The estimation of convex sets when inside and outside observations are available is often needed in current research applications. The key idea in this presentation is to compare the performance of an algorithm based on Discriminant Analysis to the algorithm proposed by Moore et al. (1988). The solution proposed here is based on a criterion from discriminant analysis. This criterion, for deciding whether a further observation (for which we do not know if it is inside or outside the original convex set, was first proposed by Baufays and Rasson (1984, 1985)). Its application here gives a robust and practical estimate of the unknown domain D. Simulation are done and compared with the results presented in Moore et al. (1988). This comparison shows the interest of the proposed estimator of the unknown domain D.