Differentials estimation of discrete signals is almost mandatory in digital segmentation. In our previous work, we introduced the fast level-wise convolution (LWC) and its complexity of
)). We present convergence proofs of two LWC compatible kernel families. The first one is the pseudo-binomial family, and the second one the pseudo-Gaussian family. In the experimental part, we compare our method to the Digital Straight Segment tangent estimator. Tests are done on different digitized objects at different discretization step using the DGtal library.