We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. We used it together with classical differentiation masks to estimate first and second derivatives and give a curvature estimator of discrete functions.