Background: Regularized regression methods such as principal component or partial least squares regression perform well in learning tasks on high dimensional spectral data, but cannot explicitly eliminate irrelevant features. The random forest classifier with its associated Gini feature importance, on the other hand, allows for an explicit feature elimination, but may not be optimally adapted to spectral data due to the topology of its constituent classification trees which are based on orthogonal splits in feature space.

Knowledge of left atrial (LA) anatomy is important for atrial fibrillation ablation guidance, fibrosis quantification and biophysical modelling. Segmentation of the LA from Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) images is a complex problem. This manuscript presents a benchmark to evaluate algorithms that address LA segmentation. The datasets, ground truth and evaluation code have been made publicly available through the http://www.cardiacatlas.org website. This manuscript also reports the results of the Left Atrial Segmentation Challenge (LASC) carried out at the STACOM'13 workshop, in conjunction with MICCAI'13. Thirty CT and 30 MRI datasets were provided to participants for segmentation. Each participant segmented the LA including a short part of the LA appendage trunk and proximal sections of the pulmonary veins (PVs). We present results for nine algorithms for CT and eight algorithms for MRI. Results showed that methodologies combining statistical models with region growing approaches were the most appropriate to handle the proposed task. The ground truth and automatic segmentations were standardised to reduce the influence of inconsistently defined regions (e.g., mitral plane, PVs end points, LA appendage). This standardisation framework, which is a contribution of this work, can be used to label and further analyse anatomical regions of the LA. By performing the standardisation directly on the left atrial surface, we can process multiple input data, including meshes exported from different electroanatomical mapping systems.

Abstract. In his original paper on random forests, Breiman proposed two different decision tree ensembles: one generated from "orthogonal" trees with thresholds on individual features in every split, and one from "oblique" trees separating the feature space by randomly oriented hyperplanes. In spite of a rising interest in the random forest framework, however, ensembles built from orthogonal trees (RF) have gained most, if not all, attention so far.In the present work we propose to employ "oblique" random forests (oRF) built from multivariate trees which explicitly learn optimal split directions at internal nodes using linear discriminative models, rather than using random coefficients as the original oRF. This oRF outperforms RF, as well as other classifiers, on nearly all data sets but those with discrete factorial features. Learned node models perform distinctively better than random splits. An oRF feature importance score shows to be preferable over standard RF feature importance scores such as Gini or permutation importance. The topology of the oRF decision space appears to be smoother and better adapted to the data, resulting in improved generalization performance. Overall, the oRF propose here may be preferred over standard RF on most learning tasks involving numerical and spectral data.

Dynamic contrast-enhanced magnetic resonance (DCE-MR) imaging can be used to study microvascular structure in vivo by monitoring the abundance of an injected diffusible contrast agent over time. The resulting spatially resolved intensity-time curves are usually interpreted in terms of kinetic parameters obtained by fitting a pharmacokinetic model to the observed data. Least squares estimates of the highly nonlinear model parameters, however, can exhibit high variance and can be severely biased. As a remedy, we bring to bear spatial prior knowledge by means of a generalized Gaussian Markov random field (GGMRF). By using information from neighboring voxels and computing the maximum a posteriori solution for entire parameter maps at once, both bias and variance of the parameter estimates can be reduced thus leading to smaller root mean square error (RMSE). Since the number of variables gets very big for common image resolutions, sparse solvers have to be employed. To this end, we propose a generalized iterated conditional modes (ICM) algorithm operating on blocks instead of sites which is shown to converge considerably faster than the conventional ICM algorithm. Results on simulated DCE-MR images show a clear reduction of RMSE and variance as well as, in some cases, reduced estimation bias. The mean residual bias (MRB) is reduced on the simulated data as well as for all 37 patients of a prostate DCE-MRI dataset. Using the proposed algorithm, average computation times only increase by a factor of 1.18 (871 ms per voxel) for a Gaussian prior and 1.51 (1.12 s per voxel) for an edge-preserving prior compared to the single voxel approach (740 ms per voxel).