{ Qiang Ji Hui Su Lisha Chen}

Abstract

Deep neural networks achieve good performance in many computer vision problems such as face alignment. However, when the testing image is challenging due to low resolution, occlusion or adversarial attacks, the accuracy of a deep neural network suffers greatly. Therefore, it is important to quantify the uncertainty in its predictions. A probabilistic neural network with Gaussian distribution over the target is typically used to quantify uncertainty for regression problems. However, in real-world problems especially computer vision tasks, the Gaussian assumption is too strong. To model more general distributions, such as multi-modal or asymmetric distributions, we propose to develop a kernel density deep neural network. Specifically, for face alignment, we adapt state-of-the-art hourglass neural network into a probabilistic neural network framework with landmark probability map as its output. The model is trained by maximizing the conditional log likelihood. To exploit the output probability map, we extend the model to multi-stage so that the logits map from the previous stage can feed into the next stage to progressively improve the landmark detection accuracy. Extensive experiments on benchmark datasets against state-of-the-art unconstrained deep learning method demonstrate that the proposed kernel density network achieves comparable or superior performance in terms of prediction accuracy. It further provides aleatoric uncertainty estimation in predictions.