Relevant bibliographies by topics / Box-counting dimension

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Box-counting dimension'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Box-counting dimension"

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PÖTZELBERGER, KLAUS. "The quantization dimension of distributions." Mathematical Proceedings of the Cambridge Philosophical Society 131, no. 3 (November 2001): 507–19. http://dx.doi.org/10.1017/s0305004101005357.

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We show that the asymptotic behaviour of the quantization error allows the definition of dimensions for probability distributions, the upper and the lower quantization dimension. These concepts fit into standard geometric measure theory, as the upper quantization dimension is always between the packing and the upper box-counting dimension, whereas the lower quantization dimension is between the Hausdorff and the lower box-counting dimension.
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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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Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form." International Journal of Artificial Life Research 3, no. 3 (July 2012): 41–63. http://dx.doi.org/10.4018/jalr.2012070104.

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The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors propose corresponding improved techniques with modified measurement design to address these issues: 1) rectangular grids and boxes setting up a proper box cover of the object; 2) pseudo-geometric sequence of box sizes providing adequate data points to study the properties of the dimension profile; 3) generalized sliding window method helping to determine the scaling range. The authors’ method is tested on a fractal image (the Vicsek prefractal) with known fractal dimension and then applied to real city data. The results show that a reliable estimate of box dimension for urban form can be obtained using their method.
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Meng, Xianmeng, Pengju Zhang, Jing Li, Chuanming Ma, and Dengfeng Liu. "The linkage between box-counting and geomorphic fractal dimensions in the fractal structure of river networks: the junction angle." Hydrology Research 51, no. 6 (October 15, 2020): 1397–408. http://dx.doi.org/10.2166/nh.2020.082.

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Abstract In the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is decreasing with the increase of the junction angle when geomorphic fractal dimension keeps constant. This relationship presents continuous and smooth convex curves with junction angle from 60° to 120° and concave curves from 30° to 45°. Then 70 river networks in China are investigated in terms of their two kinds of fractal dimensions. The results confirm the fractal structure of river networks. Geomorphic fractal dimensions of river networks are larger than box-counting dimensions and there is no obvious relationship between these two kinds of fractal dimensions. Relatively good non-linear relationships between geomorphic fractal dimensions and box-counting dimensions are obtained by considering the role of the junction angle.
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OLSON, ERIC J., JAMES C. ROBINSON, and NICHOLAS SHARPLES. "Generalised Cantor sets and the dimension of products." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 1 (October 30, 2015): 51–75. http://dx.doi.org/10.1017/s0305004115000584.

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AbstractIn this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when considering the Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show that for any α ∈ (0, 1) and any β, γ ∈ (0, 1) such that β + γ ⩾ 1 we can construct two generalised Cantor sets C and D such that dimBC = αβ, dimBD = α γ, and dimAC = dimAD = dimA (C × D) = dimB (C × D) = α.
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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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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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Miyata, Takahisa, and Tadashi Watanabe. "Approximate resolutions and box-counting dimension." Topology and its Applications 132, no. 1 (July 2003): 49–69. http://dx.doi.org/10.1016/s0166-8641(02)00362-0.

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Falconer, K. J. "The dimension of self-affine fractals II." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 1 (January 1992): 169–79. http://dx.doi.org/10.1017/s0305004100075253.

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AbstractA family {S1, ,Sk} of contracting affine transformations on Rn defines a unique non-empty compact set F satisfying . We obtain estimates for the Hausdorff and box-counting dimensions of such sets, and in particular derive an exact expression for the box-counting dimension in certain cases. These estimates are given in terms of the singular value functions of affine transformations associated with the Si. This paper is a sequel to 4, which presented a formula for the dimensions that was valid in almost all cases.
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BARBÉ, ANDRÉ, FRITZ VON HAESELER, and GENCHO SKORDEV. "LIMIT SETS OF RESTRICTED RANDOM SUBSTITUTIONS." Fractals 14, no. 01 (March 2006): 37–47. http://dx.doi.org/10.1142/s0218348x06003076.

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We consider a certain type of random substitution and show that the sets generated by it have almost surely the same box-counting and Hausdorff dimension, and that box-counting and Hausdorff dimension coincide.
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Dissertations / Theses on the topic "Box-counting dimension"

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Brandão, Daniela Teresa Quaresma Santos. "Dimensões fractais e dimensão de correlação." Master's thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/17740.

