Parametric and Nonparametric Methods for the Statistical Evaluation of Human ID Algorithms

Abstract

This paper reviews some of the major issues associated with the statistical evaluation of Human Identification algorithms, emphasizing comparisons between algorithms on the same set of sample images. A general notation is developed and common performance metrics are defined. A simple success/failure evaluation methodology where recognition rate depends upon a binomially distributed random variable, recognition count, is developed and the conditions under which this model is appropriate are discussed. Some nonparametric techniques are also introduced, including bootstrapping. When applied to estimating the distribution of recognition count for a single set of i.i.d. sampled probe images, bootstrapping is noted as equivalent to the parametric binomial model. Bootstrapping applied to recognition rate over resampled sets of images can be problematic. Specifically, sampling with replacement to form image probe sets is shown to introduce a conflict between assumptions required by bootstrapping and the way recognition rate is computed. In part to overcome this difficulty with bootstrapping, a different nonparametric Monte Carlo method is introduced, and its utility illustrated with an extended example. This method permutes the choice of gallery and probe images. It is used to answer two questions. Question 1: How much does recognition rate vary when comparing images of individuals taken on different days using the same camera? Question 2: When is the observed difference in recognition rates for two distinct algorithms significant relative to this variation? Two important general features of nonparametric methods are illustrated by the Monte Carlo study. First, within some broad limits, resampling generates sample distributions for any statistic of interest. Second, through careful choice of an appropriate statistic and subsequent estimation of its distribution, domain specific hypotheses may be readily formulated and tested.