In this paper we utilize Bayesian modeling and inference to learn a softmax classification model which performs Supervised Classification and Active Learning. For p < 1, lp-priors are used to impose sparsity on the adaptive parameters. Using variational inference, all model parameters are estimated and the posterior probabilities of the classes given the samples are calculated. A relationship between the prior model used and the independent Gaussian prior model is provided. The posterior probabilities are used to classify new samples and to define two Active Learning methods to improve classifier performance: Minimum Probability and Maximum Entropy. In the experimental section the proposed Bayesian framework is applied to Image Segmentation problems on both synthetic and real datasets, showing higher accuracy than state-of-the-art approaches.