Despite the recent developments that allowed neural networks to achieve impressive performance on a variety of applications, these models are intrinsically affected by the problem of overgeneralization, due to their partitioning of the full input space into the fixed set of target classes used during training. Thus it is possible for novel inputs belonging to categories unknown during training or even completely unrecognizable to humans to fool the system into classifying them as one of the known classes, even with a high degree of confidence. Solving this problem may help improve the security of such systems in critical applications, and may further lead to applications in the context of open set recognition and 1-class recognition. This paper presents a novel way to compute a confidence score using denoising autoencoders and shows that such confidence score can correctly identify the regions of the input space close to the training distribution by approximately identifying its local maxima.