scholarly journals Use of fractal analysis in dental images: a systematic review

2020 ◽  
Vol 49 (2) ◽  
pp. 20180457 ◽  
Author(s):  
Camila NAO Kato ◽  
Sâmila G Barra ◽  
Núbia PK Tavares ◽  
Tânia MP Amaral ◽  
Cláudia B Brasileiro ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
English Language ◽  
Bone Structure ◽  
Cone Beam Ct ◽  
Cone Beam ◽  
Inclusion Criteria ◽  
Mineral Density ◽  
Box Counting ◽  
Cephalometric Radiograph ◽  
Box Counting Method

Objectives: This study reviewed the use of fractal analysis (FA) in dental images. Methods: A search was performed using PubMed, MEDLINE, LILACS, Web of Science and SCOPUS databases. The inclusion criteria were human studies in the English language, with no date restriction. Results: 78 articles were found in which FA was applied to panoramic radiographs (34), periapical radiographs (21), bitewing radiographs (4), cephalometric radiograph (1), cone beam CT (15), micro-CT (3), sialography (2), and ultrasound (2). Low bone mineral density (21) and systemic or local diseases (22) around the bone of dental implants were the main subjects of the study of FA. Various sizes and sites of the regions of interest were used to evaluate the bone structure. Different ways were used to treat the image and to calculate FA. FA of 43 articles showed significant differences in the comparison of groups, mainly between healthy and sick patients. Conclusions: FA in Dentistry has been widely applied to the study of images. Panoramic and periapical radiographs were those most frequently used. The Image J software and the box-counting method were extensively adopted in the studies reviewed herein. Further studies are encouraged to improve clarification of the parameters that directly influence FA.

Association of cortical shape of the mandible on panoramic radiographs with mandibular trabecular bone structure in Japanese adults: a cone-beam CT-image analysis

2013 ◽  
Vol 30 (2) ◽  
pp. 160-167 ◽  
Author(s):  
Noriyasu Mochizuki ◽  
Noriyuki Sugino ◽  
Tadashi Ninomiya ◽  
Nobuo Yoshinari ◽  
Nobuyuki Udagawa ◽  
...  
Keyword(s):  
Image Analysis ◽  
Trabecular Bone ◽  
Bone Structure ◽  
Cone Beam Ct ◽  
Trabecular Bone Structure ◽  
Cone Beam ◽  
Ct Image ◽  
Panoramic Radiographs ◽  
Japanese Adults ◽  
Ct Image Analysis

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

scholarly journals Binarization methods and investigation of their influence on the fractal dimension of functional coatings

2020 ◽  
pp. 30-42
Author(s):  
Anna Zhurba ◽  
Michail Gasik
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Quantitative Characteristic ◽  
Image Binarization ◽  
Counting Method ◽  
Functional Coatings ◽  
Binary Images ◽  
Box Counting ◽  
Box Counting Method ◽  
Binarization Threshold

An essential element of fractal analysis of functional coatings is the fractal dimension, which is an important quantitative characteristic. Typically, coating images are represented as colored or halftone, and most fractal dimension algorithms are for binary images. Therefore, an important step in fractal analysis is binarization, which is a threshold separation operation and the result of which is a binary image.The purpose of the study is to study and program the methods of image binarization and to study the influence of these methods on the value of fractal dimension of functional coatings.As a result of the binarization threshold, the image is split into two regions, one containing all pixels with values below a certain threshold and the other containing all pixels with values above that threshold. Of great importance is the determination of the binarization threshold.The study analyzed a number of functional coating images, determined the fractal dimension of the image by the Box Counting method at different binarization thresholds and when applying different binarization methods (binarization with lower and upper threshold, with double restriction, and the average method for determining the optimal binarization threshold) images. The Box Counting method is used to depict any structure on a plane. This method allows us to determine the fractal dimension of not strictly self-similar objects. Each image binarization method is used for different types of images and for solving different problems.As a result, the methods of image binarization were developed and implemented, the fractal dimension of binary images was calculated, and the influence of these methods on the value of fractal dimension of functional coatings was investigated.The surfaces of composite steel structure, metallic porous materials, and natural cave structures are analyzed.

