Finding Thresholds

2019-07-08

Most of the examples from this package are centred around thresholding images, but really the core function auto_thresh() can be used to find thresholds for any non-negative integer data.

Mostly high, some low

Let’s create a vector of values, most of which are greater than 50, the rest of which are less than 10:

x <- c(sample.int(9, 2e5, replace = TRUE), sample(51:99, 8e5, replace = TRUE))

Now let’s take a look at the distribution of x:

library(ggplot2)
library(dplyr)
tibble(x = x) %>%
  ggplot() + aes(x) + stat_density(bw = 3)

If you’re trying to threshold this sort of data, you’re probably looking for a method which will find a threshold that separates the larger values from the smaller ones. The available automatic thresholding methods are “IJDefault”, “Huang”, “Huang2”, “Intermodes”, “IsoData”, “Li”, “MaxEntropy”, “Mean”, “MinErrorI”, “Minimum”, “Moments”, “Otsu”, “Percentile”, “RenyiEntropy”, “Shanbhag”, “Triangle” and “Yen”. These are well demonstrated at http://imagej.net/Auto_Threshold.

Trying all methods

“MaxEntropy” and “Yen” often fail to find a threshold, so I generally avoid them. Let’s try out all the rest.

library(autothresholdr)
thresh_methods <- c(
  "IJDefault", "Huang", "Huang2", "Intermodes", "IsoData",
  "Li", "Mean", "MinErrorI", "Minimum", "Moments", "Otsu",
  "Percentile", "RenyiEntropy", "Shanbhag", "Triangle"
)
thresholds <- purrr::map_chr(thresh_methods, ~ auto_thresh(x, .)) %>%
  tibble(method = thresh_methods, threshold = .)
print(thresholds)
#> # A tibble: 15 x 2
#>    method       threshold
#>    <chr>        <chr>    
#>  1 IJDefault    39       
#>  2 Huang        8        
#>  3 Huang2       8        
#>  4 Intermodes   38       
#>  5 IsoData      39       
#>  6 Li           24       
#>  7 Mean         59       
#>  8 MinErrorI    59       
#>  9 Minimum      32       
#> 10 Moments      55       
#> 11 Otsu         8        
#> 12 Percentile   67       
#> 13 RenyiEntropy 69       
#> 14 Shanbhag     69       
#> 15 Triangle     10

Now, which of these selected a threshold between 10 and 49?

filter(thresholds, threshold >= 10, threshold <= 49)
#> # A tibble: 6 x 2
#>   method     threshold
#>   <chr>      <chr>    
#> 1 IJDefault  39       
#> 2 Intermodes 38       
#> 3 IsoData    39       
#> 4 Li         24       
#> 5 Minimum    32       
#> 6 Triangle   10

The other methods aren’t necessarily wrong, they’re just more strict or more lax than these ones. For thresholding microscopy images to remove background, my favourite methods are “Huang” and “Triangle” because they are quite conservative in that anything even slightly above background is kept.

Using one method

auto_thresh(x, "huang")
#> [1] 8
#> attr(,"ignore_black")
#> [1] FALSE
#> attr(,"ignore_white")
#> [1] FALSE
#> attr(,"ignore_na")
#> [1] FALSE
#> attr(,"autothresh_method")
#> [1] "Huang"
#> attr(,"class")
#> [1] "th"      "integer"
auto_thresh(x, "tri")
#> [1] 10
#> attr(,"ignore_black")
#> [1] FALSE
#> attr(,"ignore_white")
#> [1] FALSE
#> attr(,"ignore_na")
#> [1] FALSE
#> attr(,"autothresh_method")
#> [1] "Triangle"
#> attr(,"class")
#> [1] "th"      "integer"
auto_thresh(x, "otsu")
#> [1] 8
#> attr(,"ignore_black")
#> [1] FALSE
#> attr(,"ignore_white")
#> [1] FALSE
#> attr(,"ignore_na")
#> [1] FALSE
#> attr(,"autothresh_method")
#> [1] "Otsu"
#> attr(,"class")
#> [1] "th"      "integer"