# Weakly Supervised Learning with Positive and Unlabeled Data for Automatic Brain Tumor Segmentation
## 1 Introduction  
The identification or semantic segmentation of regions of interest (ROIs) in medical images is a common prerequisite for image-based medical studies. The manual creation of such segmentation is often not only time- and cost-intensive but also subject to intra- and inter-rater variability--which drives a need for automatic segmentation methods [1, 2, 3]. However, there is a huge range of possible segmentation tasks that differ not only by the actual target structure, i.e., the organ or pathology, but also in the definition of boundaries as well as the imaging modality or contrast. Consequently, existing automatic approaches often need to be adapted to individual use-cases, especially in the case of Magnetic Resonance Imaging (MRI). The high variability of this imaging modality with the possibility for individual selection and configurations of MRI sequences together with the manufacturer and device-specific imaging must be accounted for to obtain robust solutions [4, 5]. Machine-learning-based approaches are currently considered the state-of-the-art solution for medical image segmentation as they combine strong performance and a straightforward adaptation to new tasks. Solutions such as the deep-learning-based nn-Unet have been successfully applied to a wide range of different problems by adapting the training data to each task [6; 7; 8]. However, annotating a training dataset can already require significant efforts that might not be justified for a single application. A solution to this challenge is the use of weakly supervised learning, i.e., not using a direct one-to-one annotation for all observations [9; 10]. Different approaches have been proposed to reduce the annotation load by employing only incomplete or sparse annotations during the training process [11; 12]. This increases the annotation speed and allows the usage of learning-based solutions even for single-time usage. A limitation of weak supervision with sparse annotations is the missing implicit information about background tissue. If the complete region of interest is segmented, anything not annotated can be considered as the background or the negative class. This is not true if the annotation is incomplete as both positive and negative parts are not annotated, and approaches such as [11] required the annotation of both background and foreground regions. We want to improve this situation by only allowing the annotation of the region of interest, which leads to a situation that resembles the learning from positive and unlabeled data scenarios (PU-learning). Here, the majority of data are unlabeled, and only a few samples from the positive or foreground class are annotated. Different deep-learning based approaches using PU-learning has been proposed for medical imaging analysis tasks [13; 14] so far. While deep-learning and the included feature learning is particularly beneficial for large datasets [15], image-based medical studies are often based on small datasets [16]. This creates a need for data-efficient learning. Using traditional machine learning with either hand-crafted or pretrained features can be a solution to this challenge. We, therefore, investigated the combination of PU-learning and random-forest-based image segmentation, as this type of classifier has shown to be efficient for medical image segmentation [17; 18; 19; 20; 21; 22]. As a foundation, the DALSA (Domain Adaptation for Learning from Sparse Annotations) algorithm is used, providing an intuitive approach for the incorporation of sparse annotations and is already being applied to small imaging datasets [23; 24]. We extended this approach to learn from tumorous annotations only and avoiding the creation of labels for the background tissue. The segmentation of brain tumor was selected as an evaluation task with tumorous tissues being the foreground or the positive class and unaffected/healthy tissue being the background/negative class.