Geometric BIC

Kenichi KANATANI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.1   pp.144-151
Publication Date: 2010/01/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E93.D.144
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Recognition, Computer Vision
Keyword: 
geometric model selection,  AIC,  BIC,  MDL,  Bayesian estimation,  degeneracy detection,  

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Summary: 
The "geometric AIC" and the "geometric MDL" have been proposed as model selection criteria for geometric fitting problems. These correspond to Akaike's "AIC" and Rissanen's "BIC" well known in the statistical estimation framework. Another well known criterion is Schwarz' "BIC", but its counterpart for geometric fitting has not been known. This paper introduces the corresponding criterion, which we call the "geometric BIC", and shows that it is of the same form as the geometric MDL. Our result gives a justification to the geometric MDL from the Bayesian principle.