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Medical image annotation is a major hurdle for developing precise and robust machine learning models. Annotation is expensive, time-consuming, and often requires expert knowledge, particularly in the medical field. Here, we suggest using minimal user interaction in the form of extreme point clicks to train a segmentation model which, in effect, can be used to speed up medical image annotation. An initial segmentation is generated based on the extreme points utilizing the random walker algorithm. This initial segmentation is then used as a noisy supervision signal to train a fully convolutional network that can segment the organ of interest, based on the provided user clicks. Through experimentation on several medical imaging datasets, we show that the predictions of the network can be refined using several rounds of training with the prediction from the same weakly annotated data. Further improvements are shown utilizing the clicked points within a custom-designed loss and attention mechanism. Our approach has the potential to speed up the process of generating new training datasets for the development of new machine learning and deep learning-based models for, but not exclusively, medical image analysis.