Relevant bibliographies by topics / Box-counting

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Box-counting'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Box-counting"

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Meisel, L. V., Mark Johnson, and P. J. Cote. "Box-counting multifractal analysis." Physical Review A 45, no. 10 (May 1, 1992): 6989–96. http://dx.doi.org/10.1103/physreva.45.6989.

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Chen, Xiang, Jingchao Li, Hui Han, and Yulong Ying. "Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors." Royal Society Open Science 5, no. 5 (May 2018): 180087. http://dx.doi.org/10.1098/rsos.180087.

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Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.
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GRASSBERGER, PETER. "ON EFFICIENT BOX COUNTING ALGORITHMS." International Journal of Modern Physics C 04, no. 03 (June 1993): 515–23. http://dx.doi.org/10.1142/s0129183193000525.

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We present two variants of a fast and storage efficient algorithm for box counting of fractals and fractal measures. In contrast to recently proposed algorithms, no sorting of the data is done. With comparable storage demands, CPU times are between 1 and 2 orders of magnitude lower than those needed with the latter algorithms.
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KYRIACOS, S., S. BUCZKOWSKI, F. NEKKA, and L. CARTILIER. "A MODIFIED BOX-COUNTING METHOD." Fractals 02, no. 02 (June 1994): 321–24. http://dx.doi.org/10.1142/s0218348x94000417.

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Fractal geometry has been widely used to characterize irregular structures. Our interest in applying this concept in biomedical research leads us to the conclusion that there are no standard methods. In order to objectively set parameters involved in the estimation of fractal dimension, a significantly more accurate and efficient box-counting method based on a new algorithm was developed. Measurements of mathematical objects with known fractal dimension was performed using the traditional method and the proposed modification. The latter always yields results with less than 1% difference from the theoretical value, which represents a significant improvement.
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ALEVIZOS, PANAGIOTIS D., and MICHAEL N. VRAHATIS. "OPTIMAL DYNAMIC BOX-COUNTING ALGORITHM." International Journal of Bifurcation and Chaos 20, no. 12 (December 2010): 4067–77. http://dx.doi.org/10.1142/s0218127410028197.

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An optimal box-counting algorithm for estimating the fractal dimension of a nonempty set which changes over time is given. This nonstationary environment is characterized by the insertion of new points into the set and in many cases the deletion of some existing points from the set. In this setting, the issue at hand is to update the box-counting result at appropriate time intervals with low computational cost. The proposed algorithm tackles the dynamic box-counting problem by using computational geometry methods. In particular, we use a sequence of compressed Box Quadtrees to store the data points. This storage permits the fast and efficient application of our box-counting approach to compute what we call the "dynamic fractal dimension". For a nonempty set of points in the d-dimensional space ℝd (for constant d ≥ 1), the time complexity of the proposed algorithm is shown to be O(n log n) while the space complexity is O(n), where n is the number of considered points. In addition, we show that the time complexity of an insertion, or a deletion is O( log n), and that the above time and space complexity is optimal. Experimental results of the proposed approach illustrated on the well-known and widely studied Hénon map are presented.
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von Hardenberg, J., R. Thieberger, and A. Provenzale. "A box-counting red herring." Physics Letters A 269, no. 5-6 (May 2000): 303–8. http://dx.doi.org/10.1016/s0375-9601(00)00265-6.

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Nikolaidis, Nikolaos S., and Ioannis N. Nikolaidis. "The box-merging implementation of the box-counting algorithm." Journal of the Mechanical Behavior of Materials 25, no. 1-2 (April 1, 2016): 61–67. http://dx.doi.org/10.1515/jmbm-2016-0006.

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AbstractFractal analysis is a powerful tool for the classification of materials. However, until now, there were no efficient tools that could process large or color images due to the processing time required. In this article we present a fast, easy to implement and very easily expandable to any number of dimensions variation, the box merging method. It is applied here to RGB test images which are considered as sets in 5-D space.
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Ndiaye, M. "Combining Fractals and Box-Counting Dimension." Applied Mathematics 12, no. 09 (2021): 818–34. http://dx.doi.org/10.4236/am.2021.129055.

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Górski, Andrzej Z. "Pseudofractals and the box counting algorithm." Journal of Physics A: Mathematical and General 34, no. 39 (September 21, 2001): 7933–40. http://dx.doi.org/10.1088/0305-4470/34/39/302.

