This paper addresses the problem of to what extent linear transformation can alleviate nonlinear distortion. We investigate a technique of global affine transformation (GAT) correlation to absorb linear distortion between gray-scale images. Features used in GAT correlation are occurrence probabilities of black pixels or gradients. Experiments using the handwritten numeral database IPTP CDROM1B show that the entropy of GAT-superimposed images decreases by around 15%. Furthermore, gray-level-based GAT correlation improves the recognition rate from 85.78% to 91.01%, while gradient-based GAT correlation improves the recognition rate from 91.80% to 94.02%. These results show that GAT correlation has a marked effect of improving both shape matching and discrimination abilities by extracting linear distortion from nonlinear one.