An image processing apparatus receives n-bit image data, carries out an α-bit bit extension, and outputs (n+α)-bit image data, where n and α are positive integers. The apparatus also performs an epsilon filtering operation that uses the additional gray levels provided by the bit extension to smooth out false edges caused by the bit extension without smoothing out real edges. The output image preserves both the smoothness of regions of gradual change and the sharpness of abrupt changes in the input image.