Minimum Risk Distance Measure for Object Recognition

The optimal distance measure for a given discrimination task underthe nearest neighbor framework has been shown to be the likelihoodthat a pair of measurements have different class labels [5]. Forimplementation and efficiency considerations, the optimal distancemeasure was approximated by combining more elementary distancemeasures defined on simple feature spaces. In this paper, weaddress two important issues that arise in practice for such anapproach:(a) What form should the elementary distance measure ineach feature space take? We motivate the need to use the optimaldistance measure in simple feature spaces as the elementarydistance measures; such distance measures have the desirableproperty that they are invariant to distance-respectingtransformations. (b) How do we combine the elementary distancemeasures? We present the precise statistical assumptions underwhich a linear logistic model holds exactly. We benchmark our modelwith three other methods on a challenging face discrimination taskand show that our approach is competitive with the state of theart.