A survey on fractal dimension for fractal structures

Fernández–Martínez, M.

doi:10.21042/amns.2016.2.00037

Cited by 30 publications

(10 citation statements)

References 35 publications

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“…To deal with the construction of the curve α, we refer the reader to ([14], Section 2.4). For additional details regarding this mathematica invariant, we refer the reader to [15].…”

Section: Discussionmentioning

confidence: 99%

Characteristics and dimensions of the infraorbital canal: a radiographic analysis using cone beam computed tomography (CBCT)

2018

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The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann-Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53.67 years with a standard deviation of 8.20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

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“…To deal with the construction of the curve α, we refer the reader to ([14], Section 2.4). For additional details regarding this mathematica invariant, we refer the reader to [15].…”

Section: Discussionmentioning

confidence: 99%

Characteristics and dimensions of the infraorbital canal: a radiographic analysis using cone beam computed tomography (CBCT)

2018

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“…We would like to point out that fractal structures allow a deep study of generalized fractal dimension models (c.f. [2]).…”

Section: Theorem 22 ([4]mentioning

confidence: 99%

A novel approach to improve the accuracy of the box dimension calculations: Applications to trabecular bone quality

Fernández–Martínez¹,

Sánchez²,

López‐Jornet³

2019

Discrete &Amp; Continuous Dynamical Systems - S

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Fractal dimension and specifically, box-counting dimension, is the main tool applied in many fields such as odontology to detect fractal patterns applied to the study of bone quality. However, the effective computation of such invariant has not been carried out accurately in literature. In this paper, we propose a novel approach to properly calculate the fractal dimension of a plane subset and illustrate it by analysing the box dimension of a trabecular bone through a computed tomography scan.

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“…To deal with the construction of the curve α, we refer the reader to ( [14], Section 2.4). For additional details regarding this mathematica invariant, we refer the reader to [15].…”

Section: Acknowledgmentsmentioning

confidence: 99%

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

et al. 2019

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The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann–Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53 . 67 years with a standard deviation of 8 . 20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

show abstract

A survey on fractal dimension for fractal structures

Cited by 30 publications

References 35 publications

Characteristics and dimensions of the infraorbital canal: a radiographic analysis using cone beam computed tomography (CBCT)

Characteristics and dimensions of the infraorbital canal: a radiographic analysis using cone beam computed tomography (CBCT)

A novel approach to improve the accuracy of the box dimension calculations: Applications to trabecular bone quality

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

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