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Jiménez, J., and J. Ruiz de Miras. "Fast box-counting algorithm on GPU." Computer Methods and Programs in Biomedicine 108, no. 3 (December 2012): 1229–42. http://dx.doi.org/10.1016/j.cmpb.2012.07.005.

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Dissertations / Theses on the topic "Box-counting"

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Yamaguti, Marcos. "Caracterização Multifractal." Universidade de São Paulo, 1997. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-28022014-142127/.

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A caracterização estática dos sistemas caóticos clássicos dissipativos tem sido realizada através do cálculo das dimensões generalizadas \'D IND. q\' e do espectro de singularidades f(alfa). Os métodos mais comuns de cálculo numérico dessas funções utilizam algoritmos de contagem de caixa. Porém, esses algoritmos produzem um erro sistemático através de \'caixas espúrias\', levando a resultados distorcidos. Por essa razão, estudamos métodos numéricos que não utilizam o algoritmo de contagem de caixa, verificando em que casos eles podem ser aplicados eficazmente e propusemos um novo algoritmo de contagem de caixa que reduz o número de \'caixas espúrias\', obtendo melhores resultados.
The static caracterization of classical dissipative chaotical systems has been achieved by the calculation of the generalized dimensions \'D IND. q\' and the spectrum of singularities f(alfa). The most used numerical methods of evaluating these functions are based on box counting algorithms. The results obtained by those methods are distorced by the presence of \'spurious boxes\' generated intrinsecally by these algorithms. For this reason, we have studied numerical methods that don\'t use box counting algorithms, and we have tried to verify in which kind of sets they give best results. We also have proposed a new box counting algorithm that reduces the number of \'spurious boxes\', and led to better results.
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Fiedler, Reno 1970. "Application of the box-counting method in evaluating statistical homogeneity in rock masses." Thesis, The University of Arizona, 1995. http://hdl.handle.net/10150/278511.

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This thesis discusses the suitability of the box-counting method as a tool describing complex geometrical phenomena in nature by estimating their fractal dimensions, D. The study evaluated the influence of the parameters of the box counting method on the estimated fractal dimension using Koch curves of known fractal properties. It became clear that the employed size range of the applied box networks has the strongest influence on the obtained fractal dimension. A successful application of the box-counting method to generated 2-D joint patterns proved the ability of the fractal dimension to capture the influence of joint size and density on the statistical homogeneity of rock masses. Joint data from a tunnel of the Three Gorges Dam site in China was examined for potential statistical homogeneity. It was possible to find five different statistically homogeneous regions by combining the estimated fractal dimension and a visual geological evaluation of the joint maps.
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Cappiello, Grazia. "A Phase Space Box-counting based Method for Arrhythmia Prediction from Electrocardiogram Time Series." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5180/.

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Arrhythmia is one kind of cardiovascular diseases that give rise to the number of deaths and potentially yields immedicable danger. Arrhythmia is a life threatening condition originating from disorganized propagation of electrical signals in heart resulting in desynchronization among different chambers of the heart. Fundamentally, the synchronization process means that the phase relationship of electrical activities between the chambers remains coherent, maintaining a constant phase difference over time. If desynchronization occurs due to arrhythmia, the coherent phase relationship breaks down resulting in chaotic rhythm affecting the regular pumping mechanism of heart. This phenomenon was explored by using the phase space reconstruction technique which is a standard analysis technique of time series data generated from nonlinear dynamical system. In this project a novel index is presented for predicting the onset of ventricular arrhythmias. Analysis of continuously captured long-term ECG data recordings was conducted up to the onset of arrhythmia by the phase space reconstruction method, obtaining 2-dimensional images, analysed by the box counting method. The method was tested using the ECG data set of three different kinds including normal (NR), Ventricular Tachycardia (VT), Ventricular Fibrillation (VF), extracted from the Physionet ECG database. Statistical measures like mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) for the box-counting in phase space diagrams are derived for a sliding window of 10 beats of ECG signal. From the results of these statistical analyses, a threshold was derived as an upper bound of Coefficient of Variation (CV) for box-counting of ECG phase portraits which is capable of reliably predicting the impeding arrhythmia long before its actual occurrence. As future work of research, it was planned to validate this prediction tool over a wider population of patients affected by different kind of arrhythmia, like atrial fibrillation, bundle and brunch block, and set different thresholds for them, in order to confirm its clinical applicability.
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Филатова, Анна Евгеньевна, and И. В. Солошенко. "Расчет фрактальной размерности для медицинских полутоновых изображений." Thesis, Національний технічний університет "Харківський політехнічний інститут", 2014. http://repository.kpi.kharkov.ua/handle/KhPI-Press/46306.

