Characterizing spatially varying performance to improve multi-atlas multi-label segmentation

Abstract

Segmentation of medical images has become critical to building understanding of biological structure-functional relationships. Atlas registration and label transfer provide a fully-automated approach for deriving segmentations given atlas training data. When multiple atlases are used, statistical label fusion techniques have been shown to dramatically improve segmentation accuracy. However, these techniques have had limited success with complex structures and atlases with varying similarity to the target data. Previous approaches have parameterized raters by a single confusion matrix, so that spatially varying performance for a single rater is neglected. Herein, we reformulate the statistical fusion model to describe raters by regional confusion matrices so that co-registered atlas labels can be fused in an optimal, spatially varying manner, which leads to an improved label fusion estimation with heterogeneous atlases. The advantages of this approach are characterized in a simulation and an empirical whole-brain labeling task.

Fig. 1

The spatial quality variation exhibited by registered atlases. A representative slice from the true labels (manually drawn) of a target brain is presented in (A). Four example observations of this slice can be seen in (B). The quality of the observations seen in (B) is compared to the true labels seen in (A) to construct the spatial quality variation heat maps presented in (C). Note that the spatial variation is independent of the actual labels of the brain.

Fig. 2

A visual representation of the Spatial STAPLE algorithm. The images in (A – D) represent varying confusion matrices for the various regions of the presented observation. The confusion matrix presented in (D) is of significantly higher quality than the other confusion matrices as represented by the fact that it is nearly a diagonal matrix. The observation can be seen in (E) where the regions corresponding to each confusion matrix is specified.

Fig. 3

Spatially varying rater quality simulation. The 3D truth model used in the simulation can be seen in both (A) and (B). (A) shows each of the individual slices of the model and (B) shows the three main cross-sections. (C) presents an example observation of the truth model. Representative estimates from both Spatial STAPLE (D) and STAPLE (E) are shown using 10 raters.

Fig. 4

Simulation results for spatial varying performance. The results from the 10 Monte Carlo iteration simulation can be seen in (A). It is evident that both STAPLE and Spatial STAPLE outperform majority vote for all numbers of raters. For increasing numbers of raters Spatial STAPLE dramatically outperforms STAPLE. The sensitivity of the implicit prior can be seen in (B). Note that for high values, the Spatial STAPLE estimate converges to the STAPLE estimate. For low values, the Spatial STAPLE estimate is unstable and results in estimations that are dramatically worse than STAPLE.

Fig. 5

Results from an empirical experiment using 6 labels. A representative truth slice from the 6-label model can be seen in (A). A cropped and rotated region (A) is presented in (B). The estimates seen in (C) and (D) represent the output from Spatial STAPLE (C) and STAPLE (D) using 8 volumes. The accuracy of the gray matter estimation (in terms of the difference in DSC values) for varying numbers of volumes can be seen in (E). For reference, the average STAPLE DSC was approximately 0.8.

Fig. 6

Results from the empirical experiment using 41 labels. A representative slice from the truth model can be seen in (A). The majority vote, STAPLE and Spatial STAPLE estimates for this slice using 8 volumes can be seen in (B), (C) and (D), respectively. A comparison of the fraction of voxels correct when fusing 5 to 15 volumes to all 24 target atlases can be seen in (E). A per label comparison between Spatial STAPLE and majority vote can be seen in (F). Only the 36 labels that were consistent between the 24 target atlases are shown. Note that both Spatial STAPLE and majority vote outperform STAPLE for increasing numbers of volumes in (E). Lastly, note that there are a large number of outliers for which Spatial STAPLE outperforms majority vote in (F).