TODO

Implement fractal dimension analysis for grayscale images, micsrocopy images and biological application following FIJI/ImageJ (for inspiration check scikit-image/scikit-image#2347).

A good and thorough explanations, introduction and motivation is to be found on the ImageJ webpage. The motivation behind this repository is to make fractal analysis (FA) of images and estimation of fractal dimension of grayscale, microscopy, or other biologically relevant images accessible to Python users. Recently, there has been introduced this extension of FA to 3D together with some applications on cytoskeleton complexity.

Furthermore, FiJi/ImageJ is used (ref) in biology for image processing, estimating the fractal dimension of a grayscale image (or for analysis of signal coming from microscopy). The relevant documentation is on those pages: introduction (link to source code) or pdf summary with links to relevant pages, box counting and many more. Most importantly, this glossary which defines three measures for grayscale images (notice that this Is basically looking at 3D)

FracLac reports 3 basic types of fractal dimension for grayscale scans.

DB

DM

Dx̄

Besides all of this, this tool also controls for other problems (tbh I think that some are negligible like the starting grid position which they sample), eg see this link.

• Fractal dimension, Fractal count: Github repo, Github-fractal count, summary page for imageJ pugins.

Besides what is mentioned in section About the Calculations on the ImageJ introduction page, the following publications may serve as a source of inspiration, method explanation and application.

1. Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements (Kam, Y., Karperien, A., Weidow, B. et al. BMC Res Notes 2, 130 (2009). https://doi.org/10.1186/1756-0500-2-130), pdf accessible at https://bmcresnotes.biomedcentral.com/articles/10.1186/1756-0500-2-130.

2. Fractal analysis in practice, article on ImageJ: https://imagej.nih.gov/ij/plugins/fraclac/FLHelp/Fractals.htm#fractalanalysisinpractice

3. Fractal Dimension Estimation Methods for Biomedical Images (Antonio Napolitano, Sara Ungania and Vittorio Cannata, http://dx.doi.org/10.5772/48760, mentioned in this issue by @SalvatoreScaramuzzino), pdf accessible at http://cdn.intechopen.com/pdfs-wm/39360.pdf. Recommended to read, Matlab implementation and algorithm description.

4. Fractal Geometry in Image Processing (A. Annadhason, accessible online at https://www.yumpu.com/en/document/view/32997338/fractal-geometry-in-image-processing).

5. Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review (Michallek, F., Dewey, M., Eur Radiol 24, 60–69 (2014). https://doi.org/10.1007/s00330-013-2977-9 , accessible at https://link.springer.com/content/pdf/10.1007/s00330-013-2977-9.pdf).

6. MULTIFRAC: An ImageJ plugin for multiscale characterization of 2D and 3D stack images (Iván .G.Torreab, Richard J.Heckc, A.M.Tarquisdef, SoftwareX Volume 12, July–December 2020, 100574, https://doi.org/10.1016/j.softx.2020.100574, pdf accessible at https://reader.elsevier.com/reader/sd/pii/S2352711020302879?token=13BA7120C8771C204919EE98C9D9F7D45100EACF82804A60E139E10499A15BD0D083862DE89818D7D5C8440B23BCB850&originRegion=eu-west-1&originCreation=20210428074543).

7. Konatar, I., Popovic, T., & Popovic, N. (2020). Box-Counting Method in Python for Fractal Analysis of Biomedical Images. 2020 24th International Conference on Information Technology (IT). doi:10.1109/it48810.2020.90704, https://ieeexplore.ieee.org/document/9070454

(Another) Dynamics of Forest Fragmentation and Connectivity Using Particle and Fractal Analysis (Andronache, I., Marin, M., Fischer, R. et al., Sci Rep 9, 12228 (2019). https://doi.org/10.1038/s41598-019-48277-z, pdf accessible at https://www.nature.com/articles/s41598-019-48277-z.pdf).

1. Fractal Analysis in MATLAB: A Tutorial for Neuroscientists, pdf of the book The Fractal Geometry of the Brain is accessible at https://link.springer.com/content/pdf/10.1007%2F978-1-4939-3995-4.pdf.
2. Boxcount in Matlab, code.
3. Fractal analysis package.

1. An efficient differential box-counting approach to compute fractal dimension of image (N. Sarker, B. B. Chaudhuri, DOI: 10.1109/21.259692)

Fractal dimension in 1D

Extension to 3D