3D Volume - Description of plugins

3D Image volume opener

• Opens an image stack treated as volume
• 8-bit grey or RGB color images
• For a stack, all images must be of same size and type
• Includes a preview (thumbnail) panel
• Note: Fiji displays RGB images as 3 channel color images. Workaround: Type Image/Type/RGB Color

3D Image volume generator

• Generates a single image volume
• 8-bit grey or RGB color
• Volume size can be set
• Maximal grey values can be set
• Random, Gaussian, Constant
• Fractal surface - Fourier (FFT) or Midpoint displacement (MPD)
  • Theoretical fractal dimension in the range of [3,4] can be set
• Fractal Iterated function system (IFS) - Menger cube, Sierpinski pyramid or Mandelbrot island
  • The number of IFS iterations can be set
  • Width is taken for the height and depth of the volume
• Note: Image volumes can be visualized with Fiji’s 3D viewer (Plugins/3D Viewer)
• Note: Fiji sometimes displays oversaturated grey values. Workaround: Image/Color/Edit LUT… and press 2x Invert

3D Preprocessing - 3D Filter

• Image volume filtering
• 8-bit grey or RGB color image volume
• Gaussian blur
  • Sigma can be set
• Mean, Median
  • Size of kernel can be set
• Low-pass, High-pass with FFT
  • Radius (Cutoff frequency) can be set

3D Preprocessing - 3D Noise

• Adding noise
• 8-bit grey or RGB color image volume
• Shot, Salt&Pepper
  • Percentage of pixels that will be changed can be set
• Uniform
  • Percentage of maximum value changes can be set
• Gaussian, Rayleigh, Exponential
  • Scaling parameter can be set

3D Preprocessing - 3D Surrogates

• Computes a surrogate image volume
• 8-bit grey or RGB color image volume
• Shuffle, Gaussian, Random phase, AAFT
• FFT windowing can be set

3D Complexity analyses - 3D Kolmogorov complexity and Logical depth

• KC is estimated in a fast way by compressing data bytes (ZIP, ZLIB, GZIB) or
• KC is estimated by the memory size of compressed images saved to disk (TIFF-LZW) - very slow!
• 8-bit grey image volume
• Lossless and lossy algorithms can be chosen
• Lossless algorithms are recommended
• LD is estimated by the decompression time of the compressed data bytes (ZIP, ZLIB, GZIB) or
• LD is estimated by the opening time of the compressed image (TIFF-LZW)
• Iterations should be set to as high a value as possible
• LD values should be taken with caution, as computers are not well suited to measure times
• Zenil et al., Complexity, 2012, DOI 10.1002/cplx.20388

3D Entropy analyses - 3D Generalised entropies

• SE, H1, H2, H3, Renyi, Tsallis, SNorm, SEscort, SEta, SKappa, SB, SBeta, SGamma
• Probabilities are computed with plain pixel grey values
• 8-bit grey image volume
• A plot of Renyi entropies can be shown
• Amigo et al., 2018, Entropy, DOI 10.3390/e20110813
• Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer, 2009

3D Fractal analyses - 3D Box counting dimension

• Fractal dimension with 3D box counting
• This is a direct expansion of the 2D algorithm
• 8-bit grey image volume
• Binary [0, >0] algorithm
• Raster box scanning
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set

3D Fractal analyses - 3D Correlation dimension

• Fractal dimension with 3D correlation
• This is a direct expansion of the 2D algorithm
• 8-bit grey image volume
• Binary [0, >0] or grey value correlation
• Fast Raster box scanning instead of slow sliding box scanning
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set

3D Fractal analyses - 3D FFT dimension

• Fractal dimension with a 3D FFT algorithm or subsequent 1D FFTs
• 8-bit grey image volume
• Several windowing filters can be set
• Spherical average of k values or
• Mean of separate line scans (horizontal and verical) or
• Integrated line scans (k should be restricted to low values - frequencies)
• Dt=3, Topological dimension is assumed to be 3
• Linear regression parameters of the double log plot can be set
• For spherical averaging, the number of regression points is higher than k itself and additionally, will be automatically lowered to the number of averages

3D Fractal analyses - 3D Fractal fragmentation indices

• FFI - Fractal fragmentation index
• FFDI - Fractal fragmentation and disorder index
• FTI - Fractal tentacularity index
• 8-bit binary image volume
• Binary [0, >0] algorithm
• Raster box scanning
• FFI = FD of mass - FD of boundary
• FFI is the Box counting dimension of the volume (mass) - Box counting dimension of the boundary volume
• Boundary volume = volume - Eroded volume (erosion by one pixel)
• FFDI = D1(1-FFI)
• D1 is the Information dimension
• FTI = FFI(convex hull) - FFI
• Fractal dimension computations with 3D Box counting (raster box scanning)
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set
• Andronache et al., Chaos, Solitons & Fractals, 2016, DOI 10.1016/j.chaos.2016.06.013

3D Fractal analyses - 3D Generalised dimensions

• 3D Generalised fractal dimensions
• 8-bit binary or grey image volume
• Binary [0, >0] or grey value mass algorithm
• Raster box scanning
• Dq and f-spectrum plots can be shown
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set
• Ahammer et al., Physica D, 2003, DOI 10.1016/S0167-2789(03)00099-X

3D Fractal analyses - 3D Higuchi dimension

• Fractal dimension with Higuchi inspired 3D algorithms
• This is a direct expansion of the 2D algorithms
• 8-bit grey image volume
• Grey value algorithm
• Several options can be chosen
• Linear regression parameters of the double log plot can be set
• Ahammer et al., Chaos, 2015, DOI 10.1063/1.4923030

3D Fractal analyses - 3D Lacunarity

• Direct expansion of the 2D algorithms
• 8-bit binary or grey image volume
• The number of boxes with distinct sizes can be set
• Shows a double logarithmic plot of lacunarities
• Raster box scanning (Sliding box and Tug of war method are planned for a future release)
• Binary [0, >0] or grey value algorithm
• Raster box scanning
• <L>-R&P… Weighted mean lacunarity according to Roy & Perfect, Fractals, 2014, DOI10.1142/S0218348X14400039
• <L>-S&V… Weighted mean lacunarity according to Sengupta & Vinoy, Fractals, 2006, DOI 10.1142/S0218348X06003313
• Reiss et al., Chaos, 2016, DOI 10.1063/1.4966539

3D Fractal analyses - 3D Minkowski dimension

• Fractal dimension with 3D morphological dilations and erosions
• 8-bit binary or grey image volume
• Binary [0, >0] dilation
• Blanket or Variation method with grey value dilation/erosion
• The number of dilation/erosion steps can be set
• The shape of the morphological structuring element can be set
• Linear regression parameters of the double log plot can be set
• Peleg et al., IEEE-TPAMI, 1984, DOI 10.1109/TPAMI.1984.4767557

3D Fractal analyses - 3D Tug of war dimension

• Fractal dimension by using the 3D tug of war algorithm
• 8-bit binary image volume
• Binary [0, >0] algorithm
• Grey value algorithm
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set
• The ToW algorithm is a statistical approach and is dependent on the accuracy and confidence settings
• In the original paper accuracy=30 and confidence=5
• But it is recommended to set accuracy and confidence as high as computation times allow
• Reiss et al., Chaos, 2016, DOI 10.1063/1.4966539