img_self_similarity returns the self-similarity of an image (i.e., the degree to which the log-log power spectrum of the image falls with a slope of -2). Higher values indicate higher image self-similarity.

img_self_similarity(img, full = FALSE, logplot = FALSE, raw = FALSE)

## Arguments

img An image in form of a matrix or array of numeric values, preferably by square size. If the input is not square, bilinear resizing to a square size is performed using the OpenImageR package. Use e.g. img_read() to read an image file into R. logical. Should the full frequency range be used for interpolation? (default: FALSE) logical. Should the log-log power spectrum of the image be plotted? (default: FALSE) logical. Should the raw value of the regression slope be returned? (default: FALSE)

## Value

a numeric value (self-similarity)

## Details

The function takes a (square) array or matrix of numeric or integer values representing an image as input and returns the self-similarity of the image. Self-similarity is computed via the slope of the log-log power spectrum using OLS. A slope near -2 indicates fractal-like properties (see Redies et al., 2007; Simoncelli & Olshausen, 2001). Thus, value for self-similarity that is return by the function calculated as self-similarity = abs(slope + 2) * (-1). That is, the measure reaches its maximum value of 0 for a slope of -2, and any deviation from -2 results in negative values that are more negative the higher the deviation from -2. For color images, the weighted average between each color channel's values is computed (cf. Mayer & Landwehr 2018).

Per default, only the frequency range betwen 10 and 256 cycles per image is used for interpolation. Computation for the full range can be set via the parameter full = TRUE.

If logplot is set to TRUE then a log-log plot of the power spectrum is additionally shown. If the package ggplot2 is installed the plot includes the slope of the OLS regression. Note that this option is currently implemented for grayscale images.

It is possible to get the raw regression slope (instead of the transformed value which indicates self-similarity) by using the option raw = TRUE.

For color images, the weighed average between each color channel's values is computed.

## Note

The function inspired by Matlab's sfPlot (by Diederick C. Niehorster).

## References

Mayer, S. & Landwehr, J, R. (2018). Quantifying Visual Aesthetics Based on Processing Fluency Theory: Four Algorithmic Measures for Antecedents of Aesthetic Preferences. Psychology of Aesthetics, Creativity, and the Arts, 12(4), 399--431. doi:10.1037/aca0000187

Redies, C., Hasenstein, J., & Denzler, J. (2007). Fractal-like image statistics in visual art: Similarity to natural scenes. Spatial Vision, 21, 137--148. doi:10.1163/156856807782753921

Simoncelli, E. P., & Olshausen, B. A. (2001). Natural image statistics and neural representation. Annual Review of Neuroscience, 24, 1193--1216. doi:10.1146/annurev.neuro.24.1.1193

img_read, img_contrast, img_complexity, img_simplicity, img_symmetry, img_typicality,

## Examples

# Example image with high self-similarity: romanesco
romanesco <- img_read(system.file("example_images", "romanesco.jpg", package = "imagefluency"))
#
# display image
grid::grid.raster(romanesco)
#
# get self-similarity
img_self_similarity(romanesco)

# Example image with low self-similarity: office
office <- img_read(system.file("example_images", "office.jpg", package = "imagefluency"))
#
# display image
grid::grid.raster(office)
#
# get self-similarity
img_self_similarity(office)