Local Binary Descriptors (LBDs) are good at matching image parts, but how much information is actually carried? Surprisingly, this question is usually ignored and replaced by a comparison of matching performances. In this paper, we directly address it by trying to reconstruct plausible images from different LBDs such as BRIEF and FREAK. Using an inverse problem framework, we show that this task is achievable with only the information in the descriptors, excluding the need of additional data. Hence, our results represent a novel justification for the performance of LBDs. Furthermore, since plausible images can be inferred using only these simple measurements, this emphasizes the concerns about privacy and secrecy of image keypoints raised by [Weinzaepfel 2011], that could have an important impact on public applications of image matching.