1. A filter circuit comprising: a first weight-coefficient calculating unit that calculates first weight coefficients concerning pixel levels in a first pixel and plural second pixels arranged around the first pixel; a first weight-coefficient adjusting unit that replaces, when the first weight coefficients of a pair of the second pixels arranged in symmetrical positions across the first pixel are different from each other, the first weight coefficient of the second pixel having a larger one of the first weight coefficients of the pair of the second pixels with the first weight coefficient of the second pixel having a smaller one of the first weight coefficients; a third weight-coefficient calculating unit that integrates the first weight coefficients of the pixels calculated by the first weight-coefficient adjusting unit and second weight coefficients concerning positions of the pixels to calculate third weight coefficients of the pixels; and a correction processing unit that corrects the pixel level of the first pixel using the third weight coefficients of the pixels calculated by the third weight-coefficient calculating unit and the pixel levels of the pixels.