It is an object to provide an image processing device, an image display device, and an image processing method therefor that are capable of curbing generation of a pseudo edge in a digital image.The image processing device and the image display device are provided including a threshold-value control unit 29 that obtains a threshold value depending on a tone in image data; a smoothing filter unit 60 that applies a smoothing process to a predetermined tone in the image data while preserving, depending on the threshold value, a predetermined edge in the image data; and an output unit that outputs image data having been processed by the smoothing filter unit 60.