Fractal Analysis in MATLAB: A Tutorial for Neuroscientists. FDC 4 is another MAC OS paid software for. Computing the FD of a black and white image. FracLac for ImageJ. FracLac is a plugin for ImageJ. It is freely available software developed and maintained by our lab at the School of Community Health, Faculty of Science, Charles Sturt University, Australia. The author of the software and project lead is also the author of this document (me, Audrey Karperien).
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![Tutorial Tutorial](https://imagej.nih.gov/ij/plugins/fraclac/FLHelp/ok.gif)
FRACLAC FOR IMAGEJ Audrey Karperien Charles Sturt University 2000-2013 Software and Guide to Fractal and Lacunarity Analysis for FracLac 2013
The software is a free, open source plugin for the free, open source imaging application ImageJ. This free plugin is accompanied by free detailed documentation (javadoc) with linked and raw source code. Did I mention that it’s all free? The advanced ImageJ user or researcher can read the detailed implementations of the math behind the program and its assumptions in the source code and javadoc. Programmers, moreover, can freely use or modify the code in their own programs. Freely and for free!
There are several components to FRACLAC FOR IMAGEJ. This document is a shell that links to the other components (see next page), which are assumed to be in a folder in the same directory as this pdf. To set up the archive, follow the steps below.
Sometimes the details of a design are more important than gross morphology. FRACLAC FOR IMAGEJ is for anyone who hopes to understand this phenomenon through fractal analysis of digital images. It presupposes that the curious analyst has little background, and provides most of what is required for one to become an accomplished fractal analyst ready to discuss the subtle, the beautiful, and the bizarre fractal features of patterns sometimes imperceptible to the eye yet mathematically detectable, and perhaps more interesting, measurable, in digital images. FRACLAC FOR IMAGEJ is a toolset to help you become such an analyst able to identify and measure fractal features. It includes a guide to fractals and fractal analysis, with tutorials about basic and advanced techniques, and software to do fractal analysis. Important topics covered include technical issues and interpreting results. Whereas FRACLAC FOR IMAGEJ is comprehensive and friendly enough for the beginner, it also has advanced features for more complicated analysis and more experienced readers.
15/11/2013 00:26
1) Get the archive. Depending on how you acquired the pdf document you are now reading, the archive will be either embedded in the pdf itself or available for download from the site you downloaded the pdf from. 2) Unzip the archive to the folder that this document is in. Otherwise the links will not work. Remember the old real estate adage, location, location, location! 3) Navigate to and fro amongst the components using the links.
Go to the starting point and main resource for learning about fractals and fractal analysis. Here you will learn about such topics as what fractals are and basic to advanced fractal analysis concepts and skills. The resources will help you learn and use a host of methods with odd sounding names such as box counting multifractal analysis lacunarity sliding box lacunarity local fractal dimension local connected fractal dimension mass-radius analysis and complementary non-fractal morphometrics.
As an alternative to using the links in the previous section, you may wish to ensure you are using the most up to date resources. You can do this by browsing directly to the FracLac site or by selecting help while running the plugin. How to set up the plugin is described in the Guide above, but is also summarized below: 1. Download and install ImageJ or ImageJ/Fiji for free from the NIH’s ImageJ download site. 2. Then, copy the Frac_Lac.jar file into the 'plugins' folder in ImageJ or ImageJ/Fiji, restart the app, and select FracLac from the Analysis menu. 3. Click on the Help icon in the running plugin. You can see the Help icon at the bottom right of the FracLac GUI in the picture.
Go to the documentation explaining the structure of the plugin’s code and details about the calculations. It is not as friendly as the guide but is a gentle interface between you and the raw source code. Refer to it if you are a coder or you need the nitty-gritty of the calculations. There is much nit and equal grit in there. Go to a collection of text files known as java classes. They are readable if you know the java programming language or some other programming language but are not usually useful to the nonprogrammer. They can be used as the basis of a new software project. Go to the folder holding the software, as a compiled “jar” file. To learn how to install it, go to the installation page. The jar file includes the source code as well as compiled class files, and can be run in ImageJ or imported to a software development environment such as NetBeans or Eclipse. If you are not a coder, ignore that last sentence.
