Maximum entropy, fractal dimension and lacunarity in quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation

Neves, Leandro Alves; Oliveira, Fabiane Nunes De; Peres, Fernando Augusto; Moreira, Roberto Douglas; Moriel, A R; Godoy, Moacir Fernandes de; Murta, Leonardo

doi:10.1088/1742-6596/285/1/012032

Cited by 8 publications

(3 citation statements)

References 15 publications

(16 reference statements)

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“…Fractal dimension is connected to the fractal nature of a geometric object and is connected to the Hausdorff dimension [36] and is usually estimated through such dimension for a graphical object or texture [39]. However, we cannot estimate the fractal dimension D this way for a univariate time series and it is needed to use an alternative estimators used for time seriesperiodogram estimator [14], Genton estimator [23], Hall-Wood estimator [26] and wavelet-based estimator [25,43].…”

Section: Efficient Market and Fractal Dimensionmentioning

confidence: 99%

Measuring capital market efficiency: Global and local correlations structure

Krištoufek

Vošvrda

2013

Physica A: Statistical Mechanics and its Applications

148

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We introduce a new measure for the capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. We find that the Japanese NIKKEI is the most efficient market. From geographical point of view, the more efficient markets are dominated by the European stock indices and the less efficient markets cover mainly Latin America, Asia and Oceania. The inefficiency is mainly driven by a local herding, i.e. a low fractal dimension.

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Section: Efficient Market and Fractal Dimensionmentioning

confidence: 99%

Measuring capital market efficiency: Global and local correlations structure

Krištoufek

Vošvrda

2013

Physica A: Statistical Mechanics and its Applications

148

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“…Fractal dimension measures the complexity of organization of pixels in a particular area and it shows how much space is filled in. Lacunarity is an index of measurement of emptiness or rather space in the fractal objects, the degree of inhomogeneity, and translational and rotational variance in the images (Plotnick et al 1993, Smith et al 1996, Iftekharuddin et al 2003, Lopes and Betrouni 2009, Neves et al 2011. Lacunarity assesses the way in which pixels are distributed and organized in a particular area of the image and it quantifies how the space or gaps are filled in.…”

Section: Introductionmentioning

confidence: 99%

Fractal analysis: fractal dimension and lacunarity from MR images for differentiating the grades of glioma

2015

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Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.

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“…On the other hand, the features of LAC are used as a measure for evaluating how the space is filled. The FD feature has been applied successfully in studies of prostatic cancer [23], relationship between aging and decreasing of the vascular complexity of the retina [24], analysis of periapical lesions [25], quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation [26] and analysis of the brain white matter, age and sex [27].…”

Section: Introductionmentioning

confidence: 99%

Features based on the percolation theory for quantification of non-Hodgkin lymphomas

Roberto

Neves

Nascimento

et al. 2017

Computers in Biology and Medicine

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Non-Hodgkin lymphomas are a health problem that affects over 70,000 people per year in the United States alone. The early diagnosis and the identification of this lymphoma are essential for an effective treatment. The classification of non-Hodgkin lymphomas is a task that continues to rank as one of the main challenges faced by hematologists, pathologists, as well as in the producing of computer vision methods due to its inherent complexity. In this paper, we present a new method to quantify and classify tissue samples of non-Hodgkin lymphomas based on the percolation theory. The method consists of associating multiscale and multidimensional approaches in order to divide the image into smaller regions and then verifying color similarity between pixels. A cluster labeling algorithm was applied to each region of interest to obtain the values for the number of clusters, occurrence of percolation and coverage ratio of the largest cluster. The method was tested on different classifiers aiming to differentiate three different groups of non-Hodgkin lymphomas. The obtained results (AUC rates between 0.940 and 0.993) were compared to those provided by methods consolidated in the Literature, which indicates that the percolation theory is a suitable approach for identifying these three classes of non-Hodgkin lymphomas, those being: mantle cell lymphoma, follicular lymphoma and chronic lymphocytic leukemia.

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Maximum entropy, fractal dimension and lacunarity in quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation

Cited by 8 publications

References 15 publications

Measuring capital market efficiency: Global and local correlations structure

Measuring capital market efficiency: Global and local correlations structure

Fractal analysis: fractal dimension and lacunarity from MR images for differentiating the grades of glioma

Features based on the percolation theory for quantification of non-Hodgkin lymphomas

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