Fractal Dimension Estimation Methods for Biomedical Images

Napolitano, Antonio; Ungania, Sara; Cannatà, Vittorio

doi:10.5772/48760

Cited by 24 publications

(19 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…41 The fractal analyses depend on the fractal analysis methods, including the algorithm and specific calculation used. 22,27,31,36,39,40 In our study, the most appropriate method of fractal analysis for the analyzed surfaces is morphological envelopes. 23 In this method 26 the upper and lower envelopes are calculated by morphological opening and closing using a structuring element which is a horizontal line segment of length e. The graph of the calculated volume for surfaces (Ve) is drawn as a function of the scale (size of the structuring elements): ln(Ve)/ln(e).…”

Section: Fractal Analysis Of the Texturementioning

confidence: 99%

“…22 It also determines how the fractal differs from Euclidean objects. 36,37,39 There are many computational approaches for estimating the fractal dimension, 22,27,31,36,40 including box-counting, mass--radius, and density-density correlation function method. In ophthalmology, fractal and multifractal analyses have been applied for the quantitative description of irregular surface microstructures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

et al. 2014

View full text Add to dashboard Cite

The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.

show abstract

Section: Fractal Analysis Of the Texturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Fractal objects are characterized by: self-similarity, large degree of heterogeneity and lack of a well-defined scale [22,23]. "Self-similarity" refers to the resemblance of small-scale structures of the fractal set to its large-scale structures.…”

Section: Methodsmentioning

confidence: 99%

“…The box-counting dimension (also called capacitive dimension) [22,24,[30][31][32] is determined by the formula [30]: where δ is the length of one side of a square cell of the grid and N (δ) is the number of square cells which contain elements of the study area. In practice, while calculating the box-counting dimension on the basis of a two-dimensional image, the object must be covered with a square grid with a known length of the side of a mesh.…”

Section: Box-counting Dimensionmentioning

confidence: 99%

Fractal dimension in textures analysis of xenotransplants

Borowska

Borys

Szarmach

et al. 2017

SIViP

View full text Add to dashboard Cite

Evaluation of the effectiveness of the healing process in postresectal and postcystal bone loss cases using techniques guided bone regeneration, observed within 1-year-long period. Radiographic images of 20 patients (17 females and 8 males) who had undergone xenotransplantation to fill jawbone losses were analyzed. The combination therapy of intraosseous deficits following xenotransplantation consisted of bone augmentation with xenogenic material together with covering regenerative membranes and tight wound closure. The bone regeneration process was estimated comparing the images taken on the day of the surgery and 12 months later, by means of digital radiography set Kodak RVG 6100. The interpretation of the RVG image depends on the assessment ability of the eye looking at it, which gives a large margin of uncertainty. Areas of interest were separated from radiographic images and binarized. On the basis of those fragments, box-counting dimension (D B ) and information dimension (D I ) were calculated. fractal dimension equals 1.0 right after the surgery and 1.6 after a year after the bone treatment, and we could use image segmentation to efficiently find fragments where this value differs from those acquired in the course of tests and quicken diagnostics of irregularities in bone tissue regeneration.

show abstract

“…This method measures a fractal dimension (D f ), a real number that represents pattern complexity, and inner self-similarity as calculated on different spatial scales [Napolitano et al, 2012;Qian et al, 2012;AlMamun et al, 2014]. Biomedically, D f has also been used as a numerical measure of retinal vascular branching [Liew et al, 2008;Cheung et al, 2014], neuronal branching and extension [Milo sević et al, 2007;Shigetomi et al, 2013] and mammary epithelial ducting networks [Fuseler et al, 2014].…”

Section: Introductionmentioning

confidence: 99%

A spatiotemporal characterization method for the dynamic cytoskeleton

et al. 2016

View full text Add to dashboard Cite

The significant gap between quantitative and qualitative understanding of cytoskeletal function is a pressing problem; microscopy and labeling techniques have improved qualitative investigations of localized cytoskeleton behavior, whereas quantitative analyses of whole cell cytoskeleton networks remain challenging. Here we present a method that accurately quantifies cytoskeleton dynamics. Our approach digitally subdivides cytoskeleton images using interrogation windows, within which box-counting is used to infer a fractal dimension (D f ) to characterize spatial arrangement, and gray value intensity (GVI) to determine actin density. A partitioning algorithm further obtains cytoskeleton characteristics from the perinuclear, cytosolic, and periphery cellular regions. We validated our measurement approach on Cytochalasin-treated cells using transgenically modified dermal fibroblast cells expressing fluorescent actin cytoskeletons. This method differentiates between normal and chemically disrupted actin networks, and quantifies rates of cytoskeletal degradation. Furthermore, GVI distributions were found to be inversely proportional to D f , having several biophysical implications for cytoskeleton formation/degradation. We additionally demonstrated detection sensitivity of differences in D f and GVI for cells seeded on substrates with varying degrees of stiffness, and coated with different attachment proteins. This general approach can be further implemented to gain insights on dynamic growth, disruption, and structure of the cytoskeleton (and other complex biological morphology) due to biological, chemical, or physical stimuli. V C 2016The Authors. Cytoskeleton Published by Wiley Periodicals, Inc.

show abstract

Fractal Dimension Estimation Methods for Biomedical Images

Cited by 24 publications

References 21 publications

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

Fractal dimension in textures analysis of xenotransplants

A spatiotemporal characterization method for the dynamic cytoskeleton

Contact Info

Product

Resources

About