Delineating the edges of objects in images is important in the context of several knowledge areas, including medicine and remote sensing. The segmentation of organs and tissues of the human brain, for instance, is a necessary step in the study of the etiology, diagnosis, and treatment of diseases such as Alzheimer's and schizophrenia. Also, the classification of types of terrains helps to prevent deforestation and measuring water levels enables issuing flood or drought alerts. Nevertheless, existing automatic and semi-automatic tools for borders delineation still suffers major flaws in dealing with discontinuities, noise, color, intensity, and texture variation. This project aims at studying alternatives to the current border delineation methodologies using graphs being: live-wire, riverbed and lazy walk. We will study mechanisms to enhance the interaction of the user in semi-automated tools for bi- and tri-dimensional delineation, the choice of functions for edge weight generation, the selection of path propagation functions in graphs, and supervised learning techniques so that the most relevant edges are identified with less effort and accuracy for each specific application.