Improved Triangle Box-Counting Method for Fractal Dimension Estimation

Kaewaramsri, Yothin; Woraratpanya, Kuntpong

doi:10.1007/978-3-319-19024-2_6

Cited by 13 publications

(7 citation statements)

References 6 publications

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“…Sometimes (I max − I min + 1) ≈ G, which is almost same to the box height used in [13,14,[18][19][20][21][22].…”

Section: Box Heightmentioning

confidence: 87%

“…In [13,14,[18][19][20][21][22], authors used a box height, h = s×G M , for their work. When M ≤ G then this box height becomes very large hence fails in providing accurate FD.…”

Section: Box Heightmentioning

confidence: 99%

“…Authors used the grid sizes as only the divisors of the image size. In [19], Kaewaramsri et al partitioned the square grid into two triangular grids to obtain better precision of box count. Interested readers can find various modifications of DBC in [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

Panigrahy

García‐Pedrero

Seal

et al. 2017

Entropy

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Abstract:The Fractal Dimension (FD) of an image defines the roughness using a real number which is highly associated with the human perception of surface roughness. It has been applied successfully for many computer vision applications such as texture analysis, segmentation and classification. Several techniques can be found in literature to estimate FD. One such technique is Differential Box Counting (DBC). Its performance is influenced by many parameters. In particular, the box height is directly related to the gray-level variations over image grid, which badly affects the performance of DBC. In this work, a new method for estimating box height is proposed without changing the other parameters of DBC. The proposed box height has been determined empirically and depends only on the image size. All the experiments have been performed on simulated Fractal Brownian Motion (FBM) Database and Brodatz Database. It has been proved experimentally that the proposed box height allow to improve the performance of DBC, Shifting DBC, Improved DBC and Improved Triangle DBC, which are closer to actual FD values of the simulated FBM images.

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“…Sometimes (I max − I min + 1) ≈ G, which is almost same to the box height used in [13,14,[18][19][20][21][22].…”

Section: Box Heightmentioning

confidence: 87%

“…In [13,14,[18][19][20][21][22], authors used a box height, h = s×G M , for their work. When M ≤ G then this box height becomes very large hence fails in providing accurate FD.…”

Section: Box Heightmentioning

confidence: 99%

See 1 more Smart Citation

An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

Panigrahy

García‐Pedrero

Seal

et al. 2017

Entropy

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“…Using the reconstructed images, the PIV algorithm developed allowed us to determine flocs characteristics like size and position. Also, with the reconstructed images two algorithms for the box-counting method were also implemented, the classical BC according to [12] and the Triangular Box Counting method (TBC) [13] in order to obtain the fractal dimension of flocs.…”

Section: Figure 2 Experimental Setup For Tests In Rotating Annular Fl...mentioning

confidence: 99%

“…By means of hologram reconstruction, the form and size of particles were obtained. With the use of the box-counting method [12] and the Triangular Box Counting method (TBC) [13], the fractal dimension of the aggregates was obtained. The results show significant differences in the aggregates' fractal dimension (thus aggregate compaction in both rivers).…”

Section: Introductionmentioning

confidence: 99%

Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers

Mondragon

Aragón

Salinas-Tapia

et al. 2022

Water

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Sampling programs for suspended sediment were carried out in the Usumacinta River and its tributary Grijalva River in Mexico during the years 2016 and 2017. Suspended sediment samples collected during these sampling programs were analyzed in the laboratory using a Rotating Annular Flume (RAF) fitted with a Particle Tracking Velocimetry (PTV) to obtain the 2D images of the suspended sediment particles as they were undergoing floc reconstruction, and subsequently using a glass settling column fitted with inline digital holography set up to obtain 3D holograms of the fully flocculated sediment particles. From these high-resolution hologram images, the fractal dimension of the flocculated sediment particles was obtained using the classical box-counting method and an improved Triangular box-counting method. The estimated fractal dimension of flocculated sediment, which is a measure of floc compactness and structure that control the settling velocity of flocculated sediment was used to validate two empirical models to estimate the fractal dimension in terms of the floc sizes of suspended sediments of these two rivers. It is shown in this study that the floc characteristic can be analyzed in laboratory experiments after floc reconstruction with the use of an RAF and it offers a viable alternative to the costly in-situ sampling that is often carried out in ocean research. The digital holography method employed in this research offers an efficient methodology to obtain the floc fractal dimension. Regarding the innovative aspects and new contribution to science, we can say that we have developed a laboratory protocol to test river waters to establish floc properties such as fractal dimensions of flocs in this research which will help to test river waters on a routine basis with manageable costs. We can also say that we have developed models to predict the relationship between floc fractal dimension and floc size, which did not exist before.

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