Fracture Surface Fractal Dimension Determined Through An Extensive 3-D Reconstruction

1995 ◽  
Vol 409 ◽  
Author(s):  
J.J. Ammann ◽  
A.M. Nazar
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface ◽  
Cross Correlation ◽  
Synthetic Image ◽  
Stereo Pair ◽  
Matching Algorithm ◽  
Contour Lines ◽  
Reconstructed Surface ◽  
Third Dimension ◽  
Slit Island Method

AbstractAn efficient image processing method is developed to determine the fractal dimension from a high resolution 3-D reconstruction of fracture surface. The third dimension of the fracture surface is obtained from a stereo pair. The elevation is locally determined through a recursive window matching algorithm centered on the cross-correlation operation. The method allows to reach high vertical and horizontal resolutions of the elevation map.The fractal dimension is obtained by an implementation of the slit-island method. A series of contour lines is extracted from the reconstructed surface. The images of the contour lines are progressively reduced in size and at every step the curve length is estimated. The result is then normalized according to the scale factor to build a Kolmogorov plot.The performance of this method is demonstrated on a synthetic image generated by a fracture surface mathematical model.

Fractal dimension of the fracture surface of porous ZrO2 – MgO composite

2020 ◽  
pp. 74-82
Author(s):  
A. S. Buyakov ◽  
◽  
Yu. A. Zenkina ◽  
S. P. Buyakova ◽  
S. N. Kulkov ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface

Fractal Dimension of the Fracture Surface of Porous ZrO2–MgO Composite

2020 ◽  
Vol 11 (5) ◽  
pp. 1253-1259
Author(s):  
A. S. Buyakov ◽  
Yu. A. Zenkina ◽  
S. P. Buyakova ◽  
S. N. Kulkov
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface

Three-Dimensional Microsphere Tracking Using Off-Focus Images Based on Cross-Correlation Matching Algorithm

2015 ◽  
Vol 35 (2) ◽  
pp. 0212002
Author(s):  
谢湘军 Xie Xiangjun ◽  
雷海 Lei Hai ◽  
常新宇 Chang Xinyu ◽  
曾雅楠 Zeng Yanan ◽  
胡晓东 Hu Xiaodong ◽  
...  
Keyword(s):  
Cross Correlation ◽  
Three Dimensional ◽  
Matching Algorithm ◽  
Correlation Matching

Fractal dimension of fracture surface and superplasticity of 7475 Al alloy

1993 ◽  
Vol 12 (20) ◽  
pp. 1616-1618 ◽  
Author(s):  
J. Xinggang ◽  
C. Jianzhong ◽  
M. Longxiang
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface ◽  
Al Alloy

CONFORMAL INVARIANCE OF CONTOUR LINES ON THE (2 + 1)-DIMENSIONAL RESTRICTED SOLID-ON-SOLID SURFACE

2011 ◽  
Vol 25 (04) ◽  
pp. 255-264 ◽  
Author(s):  
WEI ZHOU ◽  
GANG TANG ◽  
KUI HAN ◽  
HUI XIA ◽  
DA-PENG HAO ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Solid Surface ◽  
Large Scale ◽  
Fractal Dimensions ◽  
Universality Class ◽  
Invariant Curves ◽  
Conformal Invariant ◽  
Contour Lines ◽  
Loewner Evolution ◽  
Scale Limit

The contour lines of the saturated surface of the (2 + 1)-dimensional restricted solid-on-solid (RSOS) growth model are investigated by numerical method. It is shown that the calculated contour lines are conformal invariant curves with fractal dimension df = 1.34, and they belong to the universality class at large-scale limit, called the Schramm–Loewner evolution with diffusivity κ = 4. This is identical to the value obtained from the inverse cascade of surface quasigeostrophic (SQG) turbulence [Phys. Rev. Lett.98 (2007) 024501]. We also found that the measured fractal dimensions of contours on the (2 + 1)-dimensional RSOS saturated surfaces do not coincide well with that of SLE4 df = 1 + κ/8.

scholarly journals Fracture Surface Fractal Characteristics of Alkali-Slag Concrete under Freeze-Thaw Cycles

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Wantong Cai ◽  
Guoping Cen ◽  
Haifu Wang
Keyword(s):  
Fracture Toughness ◽  
Fractal Dimension ◽  
Fracture Surface ◽  
Fractal Theory ◽  
Damage Zone ◽  
Freezing And Thawing ◽  
Freeze Thaw ◽  
Force Direction ◽  
Fractal Characteristics ◽  
Slag Content

Fractal theory is introduced in fracture surface research of alkali-slag concrete (ASC) under freeze-thaw cycles; crack distribution of ASC fracture surface and freeze-thaw damage zone were calculated. Through fractal analysis of ASC sample fracture surfaces, relevance between section fractal dimension and fracture toughness and relationship between material composition and section fractal dimension are clarified. Results show that the specimen’s cracks before freeze-thaw extend along force direction gently, and there are more twists and turns after freezing and thawing; the fractal dimension D also grows from 1.10 to 1.33. SEM internal microcracks’ D of ASC internal microstructure after freezing and thawing is 1.37; 0 to 300 times ASC fractal dimension under freezing and thawing is between 2.10 and 2.23; with freeze-thaw times increasing, ASC fracture toughness decreases and fractal dimension increases, the fractal dimension and fracture toughness have a good linear relationship, and the fractal dimension can reflect the toughening effect of ASC. It is very feasible to evaluate ASC fracture behaviour under freezing and thawing with the fractal theory. Fractal dimension generally increases with activator solution-slag (A/S for short) or slag content. The greater the amount of A/S or slag content, the lower the dimension.

scholarly journals From the slit-island method to the Ising model: Analysis of irregular grayscale objects

2014 ◽  
Vol 24 (1) ◽  
pp. 49-63 ◽  
Author(s):  
Przemysław Mazurek ◽  
Dorota Oszutowsk A-M Ażurek
Keyword(s):  
Image Analysis ◽  
Fractal Dimension ◽  
Ising Model ◽  
Image Data ◽  
Input Image ◽  
Cell Nuclei ◽  
Cervical Cell ◽  
Atypical Cells ◽  
Model Context ◽  
Slit Island Method

Abstract The Slit Island Method (SIM) is a technique for the estimation of the fractal dimension of an object by determining the area- perimeter relations for successive slits. The SIM could be applied for image analysis of irregular grayscale objects and their classification using the fractal dimension. It is known that this technique is not functional in some cases. It is emphasized in this paper that for specific objects a negative or an infinite fractal dimension could be obtained. The transformation of the input image data from unipolar to bipolar gives a possibility of reformulated image analysis using the Ising model context. The polynomial approximation of the obtained area-perimeter curve allows object classification. The proposed technique is applied to the images of cervical cell nuclei (Papanicolaou smears) for the preclassification of the correct and atypical cells.

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