Quantitative texture measurement of gray-scale images: Fractal dimension using an improved differential box counting method

Panigrahy, Chinmaya; Seal, Ayan; Mahato, Nihar Kumar

doi:10.1016/j.measurement.2019.106859

Cited by 37 publications

(12 citation statements)

References 33 publications

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“…The XY-plane presents the image plane which is partitioned into grids of size r×r pixels. By the way, z coordinate denotes the intensity value of the gray-scale image [23]. The total number of boxes that cover the rough surface of the gray-scale image can be calculated and recorded corresponding to the box size r. For both the flame edge and the gray-level intensity surface of the flame image, analysis of the number of boxes versus the box size curve gives the fractal dimension.…”

Section: Methodology Of Fractal Analysismentioning

confidence: 99%

Fractal Analysis of Butanol/Gasoline Surrogate Blends Combustion in an Optical Direct-Injection Engine

Sun¹,

2021

ICLASS

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Fractal characteristics of the flame front surface and the internal flow field was experimentally observed during the propagation of the flame in the cylinder. The calculation and analysis of the flame fractal dimension based on the flame image are essential to understand the flame structure and assess its combustion quality. This paper established a fractal analysis method to predict flame characteristics. A gasoline direct injection (GDI) engine fuelled with the butanol isomer/gasoline surrogate blends of different proportions was used to get the flame images, and the box-counting method was used to calculate the fractal dimension of the flame edge in the image plane and the gray-scale intensity surface of the premixed flame region. The apparent flame speed and the area ratio of flame were calculated from the flame image and comprehensively analysed together with fractal dimension. Results showed that the addition of butanol to the gasoline surrogates makes flame propagation speed slower except TPRF-nB, and the flame propagating speed increases with a higher fractal dimension. However, the fractal dimension of the two-dimensional flame edge is unstable and unreliable due to its poor resistance against external disturbances. So, it is a better method to combine two-dimensional and three-dimensional fractal analysis, which could predict the flame speed more accurately.

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Section: Methodology Of Fractal Analysismentioning

confidence: 99%

Fractal Analysis of Butanol/Gasoline Surrogate Blends Combustion in an Optical Direct-Injection Engine

Sun¹,

2021

ICLASS

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“…They also proposed an overlapping grid partitioning approach to address box over- and undercounting problems along the xy -axis, where two nearby grids overlap by one row and one column. However, several shortcomings in this method have been identified in previous literature [ 23 ].…”

Section: Introductionmentioning

confidence: 99%

“…The choice of grid size for a square image impacts how the plane is partitioned during computing. The original DBC approach was based on consecutive integer partitioning, which discards areas that cannot be partitioned in an integer manner [ 23 ]. Currently, this strategy is frequently used in studies of state-of-the-art DBC methods [ 22 , 26 , 30 , 31 ].…”

Section: Introductionmentioning

confidence: 99%

Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy

Jiang

Liu

et al. 2022

Entropy

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The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate parameter choices, limiting the calculation accuracy. Many studies have been conducted to increase the algorithm’s computational accuracy by improving the calculating parameters of the differential box-counting method. The grid size is a crucial parameter for the DBC method. Generally, there are two typical ways for selecting the grid size in relevant studies: consecutive integer and divisors of image size. However, both methods for grid size selection are problematic. The consecutive integer method cannot partition the image entirely and will result in the undercounting of boxes; the divisors of image size can partition the image completely. However, this method uses fewer grid sizes to compute fractal dimensions and has a relatively huge distance error (DE). To address the shortcomings of the above-mentioned two approaches, this research presents an improved grid size selection strategy. The improved method enhances computational accuracy by computing the discarded image edge areas in the consecutive integer method, allowing the original image information to be used as thoroughly as the divisor strategy. Based on fractional Brownian motion (FBM), Brodatz, and Aerials image sets, the accuracy of the three grid size selection techniques (consecutive integer method, divisors of image size method, and the improved algorithm) to compute the fractal dimension is then compared. The results reveal that, compared to the two prior techniques, the revised algorithm described in this study minimizes the distance error and increases the accuracy of the fractal dimension computation.

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“…It was found that the fractal dimension is mainly affected by the cutting speed and the feed rate. Fractal dimension can help measure surface roughness [9,10] and predict surface roughness [11]. Fractal analysis is also used as a criterion to investigate thin-layer surfaces [12] and soft layers [13].…”

Section: Introductionmentioning

confidence: 99%

Assessment of the Possibility of Using Fractal Analysis to Describe the Surface Aluminum Composites After Turning

Karolczak¹,

Kowalski²,

Raszka³

2021

Adv. Sci. Technol. Res. J.

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Quantitative texture measurement of gray-scale images: Fractal dimension using an improved differential box counting method

Cited by 37 publications

References 33 publications

Fractal Analysis of Butanol/Gasoline Surrogate Blends Combustion in an Optical Direct-Injection Engine

Fractal Analysis of Butanol/Gasoline Surrogate Blends Combustion in an Optical Direct-Injection Engine

Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy

Assessment of the Possibility of Using Fractal Analysis to Describe the Surface Aluminum Composites After Turning

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