On Mathews Correlation Coefficient and Improved Distance Map Loss for Automatic Glacier Calving Front Segmentation in SAR Imagery

The vast majority of the outlet glaciers and ice streams of the polar ice sheets end in the ocean. Ice mass loss via calving of the glaciers into the ocean has increased over the last few decades. Information on the temporal variability of the calving front position (CFP) provides fundamental information on the state of the glacier and ice stream, which can be exploited as calibration and validation data to enhance ice dynamics modeling. To identify the CFP automatically, deep neural network-based semantic segmentation pipelines can be used to delineate the acquired synthetic aperture radar (SAR) imagery. However, the extreme class imbalance is highly challenging for the accurate calving front segmentation in these images. Therefore, we propose the use of the Mathews correlation coefficient (MCC) as an early stopping criterion because of its symmetrical properties and its invariance toward class imbalance. Moreover, we propose an improvement to the distance map-based binary cross-entropy (BCE) loss function. The distance map adds context to the loss function about the important regions for segmentation and helps to account for the imbalanced data. Using MCC as early stopping demonstrates an average 2.16% dice coefficient improvement for the segmentation of the slightly imbalanced ice/nonice regions and 17.43% dice coefficient improvement for segmenting the highly imbalanced CFPs, compared to the commonly used BCE. The modified distance map loss further improves the calving front segmentation performance by another 1.6%. These results are encouraging as they support the effectiveness of the proposed methods for segmentation problems suffering from extreme class imbalances.