This paper presents a simple and robust pattern matching algorithm working on image-data level and requiring no feature extraction. A model picture is transformed into an estimated picture, and the estimated picture is matched to an actually input picture. Both the geometrical affine transformation and a linear gray-level transformation are examined, and the transformation parameters relating to the rotation, translation, expansion, and brightness are estimated by using a statistical optimization technique, i.e., an iterative non-linear least squares method where the residual sum of squares between the actually input picture and the estimated picture is used as an evaluation function. The characteristic of the proposed method is that the parameters are estimated by linear matrices calculations so that the calculation is markedly simplified and it could be processed in parallel for all the pixels. The matrices are easily calculated from the gray-level and its spatial derivatives in the horizontal and vertical directions in the model picture, and the gray-level in the actually input picture. As a result of some experiments for a simple pattern and a complicated one, it is confirmed that a translation parameter value is accurately estimated with approximately 0.1 pixel. The dynamics of parameter estimation are also examined.