FRACTAL IMAGE ANALYSIS OF NATURAL SCENES AND MEDICAL IMAGES

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 463-468 ◽  
Author(s):  
TAKASHI SATO ◽  
MAKOTO MATSUOKA ◽  
HIDEKI TAKAYASU
Keyword(s):  
Normal Tissue ◽  
Medical Images ◽  
Video Data ◽  
Natural Scenes ◽  
Counting Method ◽  
Fractal Image ◽  
Box Counting ◽  
The Difference ◽  
Box Counting Method ◽  
Color Map

We construct color map images of fractal dimension distribution from natural scenes and medical images by applying the box-counting method locally. The map images clearly show the difference between clouds and rocks, as well as between cancer parts and normal tissue in the colon. The method is simple and may be expected to be applicable to a real-time video-data processing.

Effect of Perma-Zyme on Properties of Tabia Used to Protect Ancient Earthen Ruins

2011 ◽  
Vol 243-249 ◽  
pp. 327-334
Author(s):  
Hong Tao Peng ◽  
Qi Zhang ◽  
Nai Sheng Li ◽  
De Fa Wang
Keyword(s):  
Color Difference ◽  
Box Dimension ◽  
Unconfined Compression ◽  
Counting Method ◽  
Sem Images ◽  
Box Counting ◽  
The Difference ◽  
Box Counting Method ◽  
The One ◽  
Sem Microstructure

Perma-Zyme is an enzymatic stabilizer. To test the feasibility of adding Perma-Zyme to tabia used to protect ancient earthen ruins, the 28d unconfined compression strength, permeability and color-difference were tested to determine the difference between the tabia and tabia treated with Perma-Zyme. The experimental results show that the 28d unconfined compression strengths of specimens treated with Perma-Zyme are higher than those without Perma-Zyme, and the color-difference(DE*) between the tabia and tabia mixed Perma-zyme is larger than 3(suggested color tolerance Chinese standardized GB/T 15608-2006), and the permeability coefficient of tabia mixed Perma-Zyme is smaller than that without Perma-Zyme, i.e., has better impermeability. Box dimension values of SEM images(with different scale bars) of samples were computed by box-counting method. Box dimension values of SEM images of the same sample are different on different scale bars. The analysis shows that SEM microstructure of the tabia sample treated with Perma-Zyme is finer and denser than the one without Perma-Zyme.

Optimal Vertex Interval Determination for Efficient Shoreline Length Calculation

2020 ◽  
Author(s):  
Hee Sook Woo ◽  
Kwang Seok Kwon ◽  
Byung Guk Kim
Keyword(s):  
Land Management ◽  
National Policy ◽  
Fractal Dimensions ◽  
Original Data ◽  
Policy Formulation ◽  
Grid Size ◽  
Counting Method ◽  
Box Counting ◽  
The Difference ◽  
Box Counting Method

<p>Coastline extraction and decisions have important implications for efficient land management and national policy formulation. Therefore, shorelines should be determined in a reasonable manner, and consistent results should be produced for the same area. This must be calculated efficiently. For example, simple shoreline areas should be constructed using relatively large vertex intervals (point-to-point distances) for efficiency, while complex shoreline areas should be constructed using small vertex intervals, thus improving accuracy. In this study, we suggest an optimum vertex interval that can represent more than 99.7% (3σ) of the original shoreline data using a grid generated by applying a box-counting method. All coastline areas were gridded using 11 grid sizes. Generalization was performed on the shorelines contained within each grid, and the sum of the generalized shoreline lengths was calculated. As the grid size used increases, the shoreline will become more simplified, and the difference from the original data will increase. As the grid size decreases, the more precisely the shoreline will be represented, and the sum will be similar to the original value. As a result of regression analysis, using the sum of the generalized shoreline length, we could predict the vertex interval that would represent more than 99.7% (3σ) of the original data. For the experiment, three regions with distinct coastline characteristics were selected. The grid was generated by the box-counting method, a representative fractal technique, and the vertex interval was estimated. From this, the fractal dimension was then calculated. As a result of the experiment, it was confirmed that the area A had a vertex interval of 0.7m, and the areas B and C had vertex intervals of 1m. These optimal vertex interval values mean that when the coastline was reconstructed, it was the closest, efficient representation of the actual coastline. Furthermore, these interval values suggest that the area A has a more complex coastline, and therefore the coastline should be constructed with a smaller vertex interval than the other areas. Using fractal dimensions, we also found that the area B has a more complex coastline than the area C. Overall, we confirmed that the optimal vertex interval for the accurate and efficient construction of the shoreline is able to be calculated by the approach presented in this paper. This research is expected to contribute to efficient land management and national policy establishment and progress. </p>

