Abstract: This paper considers the matching of 3D objects by a geometric approach based on the iterative closest point algorithm (ICP), which, starting from an initial configuration of two rigid objects, iteratively finds their best correspondence. The algorithm does not converge always to the best solution. It can be trapped in a local minimum and miss the optimum matching. While the convergence of this algorithm towards the global minimum is known to depend largely on the initial configuration of test and model objects, this paper investigates the quantitative nature of this dependence. Considering the space C of relative configurations of the two objects to be compared, we call range of successful initial configurations, or SIC-range, the subspace of C which configurations bring the algorithm to converge to the global minimum. In this paper, we present a frame for analyzing the SIC-range of 3D objects and present a number of original experimental results assessing the SIC-range of a number of real 3D objects.