15/11/2013 00:26
FRACLAC FOR IMAGEJ is alive and dynamic. The software and guide are continually improving and changing shape to meet the needs of the digital image analyzing community. Feedback and ideas for developing the software are very welcome. All inputs will be considered! Free support for FRACLAC FOR IMAGE is available by email through the online FracLac website. The components of FRACLAC FOR IMAGEJ have been used in a variety of fields to study phenomena as diverse as agriculture, botany, dentistry, neuroscience, pathology, geography, urban planning, and the far away realms of the cosmos like the moon. If you are curious about what some of those applications are, the FLCitations page lists some 60 scientific papers in which people have used it to understand when the details of design are as important as gross morphology. Enjoy!
Fractal Dimension and Lacunarity
The software is a free, open source plugin for the free, open source imaging application ImageJ. This free plugin is accompanied by free detailed documentation (javadoc) with linked and raw source code. Did I mention that it’s all free? The advanced ImageJ user or researcher can read the detailed implementations of the math behind the program and its assumptions in the source code and javadoc. Programmers, moreover, can freely use or modify the code in their own programs. Freely and for free!
There are several components to FRACLAC FOR IMAGEJ. This document is a shell that links to the other components (see next page), which are assumed to be in a folder in the same directory as this pdf. To set up the archive, follow the steps below.
Sometimes the details of a design are more important than gross morphology. FRACLAC FOR IMAGEJ is for anyone who hopes to understand this phenomenon through fractal analysis of digital images. It presupposes that the curious analyst has little background, and provides most of what is required for one to become an accomplished fractal analyst ready to discuss the subtle, the beautiful, and the bizarre fractal features of patterns sometimes imperceptible to the eye yet mathematically detectable, and perhaps more interesting, measurable, in digital images. FRACLAC FOR IMAGEJ is a toolset to help you become such an analyst able to identify and measure fractal features. It includes a guide to fractals and fractal analysis, with tutorials about basic and advanced techniques, and software to do fractal analysis. Important topics covered include technical issues and interpreting results. Whereas FRACLAC FOR IMAGEJ is comprehensive and friendly enough for the beginner, it also has advanced features for more complicated analysis and more experienced readers.
15/11/2013 00:26
1) Get the archive. Depending on how you acquired the pdf document you are now reading, the archive will be either embedded in the pdf itself or available for download from the site you downloaded the pdf from. 2) Unzip the archive to the folder that this document is in. Otherwise the links will not work. Remember the old real estate adage, location, location, location! 3) Navigate to and fro amongst the components using the links.
Go to the starting point and main resource for learning about fractals and fractal analysis. Here you will learn about such topics as what fractals are and basic to advanced fractal analysis concepts and skills. The resources will help you learn and use a host of methods with odd sounding names such as box counting multifractal analysis lacunarity sliding box lacunarity local fractal dimension local connected fractal dimension mass-radius analysis and complementary non-fractal morphometrics.
As an alternative to using the links in the previous section, you may wish to ensure you are using the most up to date resources. You can do this by browsing directly to the FracLac site or by selecting help while running the plugin. How to set up the plugin is described in the Guide above, but is also summarized below: 1. Download and install ImageJ or ImageJ/Fiji for free from the NIH’s ImageJ download site. 2. Then, copy the Frac_Lac.jar file into the 'plugins' folder in ImageJ or ImageJ/Fiji, restart the app, and select FracLac from the Analysis menu. 3. Click on the Help icon in the running plugin. You can see the Help icon at the bottom right of the FracLac GUI in the picture.
