Segmentation of image ensembles via latent atlases

Abstract

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. However, the availability of comprehensive, reliable and suitable manual segmentations for atlas construction is limited. We therefore propose a method for joint segmentation of corresponding regions of interest in a collection of aligned images that does not require labeled training data. Instead, a latent atlas, initialized by at most a single manual segmentation, is inferred from the evolving segmentations of the ensemble. The algorithm is based on probabilistic principles but is solved using partial differential equations (PDEs) and energy minimization criteria. We evaluate the method on two datasets, segmenting subcortical and cortical structures in a multi-subject study and extracting brain tumors in a single-subject multi-modal longitudinal experiment. We compare the segmentation results to manual segmentations, when those exist, and to the results of a state-of-the-art atlas-based segmentation method. The quality of the results supports the latent atlas as a promising alternative when existing atlases are not compatible with the images to be segmented.

Fig. 1

Graphical representation of the proposed generative segmentation model. The model parameters (θ_I,n, θ_Γ) are represented with squares, the random variables (Γ_n, I_n) are represented with circles. The shaded circle indicates the observed variable I_n. A subset of the variables (Γ_n, I_n and θ_I,n) is replicated N times, as indicated by the bounding box.

Fig. 2

(a) Smooth approximation of the Heaviside function H̃_ε (Equation (11)) and (b) its derivative δ̃_ε (Equation (14)) for different values of ε.

Fig. 3

Three cross-sections of 3D segmentations of six brain structures in the right hemisphere. Automatic segmentation is shown in red. Manual segmentation is shown in blue.

Fig. 4

3D views of the manual and the automatic brain structure segmentation in one subject.

Fig. 5

Cross-sections of 3D atlases of six brain structures in the right hemispheres. Top row: Latent atlases generated as part of the proposed segmentation algorithm. Bottom row: probabilistic atlases. Each atlas is generated by averaging 39 corresponding manual labels of the input images.

Fig. 6

The mean and standard deviation of the Dice scores calculated for all images in the ensemble for six brain structures in the left and the right hemisphere. The latent atlas segmentation (red) is compared to the atlas-based segmentation (blue).

Fig. 7

(a) The mean Dice scores calculated for six brain structures in both hemispheres as a function of the number of images in the ensemble. (b) The mean Dice scores for six brain structures in both hemispheres as a function of the number of manual segmentations that initialize the latent atlas.

Fig. 8

Axial slice of the tumor volumes and the automatic 3D segmentations (red outlines) across 6 modalities and 10 time points. Not all the modalities were acquired at each time point.

Fig. 9

Manual segmentations (red, green, blue) and automatic segmentation (black) for lateral T1, T2 and DTI-FA images acquired at the same time point. The fourth image shows the corresponding section of the average of the associated 3D level-set functions. The zero level of the level-set functions average is shown in magenta. Tumor boundaries of all the modalities available for that time point are shown in black.

Fig. 10

Left: comparison of the overlap in the manual segmentations for each individual modality (red) with the overlap in the manual segmentations for all the modalities together (green). Overlap is defined as the mean Dice score between the three manual segmentations. See text for details. Right: A comparison of the average Dice scores of the proposed latent anatomy method (red) and the Dice scores of the multivariate EM for lesion segmentation of Van Leemput et al. (2001) (green). The segmentation results obtained by the proposed latent anatomy method are consistently better.