An off-line signature verification system using an extracted displacement function

This paper proposes an off-line signature verification system based on a displacement extraction method in which a questionable signature is compared with a corresponding authentic one. The optimum displacement function for any pair of signatures is extracted using minimization of a functional defined as the weighted sum of the squared Euclidean distance between two signatures and a penalty term requiring smoothness of the displacement function. A coarse-to-fine search method is applied to avoid stopping at a local minimum, i.e., the two signatures are first transformed into coarse images by Gaussian filtering. The optimum displacement function is incorporated such that the system measures the dissimilarity between a questionable signature and the corresponding authentic one. The questionable signature is accepted as genuine only if the observed dissimilarity is below a threshold determined using the dissimilarity between two authentic signatures multiplied by a threshold coefficient. An experiment was performed to evaluate the effectiveness of the proposed system, with resultant error rates being as low as 24.9%; a level much better than that obtained by a method utilizing no displacement function.