  The medical imaging literature has witnessed remarkable progress in
high-performing segmentation models based on convolutional neural networks.
Despite the new performance highs, the recent advanced segmentation models
still require large, representative, and high quality annotated datasets.
However, rarely do we have a perfect training dataset, particularly in the
field of medical imaging, where data and annotations are both expensive to
acquire. Recently, a large body of research has studied the problem of medical
image segmentation with imperfect datasets, tackling two major dataset
limitations: scarce annotations where only limited annotated data is available
for training, and weak annotations where the training data has only sparse
annotations, noisy annotations, or image-level annotations. In this article, we
provide a detailed review of the solutions above, summarizing both the
technical novelties and empirical results. We further compare the benefits and
requirements of the surveyed methodologies and provide our recommended
solutions. We hope this survey article increases the community awareness of the
techniques that are available to handle imperfect medical image segmentation
datasets.