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O objetivo deste trabalho é o estudo da dimensão fractal, nomeadamente a dimensão de Hausdorff, dimensão de capacidade e dimensão de correlação, relacionando-as e efetuando o cálculo em alguns exemplos. Sempre que se considera indispensável, são apresentadas noções introdutórias para uma melhor compreensão dos conceitos analisados. O Capítulo 2 é dedicado ao estudo da dimensão de Hausdorff, introduzindo, previamente, uma noção de medida, de Hausdorff. No Capítulo 3 analisamos a dimensão de capacidade, suas propriedades e inconvenientes, relacionando, no final, esta dimensão com a dimensão de Hausdorff. O Capítulo 4 estuda técnicas para calcular dimensões. São estudados subconjuntos de medida. Finita, sistemas de funções iteradas, conjuntos auto-semelhantes e auto-afins e dimensões de gráficos. O Capítulo 5 é dedicado à dimensão de correlação. Estuda o expoente de correlação  Introduzido por Grassberger e Procaccia. São analisadas funções de dimensão 1 e no plano. Terminamos com o estudo de séries temporais de variável única. ABSTRACT: The aim of this work is the study of the fractal dimension, namely the Hausdorff dimension, the box-counting dimension and the correlation dimension, relating and computing them in some examples. Everytime it is necessary we introduce the basic concepts to a better understanding of the concepts analysed in this work. Chapter 2 is dedicated to the study of the Hausdorff dimension, introducing first the notion of Hausdorff measure. Chapter 3 is concerned with the box-counting dimension, its properties and problems. Then we relate this dimension With Hausdorff dimension studied in Chapter 2. Chapter 4 is dedicated to the techniques for calculating dimensions. We study subsets of finite measure, iterated function schemes, self-similar and self-affine sets and dimensions of graphs. Finally, in Chapter 5 we present the correlation dimension. We study the correlation exponent, introduced by Grassberger and Procaccia. We finish this Chapter with a study of single-variable time series.
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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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Le, Huy. "Numerické metody měření fraktálních dimenzí a fraktálních měr." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417160.

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Tato diplomová práce se zabývá teorií fraktálů a popisuje patričné potíže při zavedení pojmu fraktál. Dále se v práci navrhuje několik metod, které se použijí na aproximaci fraktálních dimenzí různých množin zobrazených na zařízeních s konečným rozlišením. Tyto metody se otestují na takových množinách, jejichž dimenze známe, a na závěr se výsledky porovnávají.
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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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Simonini, Marina. "Fractal sets and their applications in medicine." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8763/.

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La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.
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Fuhrmann, G., M. Gröger, and T. Jäger. "Non-smooth saddle-node bifurcations II: Dimensions of strange attractors." Cambridge University Press, 2018. https://tud.qucosa.de/id/qucosa%3A70708.

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We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.
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ZANINI, ALESSANDRO. "Analisi dei dati da emissione acustica per la valutazione del danneggiamento strutturale." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/686.

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Viene studiata una nuova metodologia di diagnostica, basata sull’analisi di dati derivanti dall’Emissione Acustica (EA), per lo studio della nucleazione e della propagazione di difetti durante prove di laboratorio su provino sotto carico e serbatoi in pressione. L’applicazione dell’analisi frattale al segnale di EA risulta particolarmente efficace e permette di identificare la distribuzione spaziale delle sorgenti stesse, esplicitandone la correlazione tra gli eventi. E’ così possibile ottenere molte informazioni associate al danneggiamento dei differenti casi studiati. L’intensità della sollecitazione, il danneggiamento del pezzo, o lo stato di fatica del materiale, sono parametri strettamente correlati con l’EA. La dimensione frattale (Dt) evolve con il carico (sigma) o la pressione (p) o con il numero di cicli (N). Le curve Dt-sigma, Dt-p o Dt-N risultano utili per l’individuazione della nucleazione e propagazione del difetto e per l’identificazione di una condizione di incipiente collasso della struttura. I risultati ottenuti mediante questa tecnica suggeriscono la possibilità d’individuare con anticipo la formazione della cricca, rispetto a tecniche sperimentali e/o teoriche.
A new experimental methodology was investigated for the evaluation of material damage by analyzing the behavior of several specimens under stress. The application of fractal analysis to Acoustic Emission (AE) signal resulted particularly effective it is possible to characterize the spatial distribution of the prime AE sources, and the relationship between different event of AE. In fact, it is possible to obtain several information, associated with the damage of the different tested materials. The intensity of the prime stress, or the state of fatigue, of the material, i.e. of the flaws that damaged the rheology of the material during its previous stress history, is closely related to AE. The fractal dimension (D) evolves altogether with the stress (sigma) or the pressure (p) or the number of fatigue cycles (N). D-sigma, D-p and D-N curves resulted useful for identifying the condition of incipient collapse or nucleation and propagation of the fatigue cracks. The results of such experimental technique suggest that it is possible anticipating the detection of the crack onset, relating to other theoretical and/or experimental techniques.
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Dathe, Annette. "Digitale Bildanalyse zur Messung fraktaler Eigenschaften der Bodenstruktur." Doctoral thesis, [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=965898083.

