This paper presents a new method to obtain simultaneously precise N parameters of image deformation with non-iterative calculation by extending area-based matching and sub-pixel estimation. Although area-based matching and similarity interpolation for sub-pixel displacement estimation are commonly used in many areas as a fundamental procedure, they are bound to simple translation. The proposed method is based on a practical similarity model in N-dimensional parameter space. Using similarity measures obtained at discrete positions in the parameter space, our method provides a highly accurate maximum position of similarity in sub-sampling resolution; that position corresponds to image deformation parameters. Experimental results using both synthetic and real images demonstrate that our method can estimate parameters more accurately than previous methods.