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Baldacci, Martina. "La teoria dei frattali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20712/.

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Questa tesi ha lo scopo di presentare i frattali, per prima formalizzati dal matematico Benoit Mandelbrot, descrivendo a livello matematico le due principali proprietà che li caratterizzano: la dimensione frattale (dimensione di Hausdorff) e l'autosimilarità. Si pone inoltre l'attenzione alla dimensione di Box-counting, analizzandone la relazione che questa ha con la dimensione di Hausdorff.
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Commissari, Chiara. "I frattali e il loro ruolo nella diagnosi tumorale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21257/.

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In questa tesi vengono presentati i frattali, strutture matematiche accumunate da dimensione di Hausdorff non intera e proprietà di autosimilarità. Dopo alcuni concetti di base della teoria della misura, si studieranno la misura e la dimensione di Hausdorff, ponendo attenzione ad alcune loro proprietà e fornendo esempi tra cui l'insieme di Cantor e la funzione di Weierstrass. Si analizzerà inoltre la proprietà di autosimilarità descritta tramite contrazioni e punti fissi. Infine verrà presentato il metodo del box counting e il suo utilizzo in campo medico per l’analisi di immagini frattali riguardanti la vascolarizzazione tumorale.
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Craig, Patrick Shane. "Quantitative Analysis of the Polarity Reversal Pattern of the Earth's Magnetic Field and Self-Reversing Dynamo Models." Wright State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=wright1369586504.

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HUANG, KUAN-YU. "Fractal or Scaling Analysis of Natural Cities Extracted from Open Geographic Data Sources." Thesis, Högskolan i Gävle, Avdelningen för Industriell utveckling, IT och Samhällsbyggnad, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-19386.

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A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.
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Berlinkov, Artemi. "Dimensions in Random Constructions." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3160/.

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We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
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Nedvěd, Jiří. "Zpracování genomických signálů fraktály." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219634.

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This diploma project is showen possibilities in classification of genomic sequences with CGR and FCGR methods in pictures. From this picture is computed classificator with BCM. Next here is written about the programme and its opportunities for classification. In the end is compared many of sequences computed in different options of programme.
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Books on the topic "Box-counting"

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Burk, Donna. Box it or bag it mathematics: Place value counting. Salem, Or. (P.O. Box 3226, Salem 97302): Math Learning Center, 1988.

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How many bugs in a box?: A pop-up counting book. New York: Simon & Schuster, 1988.

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Carter, David A. How many bugs in a box?: A pop-up counting book. New York: Simon & Schuster, 1988.

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Out of the box: 100 years and counting : the history of LDI. Indianapolis, IN: LDI, Ltd., 2011.

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Mariko, Chouinard, ed. One magic box. New York: Doubleday, 1989.

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Kelly, Martin. A box full of puppies. New York: Sandy Creek, 2011.

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Scarry, Richard. School bus box set. Hauppauge, New York: Barron's Educational Series, 2014.

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Klein, Adria. In and out of the Toy Box. New York, NY: Metropolitan Teaching and Learning co, 1999.

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Awdry, W. Thomas the Tank Engine: Gift box. Oxford: Heinemann, 1993.

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Kwas, Susan Estelle. [Learning block books: 26 board books in a box! : shapes, animals, colors, numbers. [San Francisco, Calif: Chronicle Books, 2001.

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Book chapters on the topic "Box-counting"

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Rosenberg, Eric. "Network Box Counting Heuristics." In A Survey of Fractal Dimensions of Networks, 13–27. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90047-6_3.

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Rosenberg, Eric. "Network Box Counting Dimension." In Fractal Dimensions of Networks, 131–44. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_7.

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Rosenberg, Eric. "Network Box Counting Heuristics." In Fractal Dimensions of Networks, 145–75. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_8.

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Rosenberg, Eric. "Lower Bounds on Box Counting." In A Survey of Fractal Dimensions of Networks, 29–37. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90047-6_4.

