Convolutional Neural Networks (CNNs) have proven to be state-of-the-art models for supervised computer vision tasks, such as image classification. However, large labeled data sets are generally needed for the training and validation of such models. In many domains, unlabeled data is available but labeling is expensive, for instance when specific expert knowledge is required. Active Learning (AL) is one approach to mitigate the problem of limited labeled data. Through selecting the most informative and representative data instances for labeling, AL can contribute to more efficient learning of the model. Recent AL methods for CNNs propose different solutions for the selection of instances to be labeled. However, they do not perform consistently well and are often computationally expensive. In this paper, we propose a novel AL algorithm that efficiently learns from unlabeled data by capturing high prediction uncertainty. By replacing the softmax standard output of a CNN with the parameters of a Dirichlet density, the model learns to identify data instances that contribute efficiently to improving model performance during training. We demonstrate in several experiments with publicly available data that our method consistently outperforms other state-of-the-art AL approaches. It can be easily implemented and does not require extensive computational resources for training. Additionally, we are able to show the benefits of the approach on a real-world medical use case in the field of automated detection of visual signals for pneumonia on chest radiographs.