Real-time, accurate, and robust pupil detection is an essential prerequisite to enable pervasive eye-tracking and its applications -- e.g., gaze-based human computer interaction, health monitoring, foveated rendering, and advanced driver assistance. However, automated pupil detection has proved to be an intricate task in real-world scenarios due to a large mixture of challenges such as quickly changing illumination and occlusions. In this paper, we introduce the Pupil Reconstructor PuRe, a method for pupil detection in pervasive scenarios based on a novel edge segment selection and conditional segment combination schemes; the method also includes a confidence measure for the detected pupil. The proposed method was evaluated on over 316,000 images acquired with four distinct head-mounted eye tracking devices. Results show a pupil detection rate improvement of over 10 percentage points w.r.t. state-of-the-art algorithms in the two most challenging data sets (6.46 for all data sets), further pushing the envelope for pupil detection. Moreover, we advance the evaluation protocol of pupil detection algorithms by also considering eye images in which pupils are not present. In this aspect, PuRe improved precision and specificity w.r.t. state-of-the-art algorithms by 25.05 and 10.94 percentage points, respectively, demonstrating the meaningfulness of PuRe's confidence measure. PuRe operates in real-time for modern eye trackers (at 120 fps).