Multiple sclerosis (MS) lesions occupy a small fraction of the brain volume, and are heterogeneous with regards to shape, size and locations, which poses a great challenge for training deep learning based segmentation models. We proposed a new geometric loss formula to address the data imbalance and exploit the geometric property of MS lesions. We showed that traditional region-based and boundary-aware loss functions can be associated with the formula. We further develop and instantiate two loss functions containing first- and second-order geometric information of lesion regions to enforce regularization on optimizing deep segmentation models. Experimental results on two MS lesion datasets with different scales, acquisition protocols and resolutions demonstrated the superiority of our proposed methods compared to other state-of-the-art methods.
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