This work presents the application of a discrete medical image registration framework to multi-organ segmentation in di erent modalities. The algorithm works completely automatically and does not have to be tuned speci cally for different datasets. A robust similarity measure, using the local self-similarity context (SSC), is employed and shown to outperform other commonly used metrics. Both a ne and deformable registration are driven by a dense displacement sampling (deeds) strategy. The smoothness of displacements is enforced by inference on a Markov random eld (MRF), using a tree approximation for computational e ciency. Consensus segmentations for unseen test images of the VISCERAL Anatomy 3 data are found by majority voting.
and the experimental setting detailed thereafter. The results on both training and test datasets are discussed in Sec. 4 and compared to some state-of-the-art approaches. 2
Discrete optimisation can capture large motions by de ning an appropriate range of displacements u. It enables a exible choice of di erent similarity terms, since no derivative is required. We use the framework presented in [HJBS13], which de nes a graphical model with nodes p 2 V (with spatial location xp) that correspond to control points in a uniform B-spline grid. For each node, the hidden labels fp (from a large quantised set L) are de ned as potential 3D displacements fp = up = fup; vp; wpg between a control point p in the xed image F and moving image M . Edges between nodes used for inference of the pair-wise regularisation costs R(fp; fq) (p; q 2 E ) are modelled by a minimum spanning tree (MST) for computational e ciency. The displacement eld is regularised using the squared di erences of the displacements of neighbouring control points: (1) (2) R(fp; fq) =
X jjup (p;q)2E jjxp uqjj2 xqjj For the image similarity (data term) self-similarity descriptors are used [HJP+13]. The selfsimilarity context is based on local patch distances within each image and invariant to contrast change, robust to noise and modality independent. The dissimilarity metric D, the L1 norm between 64 bit binary descriptor representations SSCF (for xed image) and SSCM (for moving image) at two locations x and x + u, can be e ciently calculated in the Hamming space: D(xp; up) = 1=jPj X y2P fSSCF (xp + y)
SSCM (xp + up + y)g where de nes an exclusive OR, a population count and y 2 P the local patch coordinates. The combined energy function with regularisation parameter becomes: E(f ) = Pp2V D(fp) + P(p;q)2E R(fp; fq). Belief propagation [FH06] on the MST (our relaxed graphical) is employed to nd the global minimum without iterations in only two passes.
Prior to the deformable registration, a block-matching based linear registration using also the SSC metric is employed as detailed in [HPSH14].1 3
The deformations between di erent anatomies make a large number of degrees of freedoms necessary. As pre-processing the images are resampled to an isotropic resolution of 1:8 1:8 1:8 mm3 and padded or cropped to have same dimensions. For the a ne pre-registration, three scales of control-point grids with spacings of [9; 8; 7] voxels are used. The displacement label space is de ned by two parameters: number of steps lmax and quantisation step q, which together de ne the label space L = q f0; 1; : : : ; lmaxg3 voxels. We used lmax = [6; 5; 4] and q = [5; 4; 3] voxels. For the deformable registration four scale levels with spacings of [8; 7; 6; 5], numbers of steps of lmax = [6; 5; 4; 3] and quantisations of q = [4; 3; 2; 1] voxels were used. The number of random samples and the regularisation weight were left at their default parameters 50 and 2. Inverse consistent is improved by employing a symmetric calculation of deformations (see [HJP+13]).
To asses the impact of the similarity metric, we additionally performed experiments using mutual information (MI) and normalised gradient elds (NGF) [HM05]. For a more detailed comparison of the optimisation, we also applied the popular continuous-optimisation based framework NiftyReg [MRT+10] (which uses a B-spline parameterisation) with an a ne initialisation [ORPA00].
1Our software is publicly available for download at www.mpheinrich.de (deedsRegSSC) Our results are summarised in Table 1 for a subset of 10 training scans of the contrast enhanced (ce) abdominal MRI modality (or thorax/adominal ceCT) and a leave-one-out validation. It can be seen that MRI segmentation is substantially more challenging yielding average results of Dice overlap for 7 organs of at most 0.744, while the results for the same setting for CT scans are 0.13 higher. Either of the two compared discrete optimisation strategies, by Gass et al. [GSG14] and our framework [HJBS13], outperforms the continuous optimisation approach of [MRT+10]. Using SSC as similarity metric improves the segmentation by 0.12 compared to MI and by 0.06 compared to NGF within the same framework. The multi-modal segmentation, for which we used MRI scans as xed and CT scans as moving atlas scans, shows nearly identical accuracy to using same modality priors. This is an interesting nding, which could be employed for generating synthetic CT scans from MRI scans, e.g. for MR-PET reconstruction [HSS+08]. Due to time limitations only preliminary results for the hidden test datasets could be computed (last row of Table 1), for which we employed only three atlas scans each. We anticipate further improvements for our nal results, which will subsequently be published on the VISCERAL leaderboard. The run-time of our algorithm on the virtual machine was on average 4 minutes per registration, which can be reduced with an optimised CPU implementation to less than a minute. 5
We have demonstrated that deformable registration using discrete optimisation enables accurate automatic MRI organ segmentation. Choosing both a robust similarity metric and optimisation strategy has been found to be important for achieving high overlap. Local similarity-weighted atlas performance estimation and advanced label fusion [AL13] may further improve the results. While machine learning techniques alone may not achieve the same accuracy as registration-based approaches for MRI segmentation, the combination of both can boost the performance. In initial experiments, we found that an RDF trained with both atlas-based priors and intensity features [MWG+15] improves the segmentation overlap of liver, spleen and kidneys by 0.06. [AL13]
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