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Rosenberg, Eric. "Topological and Box Counting Dimensions." In Fractal Dimensions of Networks, 61–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_4.

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Rosenberg, Eric. "Computing the Box Counting Dimension." In Fractal Dimensions of Networks, 107–29. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_6.

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Ostwald, Michael J., and Josephine Vaughan. "Introducing the Box-Counting Method." In The Fractal Dimension of Architecture, 39–66. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32426-5_3.

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Che Azemin, Mohd Zulfaezal, Fadilah Ab Hamid, Jie Jin Wang, Ryo Kawasaki, and Dinesh Kant Kumar. "Box-Counting Fractal Dimension Algorithm Variations on Retina Images." In Lecture Notes in Electrical Engineering, 337–43. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24584-3_27.

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Harrar, K., and L. Hamami. "Implementation of the box-counting method in radiographic images." In Lecture Notes in Electrical Engineering, 299–311. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-76483-2_26.

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Karperien, Audrey L., and Herbert F. Jelinek. "Box-Counting Fractal Analysis: A Primer for the Clinician." In Springer Series in Computational Neuroscience, 13–43. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-3995-4_2.

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Conference papers on the topic "Box-counting"

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Miloevic, Neboja T., Nemanja Rajkovic, Herbert F. Jelinek, and Duan Ristanovic. "Richardson's Method of Segment Counting versus Box-Counting." In 2013 19th International Conference on Control Systems and Computer Science (CSCS). IEEE, 2013. http://dx.doi.org/10.1109/cscs.2013.52.

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Veleva, S., and L. Kocic. "Estimating box-dimension by sign counting." In 28th International Conference on Information Technology Interfaces, 2006. IEEE, 2006. http://dx.doi.org/10.1109/iti.2006.1708544.

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Nunsong, Walairach, and Kuntpong Woraratpanya. "Modified differential box-counting method using weighted triangle-box partition." In 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE). IEEE, 2015. http://dx.doi.org/10.1109/iciteed.2015.7408945.

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Li Yu, Kuanquan Wang, and D. Zhang. "Coarse iris classification based on box-counting method." In rnational Conference on Image Processing. IEEE, 2005. http://dx.doi.org/10.1109/icip.2005.1530388.

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Jie Feng, Wei-Chung Lin, and Chin-Tu Chen. "Fractional box-counting approach to fractal dimension estimation." In Proceedings of 13th International Conference on Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/icpr.1996.547197.

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Panigrahy, Chinmaya, Ayan Seal, and Nihar Kumar Mahato. "Is Box-Height Really a Issue in Differential Box Counting Based Fractal Dimension?" In 2019 International Conference on Information Technology (ICIT). IEEE, 2019. http://dx.doi.org/10.1109/icit48102.2019.00073.

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Liu, Yuting, Miaojing Shi, Qijun Zhao, and Xiaofang Wang. "Point in, Box Out: Beyond Counting Persons in Crowds." In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019. http://dx.doi.org/10.1109/cvpr.2019.00663.

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Li, Cancan, Longfei Cheng, Tao He, Lang Chen, Fei Yu, and Liangen Yang. "An improved differential box-counting method of image segmentation." In Seventh International Symposium on Precision Mechanical Measurements, edited by Liandong Yu. SPIE, 2016. http://dx.doi.org/10.1117/12.2214977.

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Lorenz, Wolfgang. "Combining Complexity and Harmony by the Box-Counting Method." In eCAADe 2013: Computation and Performance. eCAADe, 2013. http://dx.doi.org/10.52842/conf.ecaade.2013.2.667.

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Wurzer, Gabriel, and Wolfgang Lorenz. "Fracam - Cell Phone Application to Measure Box Counting Dimension." In CAADRIA 2017: Protocols, Flows, and Glitches. CAADRIA, 2017. http://dx.doi.org/10.52842/conf.caadria.2017.725.

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Reports on the topic "Box-counting"

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Meisel, L. V., and M. A. Johnson. Numerical Box-Counting and Correlation Integral Multifractal Analysis. Fort Belvoir, VA: Defense Technical Information Center, May 1994. http://dx.doi.org/10.21236/ada282902.

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Loehle, C. Rescaled box counting for the topological analysis of spatial data. Office of Scientific and Technical Information (OSTI), April 1994. http://dx.doi.org/10.2172/10142283.

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