We present a new approach to the matting problem which splits the task into two steps: interactive trimap extraction followed by trimap-based alpha matting. By doing so we gain considerably in terms of speed and quality and are able to deal with high resolution images. This paper has three contributions: (i) a new trimap segmentation method using parametric max-flow; (ii) an alpha matting technique for high resolution images with a new gradient preserving prior on alpha; (iii) a database of 27 ground truth alpha mattes of still objects, which is considerably larger than previous databases and also of higher quality. The database is used to train our system and to validate that both our trimap extraction and our matting method improve on state-of-the-art techniques.