This paper presents a new method to both track and segment multiple objects in videos using min-cut/max-flow optimizations. We introduce objective functions that combine low-level pixel-wise measures (color, motion), high-level observations obtained via an independent detection module, motion prediction and contrast-sensitive contextual regularization. One novelty is that external observations are used without adding any association step. The observations are image regions (pixel sets) that can be output by any kind of detector. The minimization of these cost functions simultaneously allows "detection-before-track" tracking (track-to-observation assignment and automatic initialization of new tracks) and segmentation of tracked objects. When several tracked objects get mixed up by the detection module (e.g., single foreground detection mask for objects close to each other), a second stage of minimization allows the proper tracking and segmentation of these individual entities despite the observation confusion. Experiments on different type of sequences demonstrate the ability of the method to detect, track and precisely segment persons as they enter and traverse the field of view, even in cases of partial occlusions, temporary grouping and frame dropping.