Go to the documentation explaining the structure of the plugin’s code and details about the calculations. It is not as friendly as the guide but is a gentle interface between you and the raw source code. Refer to it if you are a coder or you need the nitty-gritty of the calculations. There is much nit and equal grit in there. Go to a collection of text files known as java classes. They are readable if you know the java programming language or some other programming language but are not usually useful to the nonprogrammer. They can be used as the basis of a new software project. Go to the folder holding the software, as a compiled “jar” file. To learn how to install it, go to the installation page. The jar file includes the source code as well as compiled class files, and can be run in ImageJ or imported to a software development environment such as NetBeans or Eclipse. If you are not a coder, ignore that last sentence.
15/11/2013 00:26
FRACLAC FOR IMAGEJ is alive and dynamic. The software and guide are continually improving and changing shape to meet the needs of the digital image analyzing community. Feedback and ideas for developing the software are very welcome. All inputs will be considered! Free support for FRACLAC FOR IMAGE is available by email through the online FracLac website. The components of FRACLAC FOR IMAGEJ have been used in a variety of fields to study phenomena as diverse as agriculture, botany, dentistry, neuroscience, pathology, geography, urban planning, and the far away realms of the cosmos like the moon. If you are curious about what some of those applications are, the FLCitations page lists some 60 scientific papers in which people have used it to understand when the details of design are as important as gross morphology. Enjoy!
Author: | Audrey Karperien ([email protected]) |
This plugin, an ongoing project, was initially developed as part of a master's at Charles Sturt University with input from Dr. H. Jelinek and Dr. Alastair Buchan, and code from Thomas R. Roy, University of Alberta. It continues to develop in response to the many suggestions from users and includes inputs from the ImageJ, neuroscience, engineering, programming, etc. communities. For information on how to cite the software and work published using it, see the online guide. | |
Source: | Contained in Frac_Lac.jar, which can be opened using a ZIP utility |
Installation: | Download Frac_Lac.jar to the plugins folder, or subfolder, restart ImageJ, then run the plugin using the Plugins/Fractal Analysis/FracLac command. |
Description: | Some patterns - such as contours of biological cells, other biological structures, fractals, and some textures - are difficult to describe using Euclidean measures like diameter or length, but can be quantitatively assessed using measures of complexity. FracLac quantitates such difficult to describe details of morphology represented in binary or grayscale digital images, using mass and box counting fractal dimensions (DBs), multifractal analysis data, lacunarity (λ) data, and some other morphometrics. FracLac also includes MicroMod2015 for ImageJ, for modelling branching structures with fractal features. |
Support: |
Limited inline help is available (2014) through a window that comes up when a user selects any scan type. The help includes a single page search, help hints on hover, and other features to make the software accessible to the non-expert and explain features in context. Hovering over a component on the set up dialog shows hints, and right clicking on them loads a page of instructions for the component. This inline help complements the User's Guide available online. Contact the team for assistance, suggestions, and bug reports.
A help archive that can be unzipped into the plugins folder where FracLac will access it, is available for download. The 38 page PDF manual for previous versions is still available for download.
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Features: |
FracLac scans images using a shifting grid algorithm that can do multiple scans from different locations on each image, and uses either a nonoverlapping or an overlapping sliding box method. The overlapping method can be exhaustive or not, depending on user choices. FracLac also scans images using an optional rotation function that analyzes an image from several angles and summarizes the results. FracLac automatically generates different types of series of box sizes (e.g., power or linear). In addition, local dimension scans may be done on subareas of either images or rois to show local variation in the DB and λ. These subareas are determined according to the user's choice, using ImageJ's ParticleAnalyzer, a square grid sized according to the user's choice, randomly selected blocks, or individual pixels. Users can view or save the results, and can reapply LUT's to colour coded images or generated text images (see Adjusting LUTs).
