Bidimensional Multiscale Fuzzy Entropy and Its Application to Pseudoxanthoma Elasticum

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.

Application of Two-Dimensional Entropy Measures to Detect the Radiographic Signs of Tooth Resorption and Hypercementosis in an Equine Model

Dental disorders are a serious health problem in equine medicine, their early recognition benefits the long-term general health of the horse. Most of the initial signs of Equine Odontoclastic Tooth Resorption and Hypercementosis (EOTRH) syndrome concern the alveolar aspect of the teeth, thus, the need for early recognition radiographic imaging. This study is aimed to evaluate the applicability of entropy measures to quantify the radiological signs of tooth resorption and hypercementosis as well as to enhance radiographic image quality in order to facilitate the identification of the signs of EOTRH syndrome. A detailed examination of the oral cavity was performed in eighty horses. Each evaluated incisor tooth was assigned to one of four grade-related EOTRH groups (0-3). Radiographs of the incisor teeth were taken and digitally processed. For each radiograph, two-dimensional sample (SampEn2D), fuzzy (FuzzEn2D), permutation (PermEn2D), dispersion (DispEn2D), and distribution (DistEn2D) entropies were measured after image filtering was performed using Normalize, Median, and LaplacianSharpening filters. Moreover, the similarities between entropy measures and selected Gray-Level Co-occurrence Matrix (GLCM) texture features were investigated. Among the 15 returned measures, DistEn2D was EOTRH grade-related. Moreover, DistEn2D extracted after Normalize filtering was the most informative. The EOTRH grade-related similarity between DistEn2D and Difference Entropy (GLCM) confirms the higher irregularity and complexity of incisor teeth radiographs in advanced EOTRH syndrome, demonstrating the greatest sensitivity (0.50) and specificity (0.95) of EOTRH 3 group detection. An application of DistEn2D to Normalize filtered incisor teeth radiographs enables the identification of the radiological signs of advanced EOTRH with higher accuracy than the previously used entropy-related GLCM texture features.

Deep Learning and Entropy-Based Texture Features for Color Image Classification

In the domain of computer vision, entropy-defined as a measure of irregularity-has been proposed as an effective method for analyzing the texture of images. Several studies have shown that, with specific parameter tuning, entropy-based approaches achieve high accuracy in terms of classification results for texture images, when associated with machine learning classifiers. However, few entropy measures have been extended to studying color images. Moreover, the literature is missing comparative analyses of entropy-based and modern deep learning-based classification methods for RGB color images. In order to address this matter, we first propose a new entropy-based measure for RGB images based on a multivariate approach. This multivariate approach is a bi-dimensional extension of the methods that have been successfully applied to multivariate signals (unidimensional data). Then, we compare the classification results of this new approach with those obtained from several deep learning methods. The entropy-based method for RGB image classification that we propose leads to promising results. In future studies, the measure could be extended to study other color spaces as well.

Application of the Two-Dimensional Entropy Measures in the Infrared Thermography-Based Detection of Rider: Horse Bodyweight Ratio in Horseback Riding

As obesity is a serious problem in the human population, overloading of the horse's thoracolumbar region often affects sport and school horses. The advances in using infrared thermography (IRT) to assess the horse's back overload will shortly integrate the IRT-based rider-horse fit into everyday equine practice. This study aimed to evaluate the applicability of entropy measures to select the most informative measures and color components, and the accuracy of rider:horse bodyweight ratio detection. Twelve horses were ridden by each of the six riders assigned to the light, moderate, and heavy groups. Thermal images were taken pre- and post-exercise. For each thermal image, two-dimensional sample (SampEn), fuzzy (FuzzEn), permutation (PermEn), dispersion (DispEn), and distribution (DistEn) entropies were measured in the withers and the thoracic spine areas. Among 40 returned measures, 30 entropy measures were exercise-dependent, whereas 8 entropy measures were bodyweight ratio-dependent. Moreover, three entropy measures demonstrated similarities to entropy-related gray level co-occurrence matrix (GLCM) texture features, confirming the higher irregularity and complexity of thermal image texture when horses worked under heavy riders. An application of DispEn to red color components enables identification of the light and heavy rider groups with higher accuracy than the previously used entropy-related GLCM texture features.

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.

Three-dimensional dispersion entropy for uterine fibroid texture quantification and post-embolization evaluation

BACKGROUND AND OBJECTIVE

Uterine fibroids are benign tumors that could lead to symptoms complicating a patient's daily life. Those fibroids can be treated using uterine fibroid embolization (UFE), an effective non-surgical procedure. However, objectively quantifying the benefits of such a procedure, and the patient's quality of life, is rather challenging.

METHODS

With a novel multiscale three-dimensional (3D) entropy-based texture analysis, the multiscale 3D dispersion entropy (MDispEn_3D), this work aims to objectively quantify the evolution -  after UFE  -  of patients' health in terms of quality of life, symptoms severity, and sexual function. For this purpose, clinical data and magnetic resonance imaging (MRI) scans of fibroids are analyzed before UFE (D0), ten days after (D10), and six months after (M6).

RESULTS

An inverse correlation is observed between MDispEn_3D entropy values and both size and volume of fibroids. An inverse correlation is also observed between MDispEn_3D at M6 and the scores of symptoms severity. Moreover, the patient age is found to be related to the relative difference of DispEn_3D and MDispEn_3D values, between D0 and M6, translating into an increasing entropy value. Furthermore, we show that history of fibroma plays a role in determining the obtained DispEn_3D values at D0. Finally, we observe that the lower MDispEn_3D values at D0, the larger the size of the fibroid at M6.

CONCLUSIONS

The proposed MDispEn_3D method - by quantifying fibroid texture - could assist the medical doctors in the prognosis of uterine fibroids and the patients' quality of life assessment post-UFE. It could therefore favor the choice of this treatment compared to other more invasive surgical treatments.

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.

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.

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.