Linear discriminant analysis for signatures

A new feature for handwritten signature image description based on local binary patterns

Objectives. The problem of describing the invariant features of a digital image of handwritten signature that describes the distribution of its local features is considered. The formation of fundamentally new approach to the calculation of such features is described.Methods. Digital image processing methods are used. First an image is converted into a binary representation, then its morphological and median filtering is performed. Then using the method of principal components, the image is rotated to give the signature a horizontal orientation. A rectangle describing the signature is cut out, then it is scaled to the template of a certain size. In the article the template of 300×150 pixels was used. Then the border of the signature is formed. Local binary patterns are calculated from its binary contour, i.e. each pixel is assigned a number from 0 to 255, which describes the location of the edge pixels in 3×3 neighborhood of each pixel. A histogram of calculated patterns for 256 intervals is formed. The first and last intervals are discarded because they correspond to all black and white pixels in the neighborhood and are not informative. The remaining 254 numbers of the array form new local features of the signature.Results. The studies were performed on the bases of digitized signatures TUIT and CEDAR containing true and fake signatures of 80 persons. The accuracy of correct verification of signatures on these bases was about 78 % and 70 %.Conclusion. The possibility of using the proposed possibilities for solving the problems of verifying the authenticity of handwritten signatures has been experimentally confirmed.

Mixture subclass discriminant analysis link to restricted Gaussian model and other generalizations

In this paper, a theoretical link between mixture subclass discriminant analysis (MSDA) and a restricted Gaussian model is first presented. Then, two further discriminant analysis (DA) methods, i.e., fractional step MSDA (FSMSDA) and kernel MSDA (KMSDA) are proposed. Linking MSDA to an appropriate Gaussian model allows the derivation of a new DA method under the expectation maximization (EM) framework (EM-MSDA), which simultaneously derives the discriminant subspace and the maximum likelihood estimates. The two other proposed methods generalize MSDA in order to solve problems inherited from conventional DA. FSMSDA solves the subclass separation problem, that is, the situation in which the dimensionality of the discriminant subspace is strictly smaller than the rank of the inter-between-subclass scatter matrix. This is done by an appropriate weighting scheme and the utilization of an iterative algorithm for preserving useful discriminant directions. On the other hand, KMSDA uses the kernel trick to separate data with nonlinearly separable subclass structure. Extensive experimentation shows that the proposed methods outperform conventional MSDA and other linear discriminant analysis variants.

Complexity-reduced scheme for feature extraction with linear discriminant analysis

Owing to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. Null-space-based LDA (NLDA), which is an extension of LDA, provides good discriminant performances for SSS problems. Yet, as the original scheme for the feature extractor (FE) of NLDA suffers from a complexity burden, a few modified schemes have since been proposed for complexity reduction. In this brief, by transforming the problem of finding the FE of NLDA into a linear equation problem, a novel scheme is derived, offering a further reduction of the complexity.