Different problems of generalization of outlier rejection exist depending of the context. In this study we firstly define three different problems depending of the outlier availability during the learning phase of the classifier. Then we propose different solutions to reject outliers with two main strategies: add a rejection class to the classifier or delimit its knowledge to better reject what it has not learned. These solutions are compared with ROC curves to recognize handwritten digits and reject handwritten characters. We show that delimiting knowledge of the classifier is important and that using only a partial subset of outliers do not perform a good reject option.