Editing Multimodal distribution (section)

==== Otsu's method ====

[[Otsu's method]] for finding a threshold for separation between two modes relies on minimizing the quantity
<math display=block> \frac{ n_1 \sigma_1^2 + n_2 \sigma_2^2 }{ m \sigma^2 } </math>
where ''n''<sub>''i''</sub> is the number of data points in the ''i''<sup>th</sup> subpopulation, ''σ''<sub>''i''</sub><sup>2</sup> is the variance of the ''i''<sup>th</sup> subpopulation, ''m'' is the total size of the sample and ''σ''<sup>2</sup> is the sample variance. Some researchers (particularly in the field of [[digital image processing]]) have applied this quantity more broadly as an index for detecting bimodality, with a small value indicating a more bimodal distribution.<ref name=Chaudhuri2010>{{cite journal | last1 = Chaudhuri | first1 = D | last2 = Agrawal | first2 = A | year = 2010 | title = Split-and-merge procedure for image segmentation using bimodality detection approach | journal = Defence Science Journal | volume = 60 | issue = 3| pages = 290–301 | doi=10.14429/dsj.60.356| doi-access =  }}</ref>