The amount in offset of toner or the like is used to determine two points sandwiching lattice points of input data and divide the region between the two points equally in N−1. The output values at the two points and each point equally dividing the region are obtained to calculate gradients m1-m8 between any two adjacent ones of the points. Then, difference values dm1-dm7 in gradient between any two adjacent ones of the straight lines are calculated and (N−1) lattice points serving as dividing points are selected from the difference values in descending order. It should be noted that N is smaller than M. Then, the input and output values of the determined (N+1) lattice points N0-N4 are plotted and they are bounded by straight line and thus plotted to linearly interpolate the output data for the input data. Thus, an image processing apparatus can be provided capable of precisely modifying output images with reduced memory capacity.