PURPOSE: To perform a wide-range filter process at a high speed by an image processor by extending the product sum arithmetic element which has a relatively narrow range into a product sum element which has a relatively wide range.

CONSTITUTION: The values of respective elements of plural m×m product sum arithmetic elements are represented with the values of respective n×n (where m and n are both odd, and m < n) product sum arithmetic elements with the result value of sequential arithmetic of the m×m product sum arithmetic elements and the values of the respective elements of the n×n product sum arithmetic element so as to obtain the same result with the arithmetic by the n×n product sum arithmetic elements by performing sequential arithmetic by the m×m product sum elements for a variable density image, thereby extending the m×m product sum arithmetic elements into the n×n product sum arithmetic elements.