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.
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