, respectively. Conclusion: We concluded that developing the CDSS in this field can provide an earlier diagnosis of CRC, leading to a timely treatment, which could decrease the CRC mortality rate in the community.

Three-Dimensional Multiscale Fuzzy Entropy: Validation and Application to Idiopathic Pulmonary Fibrosis

Idiopathic Pulmonary Fibrosis (IPF) is a chronic, severe, and progressive lung disease with short life expectancy. Based on information theory and entropy measurement, a three-dimensional multiscale fuzzy entropy (MFE _3D) algorithm is proposed to identify IPF patients from their computed tomography (CT) volumetric data. First, the validation of the algorithm was performed by analyzing several volumetric synthetic noises (white, blue, brown, and pink), MIX(p) processes-based volumes, and texture-based volumes. The entropy values obtained by MFE _3D were consistent with the values obtained using the one, and two-dimensional versions, validating its use in biomedical data. Hence, MFE _3D was applied to CT scans to identify the existence of IPF within two different groups, one of healthy subjects (26) and another of IPF patients (26). Statistical differences were found (p < 0.05) between the entropy values of each group in 5 scale factors out of 10. These results demonstrate that MFE _3D could be an interesting metric to identify IPF in CT scans.

Application of Fuzzy Optimization Model Based on Entropy Weight Method in Atmospheric Quality Evaluation: A Case Study of Zhejiang Province, China

A fuzzy optimization model based on the entropy weight method for investigating air pollution problems in various cities of Zhejiang Province, China has been proposed in this paper. Meanwhile, the air quality comprehensive evaluation system has been constructed based on the six major pollutants (SO2, NO2, CO, PM10, PM2.5 and O3) involved in China’s current air quality national standards. After analyzing the monthly data of six pollutants in 11 cities of Zhejiang Province from January 2015 to April 2018 by the above method, the authors found that, although the air quality of cities in Zhejiang Province did not reach the long-term serious pollution of Beijing, Tianjin, and Hebei, the air quality changes in the northern cities of Zhejiang were worse than those in southern Zhejiang. For example, the air quality of Shaoxing in northern Zhejiang has dropped by 14.85% in the last study period when compared with that of the beginning period, and Hangzhou, the provincial capital of Zhejiang, has also seen a decrease of 6.69% in air quality. The air quality of Lishui, Zhoushan and Wenzhou in southern Zhejiang has improved by 8.04%, 4.67% and 4.22% respectively. Apart from the geographical influence, the industrial structure of these cities is also an important cause for worse air quality. From the local areas in southern Zhejiang, cities have developed targeted air pollution control measures according to their own characteristics, including adjusting the industrial structure, changing the current energy consumption structure that heavily relies on coal, and improving laws and regulations on air pollution control, etc. In the four cities in central Zhejiang, the air quality at the end of the period (April 2018) has decreased from the beginning of the period (January 2015), given that there were no fundamental changes in their industrial structure and energy pattern.

On Structural Entropy and Spatial Filling Factor Analysis of Colonoscopy Pictures

Colonoscopy is the standard device for diagnosing colorectal cancer, which develops from little lesions on the bowel wall called polyps. The Rényi entropies-based structural entropy and spatial filling factor are two scale- and resolution-independent quantities that characterize the shape of a probability distribution with the help of characteristic curves of the structural entropy–spatial filling factor map. This alternative definition of structural entropy is easy to calculate, independent of the image resolution, and does not require the calculation of neighbor statistics, unlike the other graph-based structural entropies.The distant goal of this study was to help computer aided diagnosis in finding colorectal polyps by making the Rényi entropy based structural entropy more understood. The direct goal was to determine characteristic curves that can differentiate between polyps and other structure on the picture. After analyzing the distribution of colonoscopy picture color channels, the typical structures were modeled with simple geometrical functions and the structural entropy–spatial filling factor characteristic curves were determined for these model structures for various parameter sets. A colonoscopy image analying method, i.e., the line- or column-wise scanning of the picture, was also tested, with satisfactory matching of the characteristic curve and the image.