Bayesian Image Classification in Feature Space

In this chapter, we will define image classification as probabilistic decision making in feature space. The Bayesian theorem is applied to define the most likely label for a sample based on its features. It is computed from a class-conditional feature likelihood and the a priori probability of a sample to belong to some class. We will present different means to estimate a likelihood function from labeled samples. Together with an estimate of the a priori probability this constitutes a generative model that enables computing class membership probabilities for every combination of features and classes. Classification then just requires to determine the maximum a posteriori probability of a sample for some class given its features. Functions and parameters for the mapping from features to class probabilities are estimated from labeled training samples and tested on labeled test samples. The two types of data sets will be characterized and conditions for acceptable data for this purpose will be developed. Several benchmark data sets that we will use in the exercises in the book are described and criteria to assess the success of a trained classifier are presented.