1. An image processing device comprising: a detector detecting a linear-interpolation-applicable area, as an area where a gradation change is to be smoothed by performing a gradation expanding process by way of linear interpolation on a pixel sequence of an input digital image signal, by sequentially scanning the pixel sequence of said input digital image signal; and an expansion corrector performing a gradation expanding process on the linear-interpolation-applicable area detected by said detector; wherein when said detector sequentially scans gradation values of the pixel sequence of said input digital image signal, if the detector detects a gradation change in a predetermined range and the gradation value of a pixel at a position following a position where the gradation change is detected is the same as the gradation value of a pixel at a position preceding the position where the gradation change is detected, then said detector regards the gradation value of the pixel where the gradation change is detected as the gradation value of the pixels at the positions following and preceding the pixel.