# Fuzzy Entropy Image Segmentation

*Shota Ochi*

*2018-08-04*

Automatic thresholding is important for machine vision.

Otsu’s method is a novel algorithm and widely used for machine vision.

However, Otsu’s method is not suitable for some cases.

Fuzzy entropy image segmentation can be an alternative in such cases.

I implemented fuzzy entropy image segmentation (ThresholdFuzzy) by following [1].

You can confirm it by the code below.

```
library(devtools)
install_github("ShotaOchi/imagerExtra")
library(imagerExtra)
a <- load.image("http://gahag.net/img/201604/21s/gahag-0078436493-1.jpg") %>% grayscale()
layout(matrix(1:4, 2, 2))
plot(a, main = "Original")
threshold(a) %>% plot(main = "A Variant of Otsu")
ThresholdTriclass(a) %>% plot(main = "Iterative Triclass")
ThresholdFuzzy(a) %>% plot(main = "Fuzzy Entropy")
```

Note that ThresholdFuzzy uses a particle swarm optimization algorithm becase exaustive search is time consuming.

That’s why ThresholdFuzzy returns different value every time.

Let’s confirm it.

```
test <- sapply(1:100, function(x) ThresholdFuzzy(a, returnvalue = TRUE))
hist(test)
```

You can reduce the variance by tuning the parameters of ThresholdFuzzy, although I believe the variance is sufficiently small.

[1] Linyi Li, Deren Li (2008). Fuzzy entropy image segmentation based on particle swarm optimization. Progress in Natural Science.