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README_appendix.md

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Explanication of volume similarity

There are more than one definations for the volume similarity.

  1. The first defination is: $VS = 1 - \frac{|V_{pred}−V_{gdth}|}{V_{pred}+V_{gdth}}$ where $V_{pred}$ is the volume of prediction and $V_{gdth}$ is the volume of the ground truth. This defination is from this paper. It ranges from 0 to 1. Higher value means the size (volume) of the prediction is more similar (close) with the size (volume) of the ground truth.

  2. The second defination is: $VS = \frac{2∗(V_{pred}−V_{gdth})}{V_{pred}+V_{gdth}}$. This defination is from SimpleITK. Negative VS means the volume of prediction is less than the volume of ground truth, which is called underestimation. Positive VS means the volume of prediction is greater than the volume of the ground truth, which is called overestimation.

In our package seg_metrics, we implemented the ${\color{red}second}$ defination.

Note: None of the two equations represent overlap information. VS only represent the volume size difference between prediction and ground truth.

Explanication of surface distance based metrics

For each contour voxel of the segmented volume A, the Euclidean distance from the closest contour voxel of the reference volume B is computed and stored as list1. This computation is also performed for the contour voxels of the reference volume B, stored as list2. list1 and list2 are merged to get list3.

  • Hausdorff distance is the maximum value of list3.
  • Hausdorff distance 95% percentile is the 95% percentile of list3.
  • Mean (Average) surface distance is the mean value of list3.
  • Median surface distance is the median value of list3.
  • Std surface distance is the standard deviation of list3.

References:

  1. Heimann T, Ginneken B, Styner MA, et al. Comparison and Evaluation of Methods for Liver Segmentation From CT Datasets. IEEE Transactions on Medical Imaging. 2009;28(8):1251–1265.
  2. Yeghiazaryan, Varduhi, and Irina D. Voiculescu. "Family of boundary overlap metrics for the evaluation of medical image segmentation." Journal of Medical Imaging 5.1 (2018): 015006.
  3. Ruskó, László, György Bekes, and Márta Fidrich. "Automatic segmentation of the liver from multi-and single-phase contrast-enhanced CT images." Medical Image Analysis 13.6 (2009): 871-882.