scholarly journals Box-Counting Method of 2D Neuronal Image: Method Modification and Quantitative Analysis Demonstrated on Images from the Monkey and Human Brain

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Nemanja Rajković ◽  
Bojana Krstonošić ◽  
Nebojša Milošević
Keyword(s):  
Dentate Nucleus ◽  
Dendritic Tree ◽  
Scaling Factor ◽  
Image Method ◽  
Image Size ◽  
Counting Method ◽  
Box Counting ◽  
The Difference ◽  
Box Counting Method ◽  
Shape Complexity

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of 2D neuronal images from the human neostriatum. In addition, three box dimensions (which estimate the space-filling property, the shape, complexity, and the irregularity of dendritic tree) were used to evaluate differences in the morphology of type III aspiny neurons between two parts of the neostriatum.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

Research on a precise differential box-counting method of eliminating image background

2016 ◽  
Author(s):  
Kexue Lai ◽  
Tao He ◽  
Cancan Li ◽  
Weisong Zhou ◽  
Liangen Yang
Keyword(s):  
Counting Method ◽  
Box Counting ◽  
Box Counting Method

scholarly journals Application of An Exponential Mathematical Law of Cardiac Dynamics In 16 Hours

2021 ◽  
Author(s):  
Javier Oswaldo Rodríguez Velásquez ◽  
Sandra Catalina Correra Herrera ◽  
Yesica Tatiana Beltrán Gómez ◽  
Jorge Gómez Rojas ◽  
Signed Esperanza Prieto Bohórquez ◽  
...  
Keyword(s):  
Kappa Coefficient ◽  
Medical Attention ◽  
Chaotic Attractors ◽  
Counting Method ◽  
Statistical Validation ◽  
Overlapping Grids ◽  
Box Counting ◽  
Cardiac Dynamics ◽  
Box Counting Method ◽  
Time Required

Abstract Introduction and objectives: nonlinear dynamics and fractal geometry have allowed the advent of an exponential mathematical law applicable to diagnose cardiac dynamics in 21 hours, however, it would be beneficial to reduce the time required to diagnose cardiac dynamics with this method in critical scenarios, in order to detect earlier complications that may require medical attention. The objective of this research is to confirm the clinical applicability of the mathematical law in 16 hours, with a comparative study against the Gold Standard. Methods: There were taken 450 electrocardiographic records of healthy patients and with cardiac diseases. A physical-mathematical diagnosis was applied to study cardiac dynamics, which consists of generating cardiac chaotic attractors based on the sequence of heart rate values during 16 hours, which were then measured with two overlapping grids according to the Box-Counting method to quantify the spatial occupation and the fractal dimension of each cardiac dynamic, with its respective statistical validation. Results: The occupation spaces of normal dynamics calculated in 16 hours were compatible with previous parameters established, evidencing the precision of the methodology to differentiate normality from abnormality. Sensitivity and specificity values of 100% were found, as well as a Kappa coefficient of 1. Conclusions: it was possible to establish differences between cardiac dynamics for 16 hours, suggesting that this method could be clinically applicable to analyze and diagnose cardiac dynamics in real time.

Sign in / Sign up

Export Citation Format

Share Document