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It provides functions fract2D and fract3D that binarize images into black and white, overlay boxes/cubes of varying sizes, count occupied boxes at each step, and estimate D via linear regression in log-log space. Optional outputs store estimated dimensions and raw counting data for reproducible analysis.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/estimation-of-fractal-dimension-of-a-black-area-in-2d-and-3d-slices-images-version-010/290139/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/estimation-of-fractal-dimension-of-a-black-area-in-2d-and-3d-slices-images-version-010/290139.png","ImageObject",300,407,{"name":92,"@type":93},"Aladdin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does fract2D compute?","Question",{"text":112,"@type":113},"fract2D calculates the fractal dimension (D) of a black area in a 2D image using box-counting.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What extra inputs does fract3D require compared to fract2D?",{"text":117,"@type":113},"fract3D adds dist.slice, the distance between slices, to process 3D (sliced) images.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the fractal dimension estimated from the box counts?",{"text":121,"@type":113},"For each box size, the method counts occupied boxes and estimates D using linear regression of log(number of boxes) on log(box size).","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},290139,1790922155,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},2336478503145,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Package ‘fractD’  \nMay 8, 2026  \nType Package  \nTitle Estimation of Fractal Dimension of a Black Area in 2D and 3D  \n(Slices) Images Version 0.1.0  \nMaintainer Francesco Paolo Mancuso \u003C[fscopaolo.mancuso@gmail.com](fscopaolo.mancuso@gmail.com)> Description  \nEstimate the of fractal dimension of a black area in 2D and 3D (slices) images using the boxcounting method. See Klinkenberg B. (1994) \u003Cdoi:10.1007/BF02065874> .  \nLicense GPL-3 Encoding UTF-8 LazyData true RoxygenNote 7.1.1  \nImports imager (>= 0.42.1), parallel (>= 3.5.1), plyr (>= 1.8.4), stats (>= 3.5.1), utils (>= 3.5.1)  \nSuggests knitr, rmarkdown VignetteBuilder knitr NeedsCompilation no  \nAuthor Francesco Paolo Mancuso [aut, cre](ORCID:  \n\u003C[https://orcid.org/0000-0001-7217-5131](https://orcid.org/0000-0001-7217-5131)>) Repository CRAN  \nDate/Publication 2021-02-05 08:20:02 UTC  \nContents  \nfract2D ........................................... 2  \nfract3D ........................................... 3  \nIndex 6  \n2 fract2D  \n\n| fract2D | Calculates the fractal dimension of a 2D image |\n| --- | --- |\n\nDescription  \nThis function calculates the fractal dimension of a black area in a bidimensional image using the method of box-counting.  \nUsage  \nfract2D(dir = NULL, box.size = NULL, save .dir = NULL, [save.name = NULL](save.name = NULL))  \nArguments  \ndir Specify a folder containing the image/s to be analysed.  \nbox.size A vector specifing the box size steps (in pixel) to be used to calculate fractal dimension. By default (NULL) box.size = c(1,2,4,8,16,32,64,128,256,512) . Minimun box size cannot be less then 1, corresponding to 1 pixel of the image. Box size steps must be integer.  \nsave.dir Optional. Set the name of an output folder to save the data as *.rds.  \n[save.name](save.name) Optional. Provide a name for the output data.  \nDetails  \nThe fuction calculates the fractal dimension (D) by the method of box-counting. Box-counting method is useful to calculate the fractal dimension of various sets of any dimension and patterns with or withouth self-similarity (Klinkenberg, 1994) . The method overlay a series of squares of different size (box.size), with minimun box size that is equal to the resolution of the image. Then, for each box size step the function keep track of the number of squares occupied by the black area into the image. Finally, fractal dimension (D) is estimated by linear regression of log(n°boxes) on log(box.size) .  \nValue  \nfract2D returns a list containing the following components:  \nD-A dataframe with the estimated fractal dimension.  \nraw .dat-A dataframe with the raw data used to calculate the fractal dimension. The data frame contains the name of the image (id), the box size steps (box.size), and the number of boxes for each box size step (box) .  \nfract3D 3  \nNote  \nThe function analyze the fractal dimension of a black area into an image. Then, the images must be  \nconverted in black and white before analysis.  \nUsually, the box sizes should change as a function of a power of two so that they will be evenly  \nspaced in the log space. However, this can result in too few points to fit linear regression. Therefore,  \naccording to Dubuc et al. (1989) the function allow to use box.size from 1 to +inf not necessarly  \nwith dyadic step.  \nReferences  \n• Mandelbrot B.B. (1982) - The fractal Geometry of Nature. San Francisco: W.H. Freman.  \n• Klinkenberg B. (1994) - AReview of methods used to determine the fractal dimension of linear features. Mathematical Geology, vol. 26, n° 1 . doi: 10.1007/BF02065874  \n• Dubuc B., Quiniou J.F., Roques-Carmes C., Tricot C., Zucker S.W. (1989) -Evaluating the  \nfractal dimension of profiles. Physical Review A, vol. 39, n° 3 . doi: [https://doi.org/10.1103/PhysRevA.39.1500](https://doi.org/10.1103/PhysRevA.39.1500)  \nSee Also  \nfract3D to estimate the fractal dimension of a 3D (sliced) image/s.  \nExamples  \n\\#\\# Not run:  \n\\# The example below calculates the fractal dimension  \n\\# of image/s contained in the folder \"sou","cbCaiqIr638tMfBi","https://ap.wps.com/l/cbCaiqIr638tMfBi","pdf",83738,"English","# fract2D\n## Description\n## Usage\n## Arguments\n## Details\n## Value\n# fract3D\n## Description\n## Usage\n## Arguments\n## Details\n# References\n# See Also\n# Examples","[{\"question\":\"What does fract2D compute?\",\"answer\":\"fract2D calculates the fractal dimension (D) of a black area in a 2D image using box-counting.\"},{\"question\":\"What extra inputs does fract3D require compared to fract2D?\",\"answer\":\"fract3D adds dist.slice, the distance between slices, to process 3D (sliced) images.\"},{\"question\":\"How is the fractal dimension estimated from the box counts?\",\"answer\":\"For each box size, the method counts occupied boxes and estimates D using linear regression of log(number of boxes) on log(box size).\"}]","Estimation of Fractal Dimension of a Black Area in 2D and 3D (Slices) Images Version 0.1.0 | PDF",1789640759,15]