Texture descriptors by a fractal analysis of three-dimensional local coarseness

Florindo, João Batista; Landini, Gabriel; Bruno, Odemir Martinez

doi:10.1016/j.dsp.2015.03.013

Cited by 11 publications

(3 citation statements)

References 35 publications

(75 reference statements)

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“…84 The use of reference or calibration images, similar to the Brodatz images used in digital imaging for texture classification, 85,86 would be extremely useful to researchers and developers, and could enable better calibration of and comparison between image-analysis tools and datasets.…”

Section: Challenges Of Fractal Analysismentioning

confidence: 99%

Lung cancer—a fractal viewpoint

et al. 2015

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Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.

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Section: Challenges Of Fractal Analysismentioning

confidence: 99%

Lung cancer—a fractal viewpoint

et al. 2015

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“…All vertices of a 3D model are the center of dilation spheres in which the dilation radius is variable r. V(r) is the influence volume of all spheres after the dilation process, while r represents an absolute value of 1, and this is the resolution of the mesh in the 3D model (0.2 mm in the present study; Florindo et al, 2015;Vorsatz et al, 2021). The fractal dimension (D) was calculated for every model with dilation radii of 3-20 (Reichert et al, 2017;Vorsatz et al, 2021), while log[V(r)] was estimated using the 3D Bouligand-Minkowski toolbox, which is available at no cost at https://www.facom.ufu.br/~backe s/mink3d.html.…”

Section: Evaluation Of the Oi Relative To Other Surface Complexity Qu...mentioning

confidence: 99%

A new index for quantifying the ornamentational complexity of animals with shells

Miao

Dai

Song

et al. 2022

Ecology and Evolution

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“…Figure 1 shows four figures (four patterns): a Euclidean shape, the Koch curve, the Sierpinski triangle and the Sierpinski carpet, with the fractal dimensions equaling 1.000, 1.262, 1.585 and 1.896, respectively. Fractal dimension is a measure of the complexity and irregularity of an object [19,[27][28][29].…”

Section: Methodsmentioning

confidence: 99%

Fractal dimension in textures analysis of xenotransplants

Borowska

Borys

Szarmach

et al. 2017

SIViP

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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.

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Texture descriptors by a fractal analysis of three-dimensional local coarseness

Cited by 11 publications

References 35 publications

Lung cancer—a fractal viewpoint

Lung cancer—a fractal viewpoint

A new index for quantifying the ornamentational complexity of animals with shells

Fractal dimension in textures analysis of xenotransplants

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