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Prostate MRI image segmentation has been an area of intense research due to the increased use of MRI as a modality for the clinical workup of prostate cancer. Segmentation is useful for various tasks, e.g. to accurately localize prostate boundaries for radiotherapy or to initialize multi-modal registration algorithms. In the past, it has been difficult for research groups to evaluate prostate segmentation algorithms on multi-center, multi-vendor and multi-protocol data. Especially because we are dealing with MR images, image appearance, resolution and the presence of artifacts are affected by differences in scanners and/or protocols, which in turn can have a large influence on algorithm accuracy. The Prostate MR Image Segmentation (PROMISE12) challenge was setup to allow a fair and meaningful comparison of segmentation methods on the basis of performance and robustness. In this work we will discuss the initial results of the online PROMISE12 challenge, and the results obtained in the live challenge workshop hosted by the MICCAI2012 conference. In the challenge, 100 prostate MR cases from 4 different centers were included, with differences in scanner manufacturer, field strength and protocol. A total of 11 teams from academic research groups and industry participated. Algorithms showed a wide variety in methods and implementation, including active appearance models, atlas registration and level sets. Evaluation was performed using boundary and volume based metrics which were combined into a single score relating the metrics to human expert performance. The winners of the challenge where the algorithms by teams Imorphics and ScrAutoProstate, with scores of 85.72 and 84.29 overall. Both algorithms where significantly better than all other algorithms in the challenge (p < 0.05) and had an efficient implementation with a run time of 8 minutes and 3 second per case respectively. Overall, active appearance model based approaches seemed to outperform other approaches like multi-atlas registration, both on accuracy and computation time. Although average algorithm performance was good to excellent and the Imorphics algorithm outperformed the second observer on average, we showed that algorithm combination might lead to further improvement, indicating that optimal performance for prostate segmentation is not yet obtained. All results are available online at http://promise12.grand-challenge.org/.

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Abstract. We propose and investigate novel max-flow models in the spatially continuous setting, with or without supervised constraints, under a comparative study of graph based max-flow / min-cut. We show that the continuous max-flow models correspond to their respective continuous min-cut models as primal and dual problems, and the continuous min-cut formulation without supervision constraints regards the well-known Chan-Esedoglu-Nikolova model [15] as a special case. In this respect, basic conceptions and terminologies applied by discrete max-flow / mincut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous max-flow and min-cut models. Moreover, we derive novel fast max-flow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous max-flow based algorithms outperform previous approaches in terms of efficiency and accuracy. [19,16]. There has been a vast amount of research on this topic during the last years [8,10]. Other discrete optimization methods include message passing [45,29] and linear programming [33] etc. One main drawback of such graph-based approaches is the grid bias. The interaction potential penalizes some spatial directions more than other, which leads to visible artifacts in computational results. Reducing such metrication errors can be done by considering more neighboring nodes [9,28] or high-order interaction potentials [27,25]. However, this either results in a heavy memory load and high computation cost or amounts to a more complex algorithmic scheme, e.g. QPBO [7,30].Recent studies [15] showed that formulating min-cut in the spatially continuous setting properly avoids metrication bias and leads to fast and global numerical solvers through convex optimization [11]. G. Strang [41,42] was the first to study max-flow and min-cut problems over a continuous domain. Related studies include [2,3], where Appleton et al proposed an edge-based continuous minimal surface approach to segmenting 2D and 3D objects. Chan et al [15] considered image segmentation with two regions in the form