Skip to contents

Medial axis transform

Source: R/medial_axis.R
medial_axis.Rd

Return the medial axis of a binary image: the locus of foreground pixels that are local maxima of the (squared) Euclidean distance transform in at least one of the four principal directions (horizontal, vertical, NW-SE diagonal, NE-SW diagonal). Each skeleton pixel carries width information via the distance value at that point.

Usage

medial_axis(image, return_distance = FALSE)

Arguments

image

A binary image: a matrix where non-zero values are foreground and zero values are background. Logical, integer, and numeric inputs are accepted.

return_distance

Logical. If FALSE (default), return only the binary skeleton in the same storage mode as image. If TRUE, return a list with elements skeleton (the binary skeleton) and distance (a numeric matrix of Euclidean distances from each foreground pixel to the nearest background pixel, with 0 on background pixels).

Value

Either a matrix (when return_distance = FALSE) or a list(skeleton, distance) (when return_distance = TRUE).

Details

This is different from thin(): classical thinning algorithms produce a connected, 1-pixel-wide skeleton without width information. The medial axis transform (Blum 1967) produces a skeleton with width information, useful for shape analysis where local thickness matters.

References

Blum, H. (1967). A transformation for extracting new descriptors of shape. In Models for the Perception of Speech and Visual Form (pp. 362-380). MIT Press.

Felzenszwalb, P. F., & Huttenlocher, D. P. (2012). Distance transforms of sampled functions. Theory of Computing, 8(19), 415-428. doi:10.4086/toc.2012.v008a019

Examples

# A 7x9 solid rectangle: the medial axis is the middle row.
m <- matrix(0L, nrow = 7, ncol = 9)
m[3:5, 3:7] <- 1L
medial_axis(m)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,]    0    0    0    0    0    0    0    0    0
#> [2,]    0    0    0    0    0    0    0    0    0
#> [3,]    0    0    1    1    0    1    1    0    0
#> [4,]    0    0    1    1    1    1    1    0    0
#> [5,]    0    0    1    1    0    1    1    0    0
#> [6,]    0    0    0    0    0    0    0    0    0
#> [7,]    0    0    0    0    0    0    0    0    0

# Returning width information alongside the skeleton.
result <- medial_axis(m, return_distance = TRUE)
result$skeleton
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,]    0    0    0    0    0    0    0    0    0
#> [2,]    0    0    0    0    0    0    0    0    0
#> [3,]    0    0    1    1    0    1    1    0    0
#> [4,]    0    0    1    1    1    1    1    0    0
#> [5,]    0    0    1    1    0    1    1    0    0
#> [6,]    0    0    0    0    0    0    0    0    0
#> [7,]    0    0    0    0    0    0    0    0    0
round(result$distance, 3)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,]    0    0    0    0    0    0    0    0    0
#> [2,]    0    0    0    0    0    0    0    0    0
#> [3,]    0    0    1    1    1    1    1    0    0
#> [4,]    0    0    1    2    2    2    1    0    0
#> [5,]    0    0    1    1    1    1    1    0    0
#> [6,]    0    0    0    0    0    0    0    0    0
#> [7,]    0    0    0    0    0    0    0    0    0