@article{fdi:010035740,
  title = {{M}ultifractal analysis of the pore- and solid-phases in binary two-dimensional images of natural porous structures},
  author = {{D}athe, {A}. and {T}arquis, {A}.{M}. and {P}errier, {E}dith},
  editor = {},
  language = {{ENG}},
  abstract = {{W}e use multifractal analysis ({MFA}) to investigate how the {R}enyi dimensions of the solid mass and the pore space in porous structures are related to each other. {T}o our knowledge, there is no investigation about the relationship of {R}enyi or generalized dimensions of two phases of the same structure. {I}mages of three different natural porous structures covering three orders of magnitude were investigated: a microscopic soil structure, a soil void system visible without magnification and a mineral dendrite. {I}mage size was always 1024 x 1024 pixels and box sizes were chosen as powers of 2. {MFA} was carried out according to the method of moments, i.e., the probability distribution was estimated for moments ranging from - 10 < q < 10 and the {R}enyi dimensions were calculated from the log/log slope of the probability distribution for the respective moments over box sizes. {A} meaningful interval of box sizes was determined by estimating the characteristic length of the pore space and taking the next higher power of 2 value as the smallest box size, whereas the greatest box size was determined by optimizing the coefficients of determination of the log/log fits for all q. {T}he optimized box size range spans from 32 to 1024 pixels for all images. {G}ood generalized dimension ({D}q) spectra were obtained for this box size range, which are capable of characterizing heterogeneous spatial porous structure. {T}hey are alike for all images and phases which the exception of the solid mass of the soil void system, which shows a rather flat {D}q behavior. {A} closer examination reveals that similar patterns of structure gain similar spectra of generalized dimensions. {T}he capacity dimension for q=0 is close to the {E}uclidian dimension 2 for all investigated images and phases. (c) 2006 {E}lsevier {B}.{V}. {A}ll rights reserved.},
  keywords = {multifractal analysis ; generalized dimensions ; soil structure ; pore space ; solid mass},
  booktitle = {},
  journal = {{G}eoderma},
  volume = {134},
  numero = {3-4},
  pages = {318--326},
  ISSN = {0016-7061},
  year = {2006},
  DOI = {10.1016/j.geoderma.2006.03.024},
  URL = {https://www.documentation.ird.fr/hor/fdi:010035740},
}