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Use: |
Before images can be analyzed, FracLac has to be set up. This is usually simply a matter of clicking a button for the type of scan you want to do, then selecting the defaults in the relevant options panel that appears, or making modifications if required.
Once FracLac has been set up, the type of scan appears at the bottom of the FracLac panel, and buttons to perform scans are enabled, as shown on the screen shot below. Using FracLac, one can do fractal, multifractal, and lacunarity analyses on:
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Outputs: |
The information returned by the various types of scans is summarized below:
Data Files
The measures noted above are reported in data files accompanied by various statistics for the data, including the y-intercept, standard deviation, and coefficient of variation, for instance. Reports generated can be viewed and saved as Results Windows or automatically saved as .txt files (tab-delimited;UTF-8 encoded) to be opened in a spreadsheet. These include:
Graphics Files
Some measures are represented in graphics that can be viewed and saved or automatically saved. These include:
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Limitations: |
FracLac works on binary images (black pixels on a white background, or white pixels on a black background) and on grayscale images or grayscale images that have been converted to RGB. For a binary analysis (e.g., branching patterns or single pixel wide contours of cellular outlines), the signal is black or white pixels and the noise is the opposite, white or black pixels, thus images must be thresholded prior to analysis to ensure that only the pixels of interest are assessed. For grayscale scans, images and rois are padded with a value that is ignored by the counting method. Grayscale scans are suited to textures as opposed to contours, and assess every pixel as signal, so the region of interest must be selected carefully. To ensure non-significant parts of grayscale images are not assessed, the image can be converted to RGB and the non-significant areas selected with the wand function or filled with a non-gray value, as is illustrated in the image.
You should assess your analysis against benchmark images and be aware of how the settings can affect the result. For instance, FracLac will determine the fractal dimension of a 400 x 400 pixel square as a perfect 1.000 (not fractal at all but the correct value) if the software is set to use a scaled series with a scaling factor of 2, a minimum box size of 25, and a maximum box size of 50%. But for most images, the point of the analysis is to determine a value for the fractal dimension without knowing the scaling ahead of time. See the online help for more about this.
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References: |
For details of the calculations, see the FracLac javadoc, which can be generated using the FracLac source code. For more information, the references below are the main ones used in defining the calculations:
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History: | 2002/08/26: First version 2002/09/26: Calculates circularity 2003/12/17: Major update 2004/06/30: Updated 2005/03/23: Updated to version 2.0aF 2005/11/24: Updated to version 2.3 2006/03/17: Updated to version 2.3j 2006/05/22: Updated to version 2.4b 2006/11/20: Updated to version 2.4e 2007/03/13: Major update to version 2.5 2007/03/27: Fixes bug that caused no printed and saved results for some scans (2.5a) 2007/04/04: Fixes bug that sometimes prevnted maximum epsilon from changing (2.5b) 2007/07/17: Fixes bugs that prevented box masses from being printed for sliding box lacunarity scans and prevented batches from being processed (2.5c) 2007/08/01: Fixes bug that prevented user from knowing if the number of grid orientations was changed or not; implements user suggestions for multifractal optimization and local connected fractal dimension; help file is now html (2.5d) 2011/02/03: Fixed a couple of bugs with multifractal analysis 2012/04/05: Fixed encoding of autosaved text files so Greek symbols are retained; fixed bug so autosaved files are saved in a date and time stamped folder (2.5g) 2102/04/15: release 2.5i; Fixed saved results file problem so filtered data are saved in separate files; fixed display problem so images are not displayed while being processed; changed grid location algorithm to use a series of grid positions in response to user requests; fixed bug so images having inverted LUTs are filled with the right colour. 