Editing Mixture model (section)

===Point set registration===
Probabilistic mixture models such as [[Gaussian mixture model]]s (GMM) are used to resolve [[point set registration]] problems in image processing and computer vision fields. For pair-wise [[point set registration]], one point set is regarded as the centroids of mixture models, and the other point set is regarded as data points (observations). State-of-the-art methods are e.g. [[Point_set_registration#Point_set_registration_algorithms#Coherent point drift|coherent point drift]] (CPD)<ref>
{{cite journal 
| last1 = Myronenko | first1 = Andriy
| last2 = Song | first2 = Xubo
| title = Point set registration: Coherent point drift
| number=12
| volume=32
| year=2010
| pages=2262–2275
| journal=IEEE Trans. Pattern Anal. Mach. Intell.
| doi=10.1109/TPAMI.2010.46
| pmid = 20975122
| arxiv = 0905.2635
| s2cid = 10809031
}}</ref> 
and [[Student's t-distribution]] mixture models (TMM).<ref>
{{cite journal 
| last1 = Ravikumar| first1 = Nishant
| last2 = Gooya| first2 = Ali
| last3 = Cimen| first3 = Serkan
| last4 = Frangi| first4 = Alexjandro
| last5 = Taylor| first5 = Zeike
| title = Group-wise similarity registration of point sets using Student's t-mixture model for statistical shape models
| volume=44
| year=2018
| pages=156–176
| journal=Med. Image Anal.
| doi=10.1016/j.media.2017.11.012
| pmid = 29248842
| doi-access = free
}}</ref> 
The result of recent research demonstrate the superiority of hybrid mixture models<ref>
{{cite conference 
| url = https://www.miccai2018.org/en/
| title = Intraoperative brain shift compensation using a hybrid mixture model
| last1 = Bayer| first1 = Siming
| last2 = Ravikumar| first2 = Nishant
| last3 = Strumia| first3 = Maddalena
| last4 = Tong| first4 = Xiaoguang
| last5 = Gao| first5 = Ying
| last6 = Ostermeier| first6 = Martin
| last7 = Fahrig| first7 = Rebecca
| last8 = Maier| first8 = Andreas
| date = 2018
| publisher = Springer, Cham
| book-title = Medical Image Computing and Computer Assisted Intervention – MICCAI 2018
| pages = 116–124
| location = Granada, Spain
| doi = 10.1007/978-3-030-00937-3_14
}}
</ref> 
(e.g. combining Student's t-distribution and Watson distribution/[[Bingham distribution]] to model spatial positions and axes orientations separately) compare to CPD and TMM, in terms of inherent robustness, accuracy and discriminative capacity.