Complex 3D digital objects are used in many domains such as animation films, scientific visualization, medical imaging and computer vision. These objects are usually represented by triangular meshes with many triangles. The simplification of those objects in order to keep them as close as possible to the original has received a lot of attention in the recent years. In this context, we propose a simplification algorithm which is focused on the accuracy of the simplifications. The mesh simplification uses edges collapses with vertex relocation by minimizing an error metric. Accuracy is obtained with the two error metrics we use: the Accurate Measure of Quadratic Error (AMQE) and the Symmetric Measure of Quadratic Error (SMQE). AMQE is computed as the weighted sum of squared distances between the simplified mesh and the original one. Accuracy of the measure of the geometric deviation introduced in the mesh by an edge collapse is given by the distances between surfaces. The distances are computed in between sample points of the simplified mesh and the faces of the original one. SMQE is similar to the AMQE method but computed in the both, direct and reverse directions, i.e. simplified to original and original to simplified meshes. The SMQE approach is computationnaly more expensive than the AMQE but the advantage of computing the AMQE in a reverse fashion results in the preservation of boundaries, sharp features and isolated regions of the mesh. For both measures we obtain better results than methods proposed in the literature.