2012/04/15: release 2.5i.2; fixed bug so subscans can be done using the particle analyzer again; fixed bug so subscans don't hang on stacks 2012/04/18: 2.5i.3 fixed bug that caused grid position counter to reset with very small box sizes; fixed problem with getting irregular rois 2012/04/30: 2.5k fixed bugs with particle analyzer on inverting LUTs; fixed random mass sampling bug that caused a hang on stacks 2012/05/03: 2.5m fixed bugs with lcfd stacks 2012/05/08: 2.5p fixed bug with regression lines not showing; added feature to let user choose less slices per stack so grid images don't crash 2012/05/13: 2.5r added feature to work on grayscale images with 'holes' 2012/06/21: 2.5v fixed bug with multifractal scanner autochanging the number of scans; added mass vs distance feature; updated colour coded image outputs 2012/11/02: 2.5w fixed bug with multifractal scanner to allow user to override minimum box size; changed default for edge effects; fixed grayscale bug with RGB images 2013/28/02: 2013Feb needs jdk 1.7; more compact UI; fixed bug with roi coordinates; updated output files to meet user requests to compare different fractal dimensions in one file and images in another 2013/25/04: 2013Apr jar recompiled for compatibility with jdk 1.6 2013/19/07: 2013Jul Fixed bug causing some data files to be empty in batch mode; updated parts of javadoc; 2013/24/11: 2013Nov Added feature to visualize changes in graphics showing the variation over an image; updated parts of javadoc 2013/04/12: 2013Dec Fixed bug with grayscale scans crashing; fixed batch jobs for subscans; fixed ParticleAnalyzer crashing issue; 2014/22/Mar: 2014Marb765 Added inline help window; fixed bug with colour-coding on screen; fixed bug with incorrect release number appearing on frame 2014/26/Mar: 2014Marb768 fixed bug for loading and saving settings files; changed encoding to utf-8 so symbols are encoded properly in text files 2014/03/Apr: 2014Aprb800 fixed a bug that prevented the user from changing the increment between exponents for multifractal analysis 2014/14/Apr: 2014Aprb804 recompiled to work under IJ 1.48u (in the previous release, the FracLac panel for setting up scans was not appearing in IJ 1.48u) 2014/17/Apr: 2014Aprb1012 fixed problems with the set up frame not appearing and sliders on the set up frame not working 2015/07/Jan: 2015Janb1292 Fixed problems with colour-coding dialog; added wave data processing functions. 2015/12/Jan: version 2015Janb2594 Fixed multifractal analysis ƒ(αQ) graphs; updated some icons. 2015/15/Jan: version 2015Janb2702 In response to a user request, it now generates an additional file with multifractal data separated according to datatype for comparing images. 2015/17/Jan: version 2015Janb3079 Updated help file for multifractals. Fixed problems with q-inc and q-array maker that were preventing multifractal apertures from being drawn. Included data file for multifractal analysis that describes the multifractal scaling to complement the multifractal spectra data files. Multifractal spectra plots now save as a stack for unoptimized samples. 2015/02/Feb: version 2015Febb4135 Fixed bugs in multifractal optimizer and data files so now the data set prints when the option for both optimizing and showing all is selected; fixed bug where plots were not saving for some filenames; included slice labels in data files if available as per user request. 2015/18/Feb: version 2015Febb5699 Fixed new bugs in multifractal optimizer and data files as per user request so individual file name is included on the plot. Fixed colour-coding bug so grayscale 'replace foreground pixels' option works. Fixed random sample bug that made this option crash on grayscale scans. 2015/27/Feb: version 2015Febb5810 Fixed multifractal ƒ(αQ) options dialogue so now the user can choose to print or not print optimizing data on the graph. 2015/08/March: version 2015Marb6206 Fixed 'OK' button; fixed slider bugs; fixed problem with inverted LUTs in batch mode so they are now processed the same as in screen mode. 2015/07/April: version 2015Apra4308 Added rotation function and integrated MicroMod for ImageJ. 2015/06/July: Fixed bug with loading multiple custom files in MicroMod for ImageJ; fixed bug with rotations in results file. 2015/15/Sept.: Fixed bugs in MicroMod and multifractal rotator. |
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