A Fractal Analysis of Human Cranial Sutures

2003 ◽  
Vol 40 (4) ◽  
pp. 409-415 ◽  
Author(s):  
Jack C. Yu ◽  
Ronald L. Wright ◽  
Matthew A. Williamson ◽  
James P. Braselton ◽  
Martha L. Abell
Keyword(s):  
Fractal Analysis ◽  
Cranial Sutures ◽  
Box Dimension ◽  
Counting Method ◽  
Scale Invariant ◽  
Box Counting ◽  
Invariant Features ◽  
Iteration Functions ◽  
Self Similar ◽  
Box Counting Method

Objectives Many biological structures are products of repeated iteration functions. As such, they demonstrate characteristic, scale-invariant features. Fractal analysis of these features elucidates the mechanism of their formation. The objectives of this project were to determine whether human cranial sutures demonstrate self-similarity and measure their exponents of similarity (fractal dimensions). Design One hundred three documented human skulls from the Terry Collection of the Smithsonian Institution were used. Their sagittal sutures were digitized and the data converted to bitmap images for analysis using box-counting method of fractal software. Results The log-log plots of the number of boxes containing the sutural pattern, Nr, and the size of the boxes, r, were all linear, indicating that human sagittal sutures possess scale-invariant features and thus are fractals. The linear portion of these log-log plots has limits because of the finite resolution used for data acquisition. The mean box dimension, Db, was 1.29289 ± 0.078457 with a 95% confidence interval of 1.27634 to 1.30944. Conclusions Human sagittal sutures are self-similar and have a fractal dimension of 1.29 by the box-counting method. The significance of these findings includes: sutural morphogenesis can be described as a repeated iteration function, and mathematical models can be constructed to produce self-similar curves with such Db. This elucidates the mechanism of actual pattern formation. Whatever the mechanisms at the cellular and molecular levels, human sagittal suture follows the equation log Nr = 1.29 log 1/r, where Nr is the number of square boxes with sides r that are needed to contain the sutural pattern and r equals the length of the sides of the boxes.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Islet Cells ◽  
Fractal Dimensions ◽  
Substantia Gelatinosa ◽  
Neuronal Populations ◽  
Box Counting ◽  
Morphological Descriptor ◽  
The Mean ◽  
Box Counting Method

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

scholarly journals Digital panoramic radiography and cone-beam CT as ancillary tools to detect low bone mineral density in post-menopausal women

2019 ◽  
Vol 48 (2) ◽  
pp. 20180254 ◽  
Author(s):  
Camila Nao Kato ◽  
Núbia PK Tavares ◽  
Sâmila G Barra ◽  
Tânia MP Amaral ◽  
Cláudia B Brasileiro ◽  
...  
Keyword(s):  
Bone Mineral Density ◽  
Bone Mineral ◽  
Panoramic Radiography ◽  
Cone Beam Ct ◽  
Cone Beam ◽  
Mineral Density ◽  
Low Bone Mineral Density ◽  
Menopausal Women ◽  
Digital Panoramic Radiography ◽  
Post Menopausal

scholarly journals QCBCT-NET for direct measurement of bone mineral density from quantitative cone-beam CT: a human skull phantom study

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tae-Hoon Yong ◽  
Su Yang ◽  
Sang-Jeong Lee ◽  
Chansoo Park ◽  
Jo-Eun Kim ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Cone Beam Ct ◽  
Structural Similarity ◽  
Training Data ◽  
Cone Beam ◽  
Absolute Difference ◽  
Mineral Density ◽  
Quantitative Ct ◽  
Generative Adversarial Network ◽  
Adversarial Network

AbstractThe purpose of this study was to directly and quantitatively measure BMD from Cone-beam CT (CBCT) images by enhancing the linearity and uniformity of the bone intensities based on a hybrid deep-learning model (QCBCT-NET) of combining the generative adversarial network (Cycle-GAN) and U-Net, and to compare the bone images enhanced by the QCBCT-NET with those by Cycle-GAN and U-Net. We used two phantoms of human skulls encased in acrylic, one for the training and validation datasets, and the other for the test dataset. We proposed the QCBCT-NET consisting of Cycle-GAN with residual blocks and a multi-channel U-Net using paired training data of quantitative CT (QCT) and CBCT images. The BMD images produced by QCBCT-NET significantly outperformed the images produced by the Cycle-GAN or the U-Net in mean absolute difference (MAD), peak signal to noise ratio (PSNR), normalized cross-correlation (NCC), structural similarity (SSIM), and linearity when compared to the original QCT image. The QCBCT-NET improved the contrast of the bone images by reflecting the original BMD distribution of the QCT image locally using the Cycle-GAN, and also spatial uniformity of the bone images by globally suppressing image artifacts and noise using the two-channel U-Net. The QCBCT-NET substantially enhanced the linearity, uniformity, and contrast as well as the anatomical and quantitative accuracy of the bone images, and demonstrated more accuracy than the Cycle-GAN and the U-Net for quantitatively measuring BMD in CBCT.

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