We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also uncovers the shortcomings of any optimization scheme. The strategy can be applied on any data set of native structures such as those available from the Protein Data Bank. In this work, however, we explain and test our approach on simple lattice models, where the true interactions are known a priori and a Model Protein Data Bank (MPDB) can be generated by identifying proteins as amino acid sequences having a unique ground state conformation among all possible conformations. Excellent agreement is obtained between the extracted and the true potentials even for modest numbers of protein structures in the MPDB. Comparisons with other methods are also discussed.