A logarithmic opinion pool based STAPLE algorithm for the fusion of segmentations with associated reliability weights

Abstract

Pelvic floor dysfunction is common in women after childbirth and precise segmentation of magnetic resonance images (MRI) of the pelvic floor may facilitate diagnosis and treatment of patients. However, because of the complexity of its structures, manual segmentation of the pelvic floor is challenging and suffers from high inter and intra-rater variability of expert raters. Multiple template fusion algorithms are promising segmentation techniques for these types of applications, but they have been limited by imperfections in the alignment of templates to the target, and by template segmentation errors. A number of algorithms sought to improve segmentation performance by combining image intensities and template labels as two independent sources of information, carrying out fusion through local intensity weighted voting schemes. This class of approach is a form of linear opinion pooling, and achieves unsatisfactory performance for this application. We hypothesized that better decision fusion could be achieved by assessing the contribution of each template in comparison to a reference standard segmentation of the target image and developed a novel segmentation algorithm to enable automatic segmentation of MRI of the female pelvic floor. The algorithm achieves high performance by estimating and compensating for both imperfect registration of the templates to the target image and template segmentation inaccuracies. A local image similarity measure is used to infer a local reliability weight, which contributes to the fusion through a novel logarithmic opinion pooling. We evaluated our new algorithm in comparison to nine state-of-the-art segmentation methods and demonstrated our algorithm achieves the highest performance.

Fig. 1

Illustration of Synthetic Data Segmentation Results. Comparison of segmentation differences between the ground-truth and segmentation generated by LOP-STAPLE (e), its approximate closed form solution (f), STEPS (g), and STAPLE (h) using twenty templates. Three of the generated templates are shown in (a),(b), and (c). The target image is shown in (d). It can be seen that label information alone is insufficient to achieve excellent fusion, as illustrated by the performance of STAPLE in this example. While the STEPS algorithm, which incorporates intensity-based atlas selection, improves performance, the best performance is achieved with LOP-STAPLE, by the use of intensity information through logarithmic opinion pooling. The number of misclassified voxels using the LOP-STAPLE, its closed form approximation, and STEPS are 719, 1081, and 1676, respectively. It can be seen that the closed form approximation has lower accuracy; however, it is significantly faster than the fixed point solution.

Fig. 2

Illustration of Pelvis Segmentation Fusion. (a): MRI sample slice of female pelvis, (b): estimated segmentation using local MAP STAPLE, (c): using STAPLE, and (d): using majority voting. (e,f,g) illustrate manual segmentations from each one of the experts. Legend : pink, pelvic bones; dark blue, vagina; red, obturator internus; violet, bladder; blue, coccyx; gray, rectum.

Fig. 3

Quantitative Comparison of Label Fusion of the Female Pelvis Segmentations. Comparison of the coefficient of variation of the Dice similarity coefficient (DSC) achieved by different label fusion algorithms. The lowest coefficient of variation is the best. The ratio of the coefficient of variation for each method to the lowest achieved (local MAP STAPLE with HWS=16) is reported for local MAP STAPLE (L-ST with HWS of 1, 2, 4, 8 and 16), STAPLE, Majority Voting (MV), and expert interactive segmentation (Exj-N,l corresponds to the l^th segmentation by expert j).

Fig. 4

3D visualization of segmentations of nine pelvic floor structures. (a) Majority Voting, (b) COLLATE [24], (c) SIMPLE [26], (d) STAPLER [25], (e) Sabuncu et al. algorithm [30], (f) Artaechevarria et al. method [29], (g) STAPLE [18], (h) STEPS [38], (i) Non-Local STAPLE [39], (j) MALF-PICSL [42], (k) LOP-STAPLE, (l) Weakly Regularized LOP-STAPLE, (m) Manual Segmentation. It can be seen that LOP-STAPLE and Weakly Regularized LOP-STAPLE have higher accuracy compared to the other fusion algorithms. Legend: blue violet, pelvic bones; indigo, vagina; brown, obturator internus; red, urethra; olive, bladder; dark orange, rectum; green, Levator ani; orange,coccyx; yellow, symphysis.

Fig. 5

Sensitivity analysis of the LOP-STAPLE algorithm to the shift and scale parameters of the reliability weights. We have evaluated performance of LOP-STAPLE for different shift and scale parameters by evaluating the average of the Dice coefficient of the 9 structures in 18 subjects. This figure shows that our algorithm is very robust and has very low sensitivity with respect to the change in the parameters in very broad range.