The recent popularization of social network services (SNSs), such as YouTube, Dailymotion, and Facebook, enables people to easily publish their personal videos taken with mobile cameras. However, at the same time, such popularity has raised a new problem: video privacy. In such social videos, the privacy of people, i.e., their appearances, must be protected, but naively obscuring all people might spoil the video content. To address this problem, we focus on videographers' capture intentions. In a social video, some persons are usually essential for the video content. They are intentionally captured by the videographers, called intentionally captured persons (ICPs), and the others are accidentally framed-in (non-ICPs). Videos containing the appearances of the non-ICPs might violate their privacy. In this paper, we developed a system called BEPS, which adopts a novel conditional random field (CRF)-based method for ICP detection, as well as a novel approach to obscure non-ICPs and preserve ICPs using background estimation. BEPS reduces the burden of manually obscuring the appearances of the non-ICPs before uploading the video to SNSs. Compared with conventional systems, the following are the main advantages of BEPS: (i) it maintains the video content, and (ii) it is immune to the failure of person detection; false positives in person detection do not violate privacy. Our experimental results successfully validated these two advantages.