In this paper, we propose a set of new generic automated processing tools to characterise the local asymmetries of anatomical structures (represented by surfaces) at an individual level, and within/between populations. The building bricks of this toolbox are: 1) a new algorithm for robust, accurate, and fast estimation of the symmetry plane of grossly symmetrical surfaces, and 2) a new algorithm for the fast, dense, non-linear matching of surfaces. This last algorithm is used both to compute dense individual asymmetry maps on surfaces, and to register these maps to a common template for population studies. We show these two algorithms to be mathematically well-grounded, and provide some validation experiments. Then we propose a pipeline for the statistical evaluation of local asymmetries within and between populations. Finally we present some results on real data.