This paper presents an interactive image segmentation framework which is ultra-fast and accurate. Our framework, termed "CO3", consists of three components: COupled representation, COnditional model and COnvex inference. (i) In representation, we pose the segmentation problem as partitioning an image domain into regions (foreground vs. background) or boundaries (on vs. off) which are dual but simultaneously compete with each other. Then, we formulate segmentation process as a combinatorial posterior ratio test in both the region and boundary partition space. (ii) In modeling, we use discriminative learning methods to train conditional models for both region and boundary based on interactive scribbles. We exploit rich image features at multi-scales, and simultaneously incorporate user's intention behind the interactive scribbles. (iii) In computing, we relax the energy function into an equivalent continuous form which is convex. Then, we adopt the Bregman iteration metho...