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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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Book chapters on the topic "Box-counting dimension"

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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. "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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Kaewaramsri, Yothin, and Kuntpong Woraratpanya. "Improved Triangle Box-Counting Method for Fractal Dimension Estimation." In Advances in Intelligent Systems and Computing, 53–61. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19024-2_6.

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Șerbănescu, Mircea-Sebastian. "Fractal Dimension Box-Counting Algorithm Optimization Through Integral Images." In IFMBE Proceedings, 95–101. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93564-1_11.

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Chen, Xiang, Jingchao Li, and Hui Han. "Signal Subtle Feature Extraction Algorithm Based on Improved Fractal Box-Counting Dimension." In Cloud Computing and Security, 684–96. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00021-9_61.

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Lantitsou, Konstantina, Apostolos Syropoulos, and Basil K. Papadopoulos. "On the Use of the Fractal Box-Counting Dimension in Urban Planning." In Springer Optimization and Its Applications, 275–80. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74325-7_13.

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Pershin, Ilya, Dmitrii Tumakov, and Angelina Markina. "Parallel Box-Counting Method for Evaluating the Fractal Dimension of Analytically Defined Curves." In Communications in Computer and Information Science, 86–97. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64616-5_8.

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Da Silva, D., F. Boudon, C. Godin, O. Puech, C. Smith, and H. Sinoquet. "A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns." In Advances in Visual Computing, 751–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11919476_75.

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Conference papers on the topic "Box-counting dimension"

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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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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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Palanivel, Dhevendra Alagan, Sivakumaran Natarajan, Sainarayanan Gopalakrishnan, and Rachid Jennane. "Trabecular Bone Texture Characterization Using Regularization Dimension and Box-counting Dimension." In TENCON 2019 - 2019 IEEE Region 10 Conference (TENCON). IEEE, 2019. http://dx.doi.org/10.1109/tencon.2019.8929524.

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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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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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Attikos, Christos, and Michael Doumpos. "Faster Estimation of the Correlation Fractal Dimension Using Box-counting." In 2009 Fourth Balkan Conference in Informatics. IEEE, 2009. http://dx.doi.org/10.1109/bci.2009.6.

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Xue, Song, Xinsheng Jiang, and Jimiao Duan. "A new box-counting method for image fractal dimension estimation." In 2017 3rd IEEE International Conference on Computer and Communications (ICCC). IEEE, 2017. http://dx.doi.org/10.1109/compcomm.2017.8322847.

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Wu, Longwen, Yaqin Zhao, Zhao Wang, Fakheraldin Y. O. Abdalla, and Guanghui Ren. "Specific emitter identification using fractal features based on box-counting dimension and variance dimension." In 2017 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT). IEEE, 2017. http://dx.doi.org/10.1109/isspit.2017.8388646.

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Kraitong, Atikarn, Sanpachai Huvanandana, and Settapong Malisuwan. "A box-counting fractal dimension for feature extraction in iris recognition." In 2011 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS 2011). IEEE, 2011. http://dx.doi.org/10.1109/ispacs.2011.6146121.

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10

Ivanovici, Mihai, Irina Nicolae, and Radu-Mihai Coliban. "Umbra-based Improvement of the Probabilistic Box-Counting Fractal Dimension Estimation." In 2021 International Symposium on Signals, Circuits and Systems (ISSCS). IEEE, 2021. http://dx.doi.org/10.1109/isscs52333.2021.9497383.

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