We present a novel and fast interactive approach to multi-modality cardiac image segmentation, which employs the linearly ordered surfaces as an additional constraint. We show using such a geometrical constraint helps to significantly reduce user interaction and improve the accuracy of segmentation results at the same time. We solve the proposed multiregion segmentation problem with the order constraints by means of convex optimization, resulting in a fast and reliable flow maximization approach which implicitly embeds the linear order prior without introducing extra computation load. In this regard, a new fully parallelized continuous max-flow algorithm is proposed and implemented using GPGPU to segment a 3D volume within one second. We demonstrate our results over pathological trans-esophageal echocardiogram, cardiac CT and delayed enhancement MRI data sets.